The challenges of channel estimation in reconfigurable intelligent surfaces (RIS) are well known, in particular, its high demand on pilots and channel estimation resources. This paper explores gains in channel estimation, its efficiency, and achievable rates, by leveraging the differences in antenna correlations for different links, a phenomenon known ascorrelation diversity. Antenna correlations are a well-known feature of mm-wave and massive MIMO (multiple-input multiple-output) communication, and the existence of correlation diversity in multi-user systems is well-established in the literature. In RIS systems employing frequency-division duplex (FDD) transmission, we propose a novel joint transmit/RIS beamforming that exploits antenna correlation diversity via efficient channel training and pilots. Our pilot configurations are optimized according to the degrees of freedom (DoF), and sum-rates are optimized via beamforming. The proposed approach identifies and analyzes the common and disjoint eigenspaces of the antenna correlation matrices, and exploits them utilizingproduct superpositionand rate splitting. A key contribution of this work is reconciling the requirements of transmitter/RIS beamforming on the one hand, and features of product superposition in the presence of imperfect channel state information (CSI) on the other hand. Numerical results are presented to corroborate our findings.

Due to variations in node mobility or differences in the scattering environment, wireless links in multi-user systems often experience non-identical coherence intervals; this is also true in systems assisted by reconfigurable intelligent surfaces (RIS). This paper studies RIS-assisted multi-user downlink systems under link coherence disparity. Since the RIS channel model has many parameters to be estimated, controlling the training overhead under coherence disparity has a strong impact on the practical operation of RIS. Thus motivated, we propose a novel pilot-domain non-orthogonal multiple access (NOMA) technique for RIS-assisted downlink systems. The transmit beamforming and RIS reflection coefficient vectors are jointly designed to maximize the achieved sum-rate. We analyze the resulting reduction in training overhead and the corresponding rate improvements. We investigate efficient pilot placement strategies for multi-user scenarios with arbitrary coherence intervals. Numerical results illustrate the effectiveness of the proposed technique.

In reconfigurable intelligent surfaces (RIS), the reflective elements increase the dimensionality of the overall channel model and, correspondingly, the training requirements. This paper analyzes how channel training and spectral efficiency guide the choice of the operational dimensionality of RIS. We derive an inner bound on the training-based capacity as a function of pilot power, data transmission power, and RIS array dimensions. We study the outcomes and implications of data/pilot power optimization in RIS-assisted systems according to the achievable rate metric. Further, this work sheds light on the tradeoff between the superior array gains of larger RIS on the one hand, and the respective training requirements on the other hand, when optimizing the end-to-end capacity. Beyond a certain critical array size, further increase of array size is not beneficial for spectral efficiency due to the training requirement. This critical size is calculated, and its dependence on the signal-to-noise ratio (SNR) and coherence interval of the channel is clarified. The benefits and drawbacks of different training schemes are analyzed in this context, and demonstrated by simulations.

The millimeter wave (mmWave) channel is inherently sparse, allowing sparse estimation methods such as compressive sensing to be used. This has been welcomed due to the mmWave antenna arrays leading to larger channel dimensions. These channels are sparse in the angular domain, requiring the continuous angle variables to be quantized in order to employ finite-dimensional compressive sensing. This creates a version of the well-known grid mismatch problem in compressive sensing. The impact of this grid mismatch on the accuracy of channel estimates, and the associated requirements, constraints, and guidelines for mmWave system design, have not been analyzed to date. In this work, we present a thorough analysis of grid mismatch in the context of mmWave channel estimation. We calculate the mean squared error of the popular orthogonal matching pursuit algorithm subject to grid mismatch. We clarify the needed dictionary size for a prescribed mean squared error performance, thus assisting system designers and highlighting the implied performance-complexity tradeoff. Numerical results support our analysis. We show that by proper design of compressive sensing subject to our analysis, results comparable to super-resolution methods can be obtained at much lower complexity.

We unveil a new hardware security threat that leaks unauthorized information from a wireless node by subtle manipulation of its pulse-shaping filter. We denote it as Pulse-Shaping Trojan. The leaked information is carried through a small variation to the envelope of the transmitted waveform, created by the pulse-shaping filter at the transmitter. The contamination of transmitter hardware can occur at many points in the IC fabrication supply chain; this is a well-recognized and realistic threat. We show that the pulse-shaping Trojan can be designed to have little to no impact on legitimate communication, including in the spectral mask as well as the bit-error rate of legitimate communication. Thus, it will be much more difficult to detect than earlier hardware Trojan threats. We explore the bitrate and bit-error rate of the information leaked by this Trojan, showing that this new threat is capable of effectively exfiltrating unauthorized information.

This paper studies multi-user downlink systems assisted by reconfigurable intelligent surfaces (RIS), in which individual links experience non-identical coherence intervals. This is a condition that frequently occurs in practical scenar-ios, due to variations in node mobilities or differences in the scattering environment. Training the channels and RIS states is a challenging and time-consuming process, and reducing training overhead is recognized as an important task. This becomes even more challenging under coherence disparity, where transmitting ordinary pilots without attention to the unequal need of users for pilots can adversely impact the training overhead and diminish the gains in rate and degrees of freedom. Motivated by this, we propose a pilot-domain non-orthogonal multiple access (NOMA) technique for RIS-assisted downlink systems, and demonstrate how non-orthogonal pilot/data transmission can effectively reduce the training overhead and yield rate improvements. We explore channel estimation through superposition pilots and design RIS reflection coefficients to maximize the achievable sum-rate via the proposed scheme.

This paper studies the classical problem of communication across channels with state estimated at the receiver, in the context of wireless channels with reconfigurable intelligent surfaces (RIS). The RIS channels are characterized by numerous channel parameters but often have a sparse underlying structure. Under these conditions, the communication, channel training, and the characteristics of sparse recovery algorithms, interact in intricate ways. We calculate a training-based achievable rate for the RIS-induced sparse channel. We use an efficient sparse model for the RIS-aided channel that eliminates the need for recovering angles of arrival and departure at the RIS. We incorporate in the analysis the misalignment between the discrete parameter model of compressive sensing and the actual continuous-valued channel parameters, referred to as basis mismatch. Finally, we offer insights into designing RIS size and compressive sensing-based channel estimation parameters for RIS-aided communication systems.

Reconfigurable Intelligent Surfaces (RIS) have channel models with many parameters, motivating the study and use of statistical channel state information (CSI) in this context. This paper investigates the question of separability of RIS/transmitter beamforming under spatially correlated Rician fading with statistical channel state information. Subject to any spatial correlation, as long as the transmitter-RIS channel is Rayleigh, we show that the beamforming optimization decomposes into two independent optimizations involving the RIS correlation matrix, and the transmitter array correlation matrix. The tools and techniques of this paper also lead to novel and useful optimizations for beamforming optimization when the transmitter-RIS channel is Rician with non-zero mean, even though in this case separability is not established. Numerical results support our findings and provide insights into the proposed algorithm.

Non-orthogonal transmission of data and pilots using product superposition is known to be highly efficient under unequal coherence conditions in a downlink channel, improving achievable rates and degrees of freedom (DoF). However, these techniques have not been used when transmit beamforming is present, as product superposition measures and utilizes composite (virtual) link gains, while beamforming requires knowledge of true (physical) link gains at the transmitter. This paper presents new techniques that enable the gains of pilot-domain non-orthogonal multiple access (NOMA) product superposition to be combined with transmit beamforming gain. The technical novelty of this paper lies in reconciling the requirements of transmit beamforming and product superposition under perfect or imperfect channel state feedback, and demonstrating its effectiveness under multi-user scenarios. The paper begins with a multi-user generalization of product superposition rate analysis in the absence of feedback. Then, a novel non-orthogonal scheme is proposed that harmoniously combines with either perfect or imperfect feedback under disparity in coherence time or coherence bandwidth among users. The proposed scheme includes efficient pilot placement strategies under multi-user scenarios with arbitrary coherence time and coherence bandwidth for different users. Numerical results illustrate the effectiveness of the proposed techniques.

Index modulation is a MIMO technology where some transmit antennas are idle during each transmission interval, but the receiver requires knowledge of all link gains at all times. Even though index modulation is particularly sensitive to the cost of estimating the channel state information (CSI), the impact of CSI cost and imperfections on the capacity of index modulation has not been adequately characterized until now. As a result, the marginal cost/benefit of each additional antenna, and the optimal antenna alphabet have remained unclear. This study computes the spectral efficiency of index modulation subject to training and determines optimal antenna alphabets. Our approach involves a comprehensive examination of the influence of pilot power and degrees of freedom on the achievable rate of index modulation. The results include 2.5dB improvement over the best previously known bound for$4\times2$spatial modulation at 6b/s/Hz. Additionally, we determine the conditions under which single-antenna transmission is superior to spatial modulation, and vice versa. Moreover, this training-based spectral efficiency analysis is extended to the multiuser uplink, identifying the number of users that can be accommodated while maximizing the uplink sum-rate under spatial modulation.

In spatial modulation, even though only one antenna is active in each transmission interval, the receiver needs channel estimates with respect to all transmit antennas at all times. Thus, spatial modulation is more sensitive to the cost of the estimation of channel state information (CSI) compared with conventional single-antenna transmission. Despite its importance, an accurate, joint characterization of the impact of CSI cost and CSI imperfections on the capacity of spatial modulation has been unavailable thus far. As a result, the marginal cost/benefit of each additional antenna, and hence the optimal antenna alphabet, has been unclear. This work calculates the spectral efficiency of spatial modulation subject to training through a tight characterization of the dependence of the achievable rate on the power and degrees of freedom dedicated to pilots. Our results reliably characterize the cases when conventional single-antenna transmission is superior to spatial modulation or vice versa.

Multi-user downlink systems with reconfigurable intelligent surfaces (RIS) require considerable overhead for training the channels and RIS states. This is made even more difficult when the links have non-identical coherence times, a frequently occurring condition due to the variations in node mobility and scattering environment. In the absence of RIS, previous studies have shown that pilot reuse can reduce the pilot overhead under coherence disparity and achieve gains in both rate and degrees of freedom (DoF). This work explores the impact of pilot reuse on RIS-assisted downlink channels having unequal link coherence times and shows how overlapping pilot and data transmission can reduce the training overhead and achieve rate gains. Additionally, we jointly design the transmit beamforming and RIS reflection coefficient vectors to maximize the sum-rate achieved through the proposed transmission scheme. We employ fractional programming to solve the optimization problem and determine the optimal vectors for the beamforming and RIS precoding. Numerical results are presented to corroborate our findings.

Short-block length communication is becoming increasingly important for applications such as machine-to-machine communication, among others. This paper studies polar-coded modulation in the short-block length regime for decode-forward, amplify-forward and compress-forward relays. Our work seamlessly combines multi-level signaling, polar coding/decoding, and the requirements of relaying, into encoders and decoders that exhibit excellent performance. Compared with the state of the art in decode-forward, our work demonstrates 2.5 dB improvement (at block length 512). For shorter block lengths 256 and 128, this work is the first reported implementation for any coded modulation and any relaying protocol. In the category of polar-coded full-duplex relaying, this work presents the first implementation at any block length and for any relaying protocol. For decode-forward, we propose and analyze joint iterative belief propagation decoding with polar codes, and successive list decoding with polarization-adjusted convolutional (PAC) codes. For amplify-forward, we utilize PAC codes and successive list decoding. For the three relaying protocols, the respective dispersion bounds are presented for comparison, and the error exponent of the multi-level relaying coded modulations are analyzed to shed light on the results. Extensive simulations verify the performance of the proposed coding schemes.

This paper considers community detection in the dynamic binary censored block model. Under this model, the graph is observed at successive times (snapshots), and the node label in the current snapshot is dependent on the same node label in the previous τ snapshots. In this paper, the maximum likelihood estimator of the current node labels is obtained under this model, subject to the observation of the graph in the present and past snapshots, and the exact recovery conditions are derived. Relaxing the maximum likelihood estimator, a semidefinite programming algorithm is proposed for community detection. In the asymptotic regime, a sufficient condition for exact recovery is obtained using the semidefinite programming estimator, which is shown to asymptotically match the sufficient conditions for exact recovery.

Channel training in reconfigurable intelligent surfaces (RIS) is different from MIMO; in addition to pilots, it also requires setting RIS training states. Several RIS training schemes are studied in the literature, but the effect of training overhead and accuracy on capacity has not received the deserved attention. This is necessary for guiding the choice of RIS dimensionality and the parameters of modulation and coding. The present work fills this gap and shows that the spectral efficiency of RIS with DFT training (that uses the columns of DFT matrix for the RIS training states) is higher than that with the canonical training (that uses the canonical basis for RIS training states). Specifically, with 32 RIS elements, DFT training achieves a 2 bits/s/Hz gain compared to canonical training when the coherence interval is 150 time slots. Our results also reveal that beyond a certain critical RIS array size, further increase in size is not beneficial and that the optimal array size goes down with increase in SNR.

This paper is eligible for the Jack Keil Wolf ISIT Student Paper Award. This paper investigates covert communication in the presence of a cooperative jammer. Covert communication refers to the inability of an adversary to distinguish data transmission from a so-called innocent symbol at the input. We consider three related problems: (1) a jammer without direct communication or coordination with the transmitter, (2) a jammer that cribs the output of the transmitter, and (3) a jammer that is able to coordinate with the transmitter via a secret key that is also shared with the legitimate receiver. For each model, we derive inner and outer bounds on the capacity region that are tight in some special cases. Unlike prior results in the literature, the jammer in our model does not have access to unlimited local randomness. In fact, uncovering the fundamental interplay between the covert communication rate, local randomness, and secret key rate, is one of the distinctions and contributions of the present work. In the context of a few specific channels, we calculate achievable covert rates to illuminate our results.

When the individual links in a downlink channel have different coherence intervals, previous studies have shown that pilot reuse can achieve not only rate gains, but also gains in degrees of freedom (DoF). Channel state feedback is another source of gains, but combining beamforming with pilot reuse presents new and interesting design questions. The performance of such a scheme has been an open problem under coherence disparity, the regime in which pilot reuse is most promising. We propose a new non-orthogonal transmission scheme for pilots and data that harmoniously combines with either perfect or imperfect channel state feedback. The proposed scheme employs both product superposition and zero-forcing beamforming within the same framework, and improves the resulting achievable rates. The developments include careful pilot placement and an efficient pilot reuse strategy under channel state feedback in a multi-user downlink channel. Numerical results are presented to corroborate our findings.

We consider the problem of covert communication over a state-dependent channel when the Channel State Information (CSI) is available either non-causally, causally, or strictly causally, either at the transmitter alone, or at both transmitter and receiver. Covert communication with respect to an adversary, called “warden,” is one in which, despite communication over the channel, the warden’s observation remains indistinguishable from an output induced by innocent channel-input symbols. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver, the codebook uncertainty is typically removed via a shared secret key that is unavailable to the warden. In contrast to previous work, we do not assume the availability of a large shared key at the transmitter and legitimate receiver. Instead, we only require a secret key with negligible rate to bootstrap the communication and our scheme extracts shared randomness from the CSI in a manner that keeps it secret from the warden, despite the influence of the CSI on the warden’s output. When CSI is available at the transmitter and receiver, we derive the covert capacity region. When CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also provide examples for which the covert capacity is positive with knowledge of CSI but is zero without it.

Index modulation represents the transmitted information in two parts: by selecting a subset of available transmission dimensions (antennas, sub-carriers, or time-slots) whose selection index carries information, and by modulation symbols transmitted in the selected dimensions. Index modulation is motivated by reducing the transmitter hardware complexity and has attracted significant research attention in the past decade. In practice, knowing the spectral efficiency or capacity is essential for setting the parameters of modulation and coding for index modulation, but approximations and bounds thus far have not been accurate enough for that purpose. We calculate close lower and upper bounds for the spectral efficiency of index modulation. Our lower and upper bounds meet at high-SNR when the number of receive antennas is greater than or equal to the number of transmit antennas, thus the high-SNR capacity of index modulation in these cases has been fully characterized. A catalog of results is provided for spatial modulation, generalized spatial modulation, time and frequency index modulation. Extensive simulations illustrate the usefulness and accuracy of our results. For example, for spatial modulation with$4\times 2$antennas at 8 bits/s/Hz, our results are 2dB tighter than the best available bounds in the literature.

This paper studies MIMO relays with non-identical link coherence times, a frequently occurring condition when, e.g., the nodes in the relay channel do not all have the same mobility, or the scatterers around some nodes have different mobility compared with those around other nodes. Despite its practical relevance, this condition, known ascoherence diversity, has not been studied in the relay channel. This paper studies the performance of MIMO relays and proposes efficient transmission strategies under coherence diversity. Since coherence times have a prominent impact on channel training, we do not assume channel state is available to the decoder for free; all channel training resources are accounted for in the calculations. A product superposition technique is employed at the source which allows a more efficient usage of degrees of freedom when the relay and the destination have different training requirements. Varying configurations of coherence times are studied. The interesting case where the different link coherence intervals are not a multiple of each other, and therefore the coherence intervals do not align, is studied. Relay scheduling is combined with the product superposition to obtain further gains in degrees of freedom. The impact of coherence diversity is further studied in the presence of multiple parallel relays.

We investigate the performance of multi-level polar coded modulation in the decode-forward relay channel. We begin by numerically analyzing the rates assigned to polar codes of all levels via chain rule and error exponent. The construction of polar codes follows the 5G standard. A joint decoding based on maximum ratio combining with multistage decoding is proposed for the destination. We simulate the error performance under 16QAM with gray labeling and Ungerboeck's set partitioning. In the half-duplex mode, a gain of 2.5dB is observed compared with the state of the art, consisting of 0.7 dB gain due to multistage decoding and 1.8dB gain due to the choice of labeling. In addition, the error performance according to error exponent is compared with the chain rule. A dispersion bound for the decode-forward relaying is calculated.

Index modulation emits information through the index of the activated component of a vector signal as well as the value of the activated component. Indexing could occur across antennas, subcarriers, or other degrees of freedom. When index modulation is applied to antennas, it is known as spatial modulation. Earlier bounds or estimates for the spectral efficiency of spatial modulation have been too loose for determining the parameters of coding and modulation, which are important in practice. Furthermore, the best bounds formerly available did not effectively elucidate the relationship of spatial modulation capacity with SIMO and MIMO capacity at low- and high-SNR. The present work develops novel, tighter bounds on the spectral efficiency of spatial modulation. Specifically, for a 4 × 2 antenna configuration at 8 bits/slHz, our results are 2dB tighter than the best bounds available in the literature.

This paper studies the MIMO relay with nonidentical link coherence times, a condition known as coherence diversity. This happens in practice when a node or the scatterers surrounding it have different mobility compared with the conditions at or around other nodes. In this paper, coherence diversity in relays is studied under link coherence intervals with arbitrary (unequal) length and alignment. Second, a new transmission scheme under coherence diversity is proposed in which the relay transmission is given a duty cycle based on the balance between the gain versus the channel training costs in the relay-destination link. Finally, we investigate multiple parallel relays operating under non-identical coherence intervals, propose transmission strategies, and calculate degrees of freedom.

We consider the problem of covert communication in the presence of a cooperative jammer. Covert communication refers to communication that is undetectable by an adversary, i.e., a scenario in which, despite ongoing communication, the output distribution observed by an adversary called the “warden” is indistinguishable from the distribution that would have been induced by an innocent channel-input symbol. It is known that in general, a transmitter and a receiver can communicate only$O(\sqrt{n})$covert bits over$n$channel uses, i.e., zero rate. This paper shows that a cooperative jammer can facilitate the communication of positive covert rates, subject to the transmitter having non-causal access to the jammer signal. An achievable rate region is calculated that highlights the relation between the covert communication rate, jammer's randomness (expressed as a rate), and rate of a secret key shared between transmitter and receiver.

In a multiple-input multiple-output (MIMO) broad-cast channel (BC), the difference in spatial transmit correlation matrices of different users is called transmit correlation diversity. Recently, several works have extended this concept beyond its original scope, to include channels whose transmit correlation matrices have non-overlapping eigenspaces. In contrast to earlier analyses of overlapping eigenspaces that were mostly described in terms of degrees-of-freedom, this work presents achievable rate regions. These achievable regions are derived by rate-splitting, product superposition, or a combination thereof. Our rate expressions make explicit the contribution of the common parts and individual (non-overlapping) parts of the correlation eigenspaces toward the achievable rate region. As a by-product, a result of Hassibi and Hochwald on MIMO channel training is extended to channels with spatial correlation.

Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El Gamal and the method of output statistics of random binning. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that derives an inner bound on the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels.

Community detection refers to recovering a (latent) label on which the distribution of the observed graph depends. Recent work has also investigated the impact of additionally knowing the value of another variable at each vertex that is correlated with the vertex label (side information), while assuming side information is independent of the graph edges conditioned on the label. This work extends the scope of community detection in two ways. First, we consider a side information that does not form a Markov chain with the label and graph, and analyze the detection threshold of semidefinite programming subject to knowledge of this side information, which is a non-label latent variable on which the graph edges also depend. In the second part of the work, we consider aside from vertex labels a second latent variable that is unknown both in realization and in distribution. We then investigate the performance of the semidefinite programming community detection as a function of the (unknown) composition of the nuisance latent variable. In both cases, it is shown that semidefinite programming can achieve exact recovery down to the optimal (information theoretic) threshold.

We study the randomness required at the inputs of a multiple access channel in order to produce a desired, approximately i.i.d., output distribution, subject to cooperation in one of the following forms: (i) a common message, (ii) conferencing, (iii) feedback and (iv) generalized feedback. For the cases (i)-(iii), we characterize the channel resolvability via matching inner and outer bounds, and for generalized feedback we provide two inner bounds representing the role of decoding and randomness extraction, which can also be combined. One of the main contributions of this work is to show that resolvability rates of the multiple access channel are not improved with feedback, unlike the multiple access channel capacity which is improved by feedback.

We consider the problem of covert communication when Channel State Information (CSI) is available non-causally, causally, and strictly causally at both transmitter and receiver, as well as the case when channel state information is only available at the transmitter. Covert communication with respect to an adversary referred to as the "warden", is one in which the distribution induced during communication at the channel output observed by the warden is identical to the output distribution conditioned on an innocent channel-input symbol. In contrast to previous work, we do not assume the availability of a shared key at the transmitter and legitimate receiver; instead shared randomness is extracted from the channel state, in a manner that keeps it secret from the warden despite the influence of the channel state on the warden's output. When CSI is available at both transmitter and receiver, we derive the covert capacity region; when CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also derive the covert capacity when the warden's channel is less noisy with respect to the legitimate receiver. We provide examples for which covert capacity is zero without channel state information, but is positive in the presence of channel state information.

We investigate the risk posed by amplitude-modulating analog/RF hardware Trojans in wireless networks and propose a defense mechanism to mitigate the threat. First, we introduce the operating principles of amplitude-modulating analog/RF hardware Trojan circuits and we theoretically analyze their performance characteristics. Subject to channel conditions and hardware Trojan design restrictions, this analysis seeks to determine the impact of these malicious circuits on the legitimate communication and to understand the capabilities of the covert channel that they establish in practical wireless networks, by characterizing its error probability. Next, we present the implementation of two hardware Trojan examples on a Wireless Open-Access Research Platform (WARP)-based experimental setup. These examples reside in the analog and the RF circuitry of an 802.11a/g transmitter, respectively, where they manipulate the transmitted signal characteristics to leak their payload bits. Using these examples, we demonstrate (i) attack robustness, i.e., ability of the rogue receiver to successfully retrieve the leaked data, and (ii) attack inconspicuousness, i.e., ability of the hardware Trojan circuits to evade detection by existing defense methods. Lastly, we propose a defense mechanism that is capable of detecting analog/RF hardware Trojans in WiFi transceivers. The proposed defense, termed Adaptive Channel Estimation (ACE), leverages channel estimation capabilities of Orthogonal Frequency Division Multiplexing (OFDM) systems to robustly expose the Trojan activity in the presence of channel fading and device noise. Effectiveness of the ACE defense has been verified through experiments conducted in actual channel conditions, namely over-the-air and in the presence of interference.

This paper analyzes the performance of discrete input distributions (coded modulation) in interference channels. This approach is motivated in part by the necessity of using coded modulation in practical systems, and in part by the potential of discrete distributions for interference alignment as well as the importance demonstrated by Dytso et al. of discrete input distributions for transmission over the 2 × 2 interference channel when treating interference as noise. The contribution of this work includes the establishment of achievable rates subject to discrete modulations. In the process, new bounds involving the minimum distance of the sum of discrete modulations have been developed that are useful for facilitating further work in this area. These bounds are then used for finding achievable rates for 3 × 3 interference channels. It is also shown that interference alignment can be efficiently employed with discrete modulations at finite SNR even with imperfect channel state information at the transmitter.

We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to Kullback-Leibler divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel resolvability region; the crux of our achievability result is to handle the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden. Finally, we leverage the channel resolvability results to derive achievable secrecy rate regions for each of the cribbing scenarios under strong secrecy constraints.

We study the effect of the quality and quantity of side information on the recovery of a hidden community of size K = o(n) in a graph of size n. Side information for each node in the graph is modeled by a random vector in which either the vector dimension or the LLR of each component with respect to node labels is independent of n. These two models represent the variation in quality and quantity of side information. Under maximum likelihood detection, we calculate tight necessary and sufficient conditions for exact recovery of the labels. We demonstrate how side information needs to evolve with n in terms of either its quantity, or quality, to improve the exact recovery threshold. A similar set of results are obtained for weak recovery. Under belief propagation, tight necessary and sufficient conditions for weak recovery are calculated when the LLRs are constant, and sufficient conditions when the LLRs vary with n. Moreover, we design and analyze a local voting procedure using side information that can achieve exact recovery when applied after belief propagation.

We propose a semidefinite programming (SDP) approach to community detection in graphs in the presence of additional non-graphical side information, and analyze the corresponding exact recovery threshold. The community detection problem is considered in the context of the binary symmetric Stochastic Block Model (SBM), and the side information is in the form of partially revealed labels with erasure probability ϵ. Our results show that the semidefinite programming relaxation of the maximum likelihood estimator can achieve exact recovery down to the optimal threshold. The theoretical findings of this paper are validated via simulations on finite synthetic data-sets, showing that the asymptotic results of this paper can also shed light on the performance at finite n.

Semidefinite programming is known to be both efficient and asymptotically optimal in solving community detection problems, but it has been studied in this context only when observations are purely graphical in nature. In this paper, we extend the use of semidefinite programming in community detection to observations that have both a graphical and a nongraphical component. We consider the binary censored block model with n nodes and study the effect of partially revealed labels on the performance of semidefinite programming. We address the question: do partially revealed labels help the semidefinite programming solution as much as they help the maximum likelihood solution? Our results are twofold. First, we show that partially revealed labels change the phase transition of exact recovery if and only if the information they provide grows no slower than Ω(log(n)). Second, we show that the semidefinite programming relaxation of maximum likelihood can achieve exact recovery down to the optimal threshold under partially revealed labels.

We investigate the performance of discrete (coded) modulations in the full-duplex compress-and-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information exchange algorithm are described for the joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known compress-and-forward achievable rate by two factors consisting approximately of the sum of the shaping gain (due to the scalar quantization) and the separation of the LDPC code implementation from AWGN capacity.

This paper studies the MIMO relay with non-identical link coherence times, a condition that is denoted coherence diversity. This can occur, e.g., when the nodes do not all have the same mobility, or the scatterers around some nodes have different mobility than others. Obviously this condition occurs in practice therefore the model is well motivated, but the performance of a relay under such conditions has not been studied to date. This paper calculates achievable degrees of freedom under this condition. Since different coherence times have a prominent impact on channel training, channel state is not made available to the decoder for free, and all channel training resources are accounted for in the calculations. A product superposition technique is employed at the source that allows a more efficient usage of degrees of freedom when the relay and the destination have different training requirements. Following the analysis of a representative example, a general analysis is provided and varying configurations of coherence times are studied. Numerical results demonstrate the gains of the proposed approach under coherence disparity.

We study the minimum randomness required at a source node to approximately produce a chosen i.i.d. distribution at a destination, while a relay assists in the process. In the classical relay problem, the relay does not have any message of its own to transmit, and only re-transmits a function of its observation. In the resolvability problem the variable of interest is the randomness rate, therefore we assume the relay does not have access to any randomness outside what it observes at its input, i.e., the relay output is a deterministic function of its input. A block-Markov scheme is used in which the relay decodes the source message to assist with the approximation of the i.i.d. output. In addition, the relay extracts randomness from its noisy channel observation in each block and uses it in the next block to improve the resolvability rate. The careful handling of this randomness recycling, in order to avoid the introduction of unwanted dependencies, is a key part of the contribution of this paper.

We consider the problem of covert communication over a state-dependent channel, for which the transmitter and the legitimate receiver have non-causal access to the channel state information. Covert communication with respect to an adversary, referred to as the “warden,” is one in which the distribution induced during communication at the channel output observed by the warden is identical to the output distribution conditioned on an inactive channel-input symbol. Covert communication involves fooling an adversary in part by a proliferation of codebooks; for reliable decoding at the legitimate receiver the codebook uncertainty is removed via a shared secret key that is unavailable to the warden. Unlike earlier work in state-dependent covert communication, we do not assume the availability of a shared key at the transmitter and legitimate receiver. Rather, a shared randomness is extracted at the transmitter and the receiver from the channel state, in a manner that keeps the shared randomness secret from the warden despite the influence of the channel state on the warden's output. An inner bound on the covert capacity, in the absence of an externally provided secret key, is derived.

The community detection problem, as a special case of inference on graphs, has received much attention lately. However, in the presence of continuous-valued side information, the behavior of a sharp threshold for exact recovery has remained open, and is addressed in this letter. The new proof presented herein has the further advantage of closing the gap between necessary and sufficient conditions for exact recovery threshold that has existed in community detection under finite-alphabet side information.

Downlink transmission into frequency-selective links experiencing different coherence bandwidths and coherence times has obvious practical relevance, but is often addressed via assuming for all users the coherence conditions corresponding to the fastest, most dispersive user. This paper demonstrates an alternative approach that directly exploits the differences between coherence bandwidth and coherence time of users under frequency-selective conditions, showing that it can lead to significant new efficiencies and gains. More specifically, we study a two-user downlink frequency-selective channel under three broad conditions of disparity between the link qualities: when the disparity is in coherence time, in coherence bandwidth, and in both coherence time and coherence bandwidth. Each of the coherence scenarios calls for a distinct treatment; for each, we provide an analysis demonstrating the gains in achievable rates due to exploiting coherence disparity. Numerical simulations demonstrate the advantages of the proposed schemes.

We discuss the threat that malicious circuitry (a.k.a. hardware Trojan) poses in wireless communications and propose a remedy for mitigating the risk. First, we present and theoretically analyze a stealthy hardware Trojan embedded in the forward error correction (FEC) block of an 802.11a/g transceiver. FEC seeks to shield the transmitted signal against noise and other imperfections. This capability, however, may be exploited by a hardware Trojan to establish a covert communication channel with a knowledgeable rogue receiver. At the same time, the unsuspecting legitimate receiver continues to correctly recover the original message, despite experiencing a slight reduction in signal-to-noise ratio (SNR) and, therefore, remains oblivious to the attack. Next, we implement this hardware Trojan on an experimental setup based on the Wireless Open Access Research Platform (WARP) and we demonstrate (i) attack robustness, i.e., the ability of the rogue receiver to correctly receive the leaked information and (ii) attack inconspicuousness, i.e., imperceptible impact on the legitimate transmission. Lastly, we theoretically analyze and experimentally evaluate a Trojan-agnostic detection mechanism, namely, channel noise profiling, which monitors the noise distribution to identify inconsistencies caused by hardware Trojans, regardless of their implementation details. The effectiveness of channel noise profiling is experimentally assessed using the proposed hardware Trojan under various channel conditions and a different covert Wi-Fi attack previously proposed in the literature.

We study channel resolvability for the discrete memoryless multiple access channel with cribbing, i.e., the characterization of the amount of randomness required to approximate an i.i.d. output distribution in terms of Kullback-Leibler divergence. We analyze the cases in which one encoder cribs (i) the input of the other encoder; or the output of the other encoder (ii) noncausally, (iii) causally, or (iv) strictly-causally. For cases (i)-(iii), we exactly characterize the channel resolvability region. For case (iv), we provide inner and outer bounds for the channel resolvability region; our achievability result handles the strict causality constraint with a block-Markov coding scheme in which dependencies across blocks are suitably hidden.

In this paper, we study the effect of side information on the recovery of a hidden community of size K inside a graph consisting of n nodes with K=o(n). We focus on side information with finite cardinality and bounded (as n→ ∝) log-likelihood ratios (LLRs). We calculate tight necessary and sufficient conditions for weak recovery of the labels subject to observation of the graph and side information under belief propagation (BP). Also, we show that BP with side information is strictly inferior to the maximum likelihood detector without side information. Finally, we validate our results through simulations on finite synthetic data-sets that shows the power of our asymptotic results in characterizing the performance even at finite n.

In this paper, we study the effect of side information on the information limits of recovering a hidden community of size K inside a graph consisting of n nodes with K = o(n). Side information for each node in the graph is modeled by a random vector whose components have finite cardinality. The variation in quantity of side information as a function of graph size n is represented by varying the size of the vector of side information while keeping the log-likelihood ratio (LLR) of each component with respect to the node labels fixed. We show when and by how much side information can improve the information limits of weak and exact recovery by providing tight necessary and sufficient conditions for both weak and exact recovery. Furthermore, we show that, under certain conditions, any algorithm achieving weak recovery can also achieve exact recovery if followed by a local voting procedure.

The spatially correlated MIMO broadcast channel has grown in importance due to emerging interest in massive MIMO and mm-wave communication, but much about this channel remains unknown. In this paper, we study a two-user MIMO broadcast channel where the spatial correlation matrices corresponding to the two receivers have eigenspaces that are neither identical nor disjoint, but are partially overlapped. Spatially correlated channels occur in e.g. massive MIMO and furthermore different links may credibly have correlation eigenspaces that are neither disjoint nor equal, therefore this problem is practically motivated. This paper develops a new approach for this scenario and calculates the corresponding degrees of freedom. Our technique involves a careful decomposition of the signaling space to allow a combination of pre-beamforming along directions that depend on the relative positioning of the non-overlapping and overlapping components of the eigenspaces, along with the product superposition technique. The ideas are demonstrated with a toy example, are developed in two conditions of varying complexity, and are illuminated by numerical results.

We pursue interference mitigation via the integration of two key ideas. First, understanding the behavior of available rates under discrete signaling which has recently been shown to be promising in the interference channel. This part calls for calculation of good bounds on post-interference mutual information under discrete signaling, as a function of the forward and cross channel gains. Second, the capacity of the interference channel is known to be very irregular, so for any target capacity there are “outage” sets that we aim to avoid by using reconfigurable antennas. For the first component, we report an analytical lower bound on the mutual information and establish a constant gap O(logγ) to capacity (excepting an outage set) that is derived using a purely discrete signaling. This result outperforms the gap reported by Dytso et al that was generated via a mixed discrete-continuous input strategy. In the second part of this work, we propose to use a reconfigurable antenna technology involving liquid metal antennas that can steer the channel away from the outage scenarios and therefore facilitate higher values of coded rates for the two-user symmetric Gaussian interference channel. The viability of the proposed technique is studied via simulations.

This paper addresses point-to-point communication over block-fading channels with independent fading blocks. When both channel state information at the transmitter and receiver (CSIR) are available, most achievable schemes use separable coding, i.e., coding independently and in parallel over different fading states. Unfortunately, separable coding has drawbacks, including large memory requirements at both communication ends. In this paper, a lattice coding and decoding scheme is proposed that achieves the ergodic capacity without separable coding, with lattice codebooks and decoding decision regions that are universal across channel realizations. We first demonstrate this result for fading distributions with discrete, finite support whose sequences are robustly typical. Results are then extended to continuous fading distributions, as well as multiple-input multiple-output (MIMO) systems. In addition, a variant of the proposed scheme is presented for the MIMO ergodic fading channel with CSIR only, where we prove the existence of a universal codebook that achieves rates within a constant gap to capacity for finite-support fading distributions. The gap is small compared with other schemes in the literature. Extension to continuous-valued fading is also provided.

We investigate coded modulation for full-duplex relay channels, proposing and analyzing a multilevel coding (MLC) framework with capacity approaching performance and practical features. Sufficient conditions are derived under which multilevel coding meets the known achievable rates for decode-and-forward relaying. The effect of a bit additive superposition and the linearity of multilevel code components on the performance of the system are studied. It is shown that linearity of the relay component codes imposes no penalty on rate, however, the linearity of the source-to-relay component codes may impose a performance penalty especially for small modulation constellations. We show that this rate loss occurs because a linearity constraint on codebooks at the source node introduces a new tension between optimality of rate allocation in multilevel coding layers and optimality of source/relay codebook correlations. Motivated by this insight, an alternative modulation labeling is proposed that minimizes the rate loss. The results are extended to multi-antenna relays. Slow fading and fast Rayleigh fading without channel state at the transmitter are also analyzed. The error exponent of the proposed scheme is studied. Finally, the frame- and bit-error rate performance of the proposed scheme is studied via simulations using point-to-point LDPC codes, showing that the proposed MLC relaying has excellent performance.

We propose a defense method capable of detecting hardware Trojans (HTs) in the analog/RF circuitry of wireless local area network (WLAN) transceivers. The proposed method, which is implemented on the receiver (RX) side and cannot be tampered with by the attacker, leverages the channel estimation capabilities present in Orthogonal Frequency Division Multiplexing (OFDM) systems. Specifically, it employs an adaptive approach to robustly isolate possible HT activity from channel and device noise, thereby exposing the Trojan's presence. The adaptive channel estimation (ACE) defense mechanism is put to the test using a HT which is implemented on a printed circuit board (PCB) and mounted on the Wireless Open-Access Research Platform (WARP). This HT, which is introduced through minute modifications in the power amplifier (PA), manipulates the transmission power characteristics of an 802.11a/g transmitter (TX) in order to leak sensitive data, such as the encryption key. Effectiveness of the proposed defense has been verified through experiments conducted in actual channel conditions, namely over-the-air and in the presence of interference.

This paper analyzes the performance of discrete input distributions (coded modulation) in certain 3 user interference channels. This approach is motivated in part by the necessity of using coded modulation in practical systems, and in part by the potential of discrete distributions for interference alignment as well as the demonstrated importance of discrete input distributions for transmission over the 2 × 2 interference channel when treating interference as noise. The contribution of this work includes the establishment of achievable rates subject to discrete (PAM) modulations. In the process, new bounds involving the minimum distance of the sum of discrete modulations have been developed that are useful for facilitating further work in this area.

The broadcast channel under delayed, mixed, hybrid, or no CSIT Is a subject of much Interest but has been studied only under i.i.d. fading and perfect CSIR for all users. Models that go beyond i.i.d. fading and perfect CSIR are of practical Importance since users may experience unequal fading block-length (coherence time) and unequal CSIR availability due to different mobility and scattering environment. This paper studies a two-user MISO broadcast channel with hybrid CSIR, where one static user (with slower fading) has CSIR and one dynamic user (with faster fading) does not have free CSIR. Under this hybrid CSIR condition, the paper studies the degrees of freedom under various CSIT scenarios: no, delayed, and hybrid CSIT. For no CSIT, we provide an outer bound that meets the achievable degrees of freedom region when the coherence times of the users are the same. For both delayed and hybrid CSIT, the achievable regions partially meet their corresponding outer bounds, and furthermore the corresponding gaps decrease with the dynamic user coherence time.

This paper Introduces the discrete memoryless multiple access wiretap channel with noiseless cribbing, where the cribbing may be either causal or strictly causal. We derive lower bounds for secrecy rates for both causal and strictly causal cribbing under either a decode-forward or partial-decode-forward strategy. Our results recover the achievable rate regions of the MAC wiretap and MAC with cribbing, and demonstrate improvement of secrecy rate due to cribbing. An outer bound is presented for this channel under causal cribbing, which also serves as an outer bound for strictly causal case.

One of the main challenges of communication in the absence of transmitter channel knowledge is codebook universality, i.e., the existence of a single codebook that guarantees a given rate for all channel states. We address this problem for a class of ergodic fading multiple-input multiple-output (MIMO) channels, whose fading distribution is not necessarily isotropic. It is shown that a universal codebook drawn from a nested lattice code achieves the ergodic capacity to within a constant gap. Interestingly, the gap vanishes in some scenarios.

Antenna correlation is prevalent in higher frequencies as well as in massive MIMO, thus the study of correlated MIMO broadcast channels is becoming a subject of increasing interest. This paper explores the fundamental limits of such systems, focusing on cases where correlation eigenspaces are neither independent nor identical, so that known beam-space division techniques do not directly apply. We begin by introducing a simple but novel tight outer bound on the degrees of freedom of noncoherent point-to-point MIMO channels under transmit antenna correlation. We then analyze the performance of a two-user MIMO broadcast channel when one correlation eigenspace is a subspace of the other. We extend the result to K-user MIMO broadcast channel. Our results show that it is possible to exploit the differences between the correlation structure of transmit antennas towards different receivers to extract degrees of freedom gains out of the system. The extent of these gains are highlighted via several examples.

Unlike the half-duplex relay, the performance of the full-duplex relay is highly sensitive to the correlation between the source and relay codebooks. Linear coding complicates the design of correlated codebooks, for example in multilevel coding (MLC) linear codes at each layer can only have correlation zero or one, leading to a performance penalty that has been characterized in earlier work. In this paper, we propose a new design technique that significantly reduces the correlation penalty of linear codes via intelligent labeling for the modulation. The basic idea is as follows: the chain rule for mutual information, which is the backbone of MLC, is not-unique in two ways: the labeling of modulation constellation as well as the ordering of the chain rule. Our optimization at each level pushes the mutual information terms involving new information (for the relay) or beamforming information to zero or one. In effect this finds a suitable decomposition of overall correlation to a set of binary correlations at individual levels of MLC. Simulations show that point-to-point LDPC codes in combination with the proposed correlation design lead to excellent performance.

Even though there exists a lot of different transmission techniques, the capacity of the general relay channel is still unknown. This paper shows that combining decode-and-forward (DF) with compress-and-forward (CF) can have a performance advantage over each of the two techniques individually. Combining the two techniques goes back to the celebrated work of Cover and El-Gamal [1], more specifically, they gave an achievable rate for the DF-CF combination. In this paper, we re-derive the achievable rate of combining DF with CF in the full-duplex discrete memoryless relay channel. We derive the achievable rate in the AWGN relay channel as well as the constrained constellation AWGN relay channel. We show that even though in the AWGN channel, DF-CF combination does not provide any advantage, under constrained constellation, combining the two techniques has an advantage.

The capacity region of the ergodic fading interference channel remains unknown. Moreover, most achievable rate regions known to date for fading interference channels are based on Gaussian codes, whose encoding and decoding complexity is too high. In this paper, we study the two-user ergodic interference channel with channel knowledge only at the receiver side. First, we establish the capacity region for the case where interference (cross) link gains are statistically stronger than forward link gains, denoted the ergodic strong interference channel. Additionally, we establish the rate region for this channel under lattice coding and decoding, whose complexity is significantly less than Gaussian codes. We show that the sum rate achieved using lattice codes is very close to sum capacity.

The capacity of the AWGN broadcast channel is achieved by superposition coding, but the superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Hierarchical modulations, which appear in the literature mostly in the context of unequal error protection, can approach only a few isolated points on the boundary of the broadcast capacity region. This paper studies multilevel coding (MLC) for constellation-constrained broadcast-coded modulation. The conditions under which multilevel codes can achieve the constellation-constrained capacity of the AWGN broadcast channel are derived. We propose a pragmatic multilevel design technique with near-constellation-constrained-capacity performance where the coupling of the superposition inner and outer codes is localized to each bit-level. It is shown that this can be further relaxed to a code coupling on only one bit-level, with a little or no penalty under natural labeling. The rate allocation problem between the bit levels of the two users is studied and a pragmatic method is proposed, again with near-capacity performance. In further pursuit of lower complexity, a hybrid MLC-bit-interleaved-coded modulation is proposed, whose performance is shown to be very close to the boundary of the constellation-constrained capacity region. Simulation results show that good point-to-point LDPC codes produce excellent performance in the proposed coded modulation framework.

For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacity that does not depend on the signal-to-noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the K-user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations.

This paper studies the interference channel with a cognitive relay under delayed feedback. Three types of delayed feedback are studied: delayed channel state information at the transmitter, delayed output feedback, and delayed Shannon feedback. Outer bounds are derived for the degrees of freedom (DoF) region of the two-user multiple-input multiple-output interference channel with a cognitive relay with delayed feedback as well as without feedback. For the single-input single-output scenario, optimal schemes are proposed based on retrospective interference alignment. It is shown that while a cognitive relay without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to 4/3. For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds.

Using silicon measurements from 40 chips fabricated in Taiwan Semiconductor Manufacturing Company's (TSMC's) 0.35-μm technology, we demonstrate the operation of two hardware Trojans, which leak the secret key of a wireless cryptographic integrated circuit (IC) consisting of an Advanced Encryption Standard (AES) core and an ultrawideband (UWB) transmitter (TX). With their impact carefully hidden in the transmission specification margins allowed for process variations, these hardware Trojans cannot be detected by production testing methods of either the digital or the analog part of the IC and do not violate the transmission protocol or any system-level specifications. Nevertheless, the informed adversary, who knows what to look for in the transmission power waveform, is capable of retrieving the 128-bit AES key, which is leaked with every 128-bit ciphertext block sent by the UWB TX. Moreover, through physical measurements and MATLAB simulations, we show that the attack facilitated by these hardware Trojans is robust to test equipment and communication channel noise. Finally, we experimentally evaluate the effectiveness of a popular hardware Trojan detection method, namely, statistical side-channel fingerprinting via trained one-class classifiers, in detecting the hardware Trojans introduced in our fabricated IC population.

A multiple-input multiple-output (MIMO) version of the dirty paper channel is studied, where the channel input and the dirt experience the same fading process, and the fading channel state is known at the receiver. This represents settings where signal and interference sources are co-located, such as in the broadcast channel. First, a variant of Costa's dirty paper coding is presented, whose achievable rates are within a constant gap to capacity for all signal and dirt powers. In addition, a lattice coding and decoding scheme is proposed, whose decision regions are independent of the channel realizations. Under Rayleigh fading, the gap to capacity of the lattice coding scheme vanishes with the number of receive antennas, even at finite Signal-to-Noise Ratio (SNR). Thus, although the capacity of the fading dirty paper channel remains unknown, this paper shows it is not far from its dirt-free counterpart. The insights from the dirty paper channel directly lead to transmission strategies for the two-user MIMO broadcast channel, where the transmitter emits a superposition of desired and undesired (dirt) signals with respect to each receiver. The performance of the lattice coding scheme is analyzed under different fading dynamics for the two users, showing that high-dimensional lattices achieve rates close to capacity.

The most popular methods for the analysis of LDPC codes, e.g. density evolution and EXIT charts, apply to infinite length ensembles. Finite length analysis is less common, among the notable examples are scaling law analysis and the EXIT band chart. The scaling law is limited to the waterfall region and furthermore is limited to the final error rates and does not give insight into the progression and dynamics of belief propagation decoding. The EXIT band chart was based on empirical considerations and does not enjoy a strong underlying theory. The developments of this paper are motivated by the recent results by Polyanskiy, Poor and Verdu showing that the rate penalty due to finite blocklength depends on the channel dispersion. We propose tracking the dispersion between the transmitted bits and the log-likelihood ratio across the decoder iterations to capture the effect of the codeword length. Based on the proposed analysis, a simple lower bound on the block error probability as a function of the blocklength is derived. The bound is corroborated by simulation.

The capacity of the AWGN broadcast is achieved by superposition coding, but superposition of individual coded modulations does not in general obey a predefined constellation. We propose a coded modulation broadcast with strict channel input modulation constraint via multilevel coding (MLC). For a degraded broadcast channel, conditions of optimality of the multilevel decomposition of a superposition code are derived. Furthermore, a constructive scheme is proposed that simplifies the superposition multilevel code and facilitates the design process, by reducing the inter-dependencies between the levels of the two component codes, and yet achieves rates very close to the constellation constrained capacity. Simulation results on several modulations verify the operation of the proposed coding scheme at or near the constellation constrained capacity.

In practice, wireless nodes may have different mobility and/or different scattering environment leading to disparity in coherence time and/or coherence bandwidth. Coherence diversity, as a novel source of gain, exploits fading condition disparity of different nodes to provide gain. Downlink transmission for two wireless nodes is considered in three scenarios of fading conditions disparity: in coherence time, in coherence bandwidth, and in both coherence time and coherence bandwidth. Coherence diversity gain is calculated in the three scenarios using product superposition transmission, and furthermore, numerical simulations are presented to demonstrate the gains.

Many aspects of lattice coding and decoding under time-varying multiple-antenna systems remain unexplored. This paper studies the achievable rates using lattice codes for the multiple-input- multiple-output (MIMO) point-to-point channel with ergodic fading and channel state information at the receiver. The proposed lattice coding scheme involves the use of decision regions that are universal for almost all realizations of a given fading distribution and hence providing a significant computational advantage over channel- matching decision regions. Under Rayleigh fading, the rates achieved are within a constant gap to the ergodic capacity. The gap is also shown to diminish as the number of receive antennas increases, implying the asymptotic optimality of lattice codes even at finite signal-to-noise ratio (SNR).

A multiple-input-multiple-output (MIMO) version of Costa's dirty paper channel is studied, where both the input signal and the state experience ergodic fading with channel state information at the receiver. An inner bound using lattice coding and decoding is derived and its gap to the point-to- point ergodic capacity is computed. Under Rayleigh fading, the gap is a constant that vanishes as the number of receive antennas increases, even at finite signal-to-noise ratio (SNR). This implies that under certain configurations the point-to- point capacity can be almost realized in the presence of fading dirt, similar to Costa's result for the non-fading scalar case. The proposed scheme is applied to a class of MIMO broadcast channels with receive channel state information. The scheme is compared to time sharing as well as a dirty paper scheme with non-causal channel state information at the transmitter. The lattice coding scheme is shown to outperform time sharing as well as achieve most of the region of the dirty paper scheme for the cases under study.

For the Gaussian broadcast channel, transmission at or near the capacity subject to a specific modulation constraint, has been an essentially open problem. The capacity of the AWGN broadcast is achieved by superposition coding, but superposition of individual coded modulations does not in general obey a predefined constellation. We approach this coded modulation problem with multilevel coding (MLC) which is known to achieve the constellation constrained capacity in the point-to-point channel. In channels involving multiple transmitters or receivers, the application of multilevel coding has received little attention. In this paper, a method is proposed that decomposes superposition coding into binary multilevel superposition coding. The problem of rate allocation through every level for each user is studied and a pragmatic rate allocation procedure is presented. The problem of rate allocation to levels is studied and a pragmatic method for its solution is proposed. The coded modulation with proposed rate allocation achieves rates that are very close to the constellation constrained capacity.

In practical multiuser wireless networks, different links often experience unequal coherence lengths due to differences in mobility as well as scattering environment, a common scenario that has largely been neglected in the fundamental studies of the wireless channel. A key feature of unequal coherence lengths is that the per-transmission cost of acquiring CSI and its effect on achievable rates may vary significantly among the nodes, thus pre-existing receive CSI on a typical node should not be assumed as it will hide this key feature of the problem. In this paper, the method of product superposition is employed to find the achievable degrees of freedom region of multiuser broadcast channel where the users coherence lengths have arbitrary integer ratios. The achievable degrees of freedom region meets the outer bound when the transmitter has fewer antennas than the receivers, or when all receivers have the same number of antennas, hence for this class of antenna configurations the optimal degrees of freedom is now known.

A modified version of Costa's dirty paper channel is studied, in which both the input signal and the state experience stationary and ergodic time-varying fading. The fading coefficients are assumed to be known exclusively at the receiver. An inner bound of the achievable rates using lattice codes is derived and compared to an outer bound of the capacity. For a wide range of fading distributions, the gap to capacity is within a constant value that does not depend on either the power of the input signal or the state. The results presented in this paper are applied to a class of ergodic fading broadcast channels with receive channel state information, where the achievable rate region is shown to be close to capacity under certain configurations.

This paper proposes the extrinsic information transfer (EXIT) method for the analysis of belief propagation in community detection on random graphs, specifically under the degree correlated stochastic block model. Belief propagation in community detection has been studied under density evolution; this work for the first time brings EXIT analysis to community detection on random graphs, which has certain advantages that are well documented in the parallel context of error control coding. We show using simulations that in the case of equally-sized communities, when the probability of connectivity in the communities are different, there is only one intersection point on the EXIT curves, hence belief propagation is optimal. When the probability of connectivity in the communities are the same, we show that belief propagation is equivalent to random guessing and the EXIT curves intersect at the trivial zero-zero point. For the roughly equal-sized communities, we show that there is always only one intersection point on the EXIT curves, suggesting that belief propagation is optimal. Finally, for the communities with disparate size, we show that there are multiple intersection points, hence belief propagation is likely to be sub-optimal.

Individual links in a wireless network may experience unequal fading coherence times due to differences in mobility or scattering environment. This paper studies broadcast and multiple access channels whose nodes experience unequal fading block lengths. Channel state information (CSI) is not available at the transmitters, and the cost of acquiring CSI at the receivers is fully accounted for in the degrees of freedom. In the broadcast channel, the method of product superposition is employed to find the achievable degrees of freedom. When the number of symbols in any fading block is at least twice the number of antennas at any active node and the fading block lengths have integer ratios, achievable degrees of freedom meet the upper bound in four cases: when the transmitter has fewer antennas than the receivers, when all receivers have the same number of antennas, when the coherence time of one receiver is much shorter than all others, or when all receivers have identical block fading length. The degrees of freedom region of the broadcast under identical coherence times was also previously unknown and is settled by the results of this paper. The disparity of coherence times leads to gains that are distinct from those arising from other techniques, such as spatial multiplexing or multiuser diversity. This new class of gains is denoted coherence diversity. The inner bounds in the broadcast channel are further extended to fading block lengths of arbitrary ratio or alignment. In addition, in the multiple access channel with unequal coherence times, achievable and outer bounds on the degrees of freedom are obtained.

The overwhelming majority of the large literature on coding for the relay channel has been dedicated to the low-SNR regime (binary signaling) and the half- duplex scenario. For non-binary full-duplex signaling, important challenges remain in the simultaneous design of coded modulation at the source and relay. Part of the difficulty is to design the codes with the requisite correlation prescribed by theory. This paper proposes a systematic code design methodology for the relay channel via multilevel coding (MLC). The main difficulty was that a straightforward extension of the chain rule MLC decomposition, as was previously used in the point to-point MLC, would result in many dependencies between the coded layers of the source and relay. A key contribution of this paper is showing that MLC joint source/relay code design can be implemented via standard binary code design procedures. Specifically, we outline a design process where the correlation between the source and relay codes are implemented purely via pairwise correlations between the binary codes of source and relay at each layer, without any other inter-layer correlations. Moreover, a specific design example is provided via a simple XOR operation on two conventionally designed codes. Numerical results show excellent performance for the proposed scheme.

The performance of lattice codes in the additive white Gaussian noise (AWGN) channel has attracted much attention lately, however, their performance under ergodic fading channels has been relatively unexplored. We show that lattice coding and decoding achieve the capacity of the ergodic point-to-point and multiple-access channels (MAC). Additionally, a low-complexity scheme is proposed for the ergodic MAC. At moderate and high signal-to-noise ratio (SNR), the sum rate achieved by the low-complexity scheme is within a constant gap to the ergodic MAC sum capacity, whereas at low SNR the gap to capacity diminishes quadratically with linear SNR decrease.

In a two-user broadcast channel where one user has full CSIR and the other has none, a recent result showed that TDMA is strictly suboptimal and a product superposition requiring non-coherent signaling achieves DoF gains under many antenna configurations. This work introduces product superposition in the domain of coherent signaling with pilots, demonstrates the advantages of product superposition in low-SNR as well as high-SNR, and established DoF gains in a wider set of receiver antenna configurations. Two classes of decoders, with and without interference cancellation, are studied. Achievable rates are established by analysis and illustrated by simulations.

It is known that lattice coding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This paper addresses the performance of lattice codes in the ergodic fading channel. Using nested lattice codes and ambiguity decoding, we show that the rates achieved by lattice coding and decoding are within a constant gap of the capacity of the ergodic channel at moderate and high signal-to-noise-ratio (SNR), and within a gap that decreases quadratically with the SNR for the low SNR regime.

It is known that multi-level coding (MLC) with multi-stage decoding (MSD) approaches the point-to-point constellation constrained channel capacity subject to appropriate choice of code rates at each level. MLC/MSD in the context of multi-node networks has not been previously investigated, and is the subject of this paper. It is shown that MLC/MSD can approach the MAC capacity. Issues related to achieving non-corner points of the capacity region are discussed. A MLC-based superposition scheme for the degraded broadcast channel is discussed and an achievable region outlined. The half-duplex orthogonal degraded relay channel is studied under MLC/MSD. The achievable rate is calculated under two conditions: First we consider end-to-end layer-by-layer decoding, where each layer is decoded at the relay and destination only with help from previous layers. Then, we remove this constraint via a parity-forwarding approach at the relay, where the destination performs two multi-stage decoding operations: one corresponding to the relay-destination link and then one corresponding to the source-destination link. The achievable rate under parity forwarding is shown to be superior.

The degrees of freedom (DoF) of the MIMO broadcast channel under various conditions remains an important open problem. This paper makes contributions towards completing the picture of the DoF of broadcast channels in the absence of CSIT (Channel State Information at Transmitter). First, the DoF of the quasi-static coherent broadcast channel (with CSIR) is established. Second, the DoF of the two-user asymmetric MIMO broadcast channel without CSIR is established, and is extended to multiple users with arbitrary antenna configurations. Third, an achievable DoF for mixed-CSIR multiuser broadcast channel, which was only known for certain antenna configurations, is extended to other antenna configurations.

This paper studies multiple-input multiple-output linear precoding in the high-signal-to-noise-ratio regime under flat fading. The diversity at all fixed rates is analyzed for a number of linear precoders. The diversity-multiplexing tradeoffs (DMTs) are also obtained, discovering that for many linear precoders the DMT gives no direct insight into the intricate behavior of fixed-rate diversity. The zero-forcing (ZF), regularized ZF, matched filtering, and Wiener filtering precoders are analyzed. It is shown that regularized ZF (RZF) or matched filter (MF) suffers from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity for spectral efficiencies up to a certain threshold and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the minimum mean square error sense, the structure is known as the Wiener precoder, which in the fixed-rate regime is shown to have diversity that depends not only on the number of antennas, but also on the spectral efficiency. The diversity in the presence of both precoding and equalization is also analyzed.

MIMO precoding matches the transmission to channel conditions in order to reduce or eliminate interference at the receiver. In this paper, we are interested in the case where the receiver is also equipped with a linear processor, specifically a ZF filter. We analyze the effect of the ZF receive filter on the performance of a variety of MIMO precoders. It is shown that receive-side ZF equalization can remove the error floors that sometimes appear with regularized zero-forcing precoding and matched-filter precoding.

This paper investigates the performance of the minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO linear ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. It is shown that the MMSE MIMO receiver exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies.

In the fading MIMO broadcast channel, until recently the results under full CSIR and no CSIR indicated that degrees of freedom (DoF) cannot be improved beyond what is available via TDMA. Recently, however, it was discovered that when one node has full CSIR and the other has none, TDMA is no longer DoF-optimal and a product decomposition with noncoherent (Grassmannian) signaling achieves the optimal DoF under certain receiver antenna configurations. This work extends product superposition to the domain of coherent signaling with pilots, showing that it can also achieve the optimal DoF. In addition, this work demonstrates the advantages of product superposition in low-SNR as well as high-SNR, and extends the set of receiver antenna configurations under which product decomposition achieves optimal DoF.

This paper investigates the throughput-reliability tradeoff (TRT) for dual-hop amplify-and-forward relay systems with one source, one destination, and multiple relays, and its relationship with the diversity-multiplexing tradeoff (DMT). The TRT was proposed in the context of MIMO block fading channels to reveal the interplay between the signal-to-noise ratio (SNR), rate R, and outage probability that are not accessible through the DMT. The contributions of this paper include the calculation of the TRT expressions for two classes of amplify-and-forward protocols: the slotted amplify-and-forward and the non-orthogonal amplify-and-forward. Based on the derived expressions, relationships between the SNR, rate and outage probability are explored. The relationship between the TRT and the DMT is investigated. One of the goals of the TRT is to predict the slope and offset of the outage vs. SNR set of curves parameterized by different rates. We verify the accuracy of the TRT predictions in the context of amplify-and-forward relays.

In underlay cognitive radio, a secondary user transmits in the transmission band of a primary user without serious degradation in the performance of the primary user. This paper proposes a method of underlay cognitive radio where the secondary pair listens to the primary ARQ feedback to glean information about the primary channel. The secondary transmitter may also probe the channel by transmitting a packet and listening to the primary ARQ, thus getting additional information about the relative strength of the cross channel and primary channel. The method is entitled Spectrum Harvesting with ARQ Retransmission and Probing (SHARP). The probing is done only infrequently to minimize its impact on the primary throughput. Two varieties of spectrum sharing, named conservative and aggressive SHARP, are introduced. Both methods avoid introducing any outage in the primary; their difference is that conservative SHARP leaves the primary operations altogether unaffected, while aggressive SHARP may occasionally force the primary to use two instead of one transmission cycle for a packet, in order to harvest a better throughput for the secondary. The performance of the proposed system is analyzed and it is shown that the secondary throughput can be significantly improved via the proposed approach, possibly with a small loss of the primary throughput during the transmission as well as probing period.

We consider a spectrum-sharing network where n secondary relays are used to increase secondary rate and also mitigate interference on the primary by reducing the required overall secondary emitted power. We propose a distributed relay selection and clustering framework, obtain closed-form expressions for the secondary rate, and show that secondary rate increases proportionally to log n. Remarkably, this is on the same order as the growth rate obtained in the absence of a primary system and its imposed constraints. Our results show that to maximize the rate, the secondary relays must transmit with power proportional to n-1(thus the sum of relay powers is bounded) and also that the secondary source may not operate at its maximum allowable power. The tradeoff between the secondary rate and the interference on the primary is also characterized, showing that the primary interference can be reduced asymptotically to zero as n increases, while still maintaining a secondary rate that grows proportionally to log n. Finally, to address the rate loss due to half-duplex relaying in the secondary, we propose an alternating relay protocol and investigate its performance.

Interference alignment (IA) is known to significantly increase sum-throughput at high SNR in the presence of multiple interfering nodes, however, the reliability of IA is little known, which is the subject of this paper. We study the error performance of IA and compare it with conventional orthogonal transmission schemes. Since most IA algorithms require extensive channel state information (CSI), we also investigate the impact of CSI imperfection (uncertainty) on the error performance. Our results show that under identical rates, IA attains a better error performance than the orthogonal scheme for practical signal to noise ratio (SNR) values but is more sensitive to CSI uncertainty. We design bit loading algorithms that significantly improve error performance of the existing IA schemes. Furthermore, we propose an adaptive transmission scheme that not only considerably reduces error probability, but also produces robustness to CSI uncertainty.

Relay selection, a simple and efficient method of operating multi-relay networks, has in the past been considered only when all relays follow the same protocol. This work studies relay selection in heterogeneous relay networks where relays with different protocols can co-exist. The new techniques for the analysis of such networks are demonstrated on a mixture of decode-forward relays and amplify-forward relays, as well as a mixture of non-orthogonal amplify-forward (NAF) and dynamic decode-forward (DDF) relays, and also a mixture of NAF and compress-forward relays. In each case the diversity-multiplexing tradeoff is calculated. In the process, a noteworthy limitation of previous relay selection schemes is also relaxed and removed: In the past in multi-relay networks the direct source-destination link has been ignored whenever it introduces dependencies among selection decision variables, as it often does. This has been motivated chiefly by the lack of suitable analytical techniques for order statistics of dependent random variables. In this work, relay selection analysis is extended to allow the presence of a direct source-destination link. As a side benefit, the relay selection results in homogeneous networks (where relays are all of the same type) are also extended to include the presence of a source-destination link.

This paper presents a spectrally efficient protocol for half-duplex multi-relay systems in block fading channels where a direct source-destination link is unavailable. The proposed protocol adaptively selects either successive interference cancelation (SIC) or joint decoding according to the causal decoding status of each relay. We also adopt dynamic refreshing that restarts the protocol whenever it is advantageous to do so, even if the relay decoding set (the set of relays that are able to decode the message) is not empty. The achievable diversity-multiplexing tradeoff (DMT) of the proposed protocol with m-antenna nodes is analyzed via a Markov chain whose states are related to the cardinality of a decoding set. This protocol strictly improves the DMT of the existing DF half-duplex relay-selection protocols without decoding delay, and in the low multiplexing gain region is able to meet the DMT upper bound. The main contributions of the paper are the state-dependent decoding strategies in DF multi-relay systems and also the dynamic refresh for the flushing of residual interferences in the system, concepts that may find usefulness beyond the gains in the high-SNR regime.

Single-carrier (SC) block transmission with cyclic prefix (CP) is a method with several advantages that has been incorporated into standards. This paper investigates the performance of multi-antenna SC-FDE under cyclic-delay diversity (CDD) and Alamouti signaling. Our analysis fully characterizes the diversity, showing that it depends not only on the antenna configuration and channel memory, but also on data block length and data transmission rate. Below a certain rate threshold, full diversity is available to both CDD and Alamouti signaling, while at higher rates their diversity diminishes, albeit not quite in the same way. Our analysis shows that at high rates the CDD diversity degenerates to the diversity of the SISO SC-FDE, while Alamouti signaling provides twice the diversity of SISO SC-FDE.

This paper investigates the performance of the zero-forcing (ZF) and minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO zero-forcing ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. The MMSE ZP is also investigated, showing that it exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies. Thus MMSE ZP works better than ZF ZP, but not quite as well as ML. To further improve the performance, lattice-reduction aided equalization in the frequency-selective channel is investigated. It is shown that lattice-reduction-aided zero forcing equalizer as well as MMSE equalizer achieve the maximum spatial and temporal diversity at all spectral efficiencies.

Despite encouraging advances in the design of relay codes, several important challenges remain. Many of the existing LDPC relay codes are tightly optimized for fixed channel conditions and not easily adapted without extensive re-optimization of the code. Some have high encoding complexity and some need long block lengths to approach capacity. This paper presents a high-performance protograph-based LDPC coding scheme for the half-duplex relay channel that addresses simultaneously several important issues: structured coding that permits easy design, low encoding complexity, embedded structure for convenient adaptation to various channel conditions, and performance close to capacity with a reasonable block length. The application of the coding structure to multi-relay networks is demonstrated. Finally, a simple new methodology for evaluating the end-to-end error performance of relay coding systems is developed and used to highlight the performance of the proposed codes.

We consider a spectrum-sharing network where n secondary relays are used to increase the secondary rate. We propose a distributed amplify-and-forward (AF) relaying scheme combined with relay selection and clustering. For the proposed method we obtain a closed-form expression for the secondary rate, which shows that the rate grows proportionally to log n. Remarkably, this growth rate is on the same order as that achieved in the absence of a primary system and its imposed constraints. We find the optimal power strategy for the relays subject to primary constraints: to maximize the secondary rate, each of the selected relays need to transmit with power proportional to n-1(thus the sum of relay powers is bounded).

We characterize the DMT of finite-length linear equalizers in the MIMO frequency-selective channel. We obtain the DMT in the case of cyclic-prefix transmission and provide an upper bound for the DMT in the case of zero-padding transmission. We also provide in-depth analysis for the diversity of the MMSE receiver in the fixed rate regime (i.e. zero multiplexing gain) in the cyclic-prefix transmission and obtain a lower bound on diversity. This gives better insight about the diversity of the MMSE in this regime since only upper bound exists in the literature. The MMSE diversity in this regime is function of the spectral efficiency, the data block length and the number of transmit and receive antennas.

Cyclic Delay Diversity (CDD) is a simple method that converts transmit antenna diversity into frequency selectivity, thus allowing simple operation and use of conventional receivers to capture the diversity. This paper shows that single-carrier CDD methods are capable of producing diversity without channel coding or linear precoding, and that this is made possible via the appropriate design and use of linear equalizers. At the heart of our result is the establishment of a functional equivalence between effective channels seen by the CDD MISO system and the cyclic-prefix SISO ISI system. Specifically, we show that in an M×1 CDD MSIO system, the MMSE receiver achieves maximum diversity for rate values R ≤ log L/M(ν+1)-1, where L is the data block length, R the spectral efficiency in b/s/Hz, and ν is the channel memory. The equivalence between the delay diversity (DD) system and a zero-padding single-carrier system can be also established (as long as the DD delay taps are carefully chosen) for which linear equalizers can achieve maximum diversity with no constraint on rate.

This paper addresses the design of a protograph-based LDPC code which can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels. We propose a method to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic information transfer (EXIT) chart. We then describe a simple method to search for a protograph code whose threshold is close to the i.u.d. capacity limit. This new class of codes is needed because experiments show a protograph that is capacity approaching in the AWGN channel may not perform well in partial response channels. In particular, protographs with punctured nodes are often used to produce good AWGN codes, but they perform poorly with the BCJR equalizer. Numerical results support our analysis.

In multiantenna broadcast channels without channel state information at transmitter (CSIT), orthogonal transmission (e.g., TDMA) is known to achieve maximal degrees of freedom either with perfect channel state information at receiver (CSIR), or when no receiver has CSIR. Recently, it has been shown [1] that TDMA is no longer optimal in cases of unequal CSIR, e.g., when one receiver has CSIR and another does not. This paper proposes a multiplicative superposition that attains degrees of freedom uniformly higher than [1] and TDMA. The proposed scheme uses coherent signaling for the receiver with CSIR, and Grassmannian signaling for the receiver without CSIR. This signaling structure is shown to attain the optimal degrees of freedom under a wide set of antenna configurations.

For linear MIMO precoders, the diversity is an important parameter affecting broad tradeoffs in system design, however, the diversity of many MIMO precoders has not been available in the open literature. This paper analyzes the diversity of the following MIMO precoders: the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering. Several interesting properties of these precoders are revealed by this analysis. It is shown that regularized ZF (RZF) and the matched filter (MF) exhibit two-mode diversity: full diversity at low rates R and error floor at high rates. The rate threshold of this two-mode behavior is analytically determined. The Wiener precoder is also shown to produce a diversity that depends on the spectral efficiency and can be as small as one and as large as the product of the number of transmit and receive antennas.

Single-carrier frequency domain equalization (SC-FDE) has many advantages, but in the MIMO frequency selective channel its performance has not been fully characterized and several important open questions remain. This paper analyzes the diversity of zero-forcing MIMO SC-FDE. It is shown that the diversity of the ZF receiver over this channel is the same as that of the ZF receiver in the frequency-flat channel. To improve the performance, a lattice-reduction (LR) aided ZF equalization is proposed and analyzed. It is shown that the full spatial and temporal diversity is achieved by he LR-aided ZF receiver for the uncoded transmission. This is the first analytical proof for the LR-aided equalization for MIMO frequency selective channel.

This paper presents a simple yet effective method for designing nested families of LDPC codes. Rate compatible codes are essential for many communication applications, e.g. hybrid automatic repeat request (HARQ) systems, and their design is nontrivial due to the difficulty of simultaneously guaranteeing the quality of several related codes. Puncturing can be used to generate rate-compatible LDPC codes, but it produces a gap to capacity that, in practice, often significantly exceeds the gap of the mother code. We propose an alternative method based on successively extending a high-rate protograph. The resulting codes not only inherit the advantages of protograph codes, namely low encoding complexity and efficient decoding algorithms, but also cover a wide range of rates and have very good performance with iterative decoding thresholds that are within 0.2 dB of their capacity limits.

Unlike point-to-point cognitive radio, where the constraint imposed by the primary rigidly curbs the secondary throughput, multiple secondary users have the potential to efficiently harvest the spectrum and share it among themselves. This paper analyzes the sum throughput of a multiuser cognitive radio system with multiantenna base stations, either in the uplink or downlink mode. The primary and secondary have N and n users, respectively, and their base stations have M and m antennas, respectively. We show that an uplink secondary throughput grows with m/N+1 log n if the primary is a downlink system, and grows with m/M+1 log n if the primary is an uplink system. These growth rates are shown to be optimal and can be obtained with a simple threshold-based user selection rule. In addition, we show that the secondary throughput can grow proportional to , while simultaneously the interference on the primary is forced down to zero, asymptotically. For a downlink secondary, it is shown that the throughput grows with in the presence of either an uplink or downlink primary system. In addition, the interference on the primary can be made to go to zero asymptotically, while the secondary throughput increases proportionally to . The effect of unequal path loss and shadowing is also studied. It is shown that under a broad class of path loss and shadowing models, the secondary throughput growth rates remain unaffected.

This paper considers the multiantenna broadcast channel without transmit-side channel state information. For this channel, it has been known that when all receivers have channel state information (CSIR), the degrees of freedom (DoFs) cannot be improved beyond what is available via time-division multiple access. The same is true if none of the receivers possess CSIR. This paper shows that an entirely new scenario emerges when receivers have unequal CSIR. In particular, orthogonal transmission is no longer DoF optimal when one receiver has CSIR and the other does not. A multiplicative superposition is proposed for this scenario and shown to attain the optimal DoFs under a wide set of antenna configurations and coherence lengths. Two signaling schemes are constructed based on the multiplicative superposition. In the first method, the messages of the two receivers are carried in the row and column spaces of a matrix, respectively. This method works better than orthogonal transmission while reception at each receiver is still interference-free. The second method uses coherent signaling for the receiver with CSIR, and Grassmannian signaling for the receiver without CSIR. This second method requires interference cancellation at the receiver with CSIR, but achieves higher DoF than the first method.

In most multiple-input multiple-output (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signal-to-noise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple-access channel. Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight.

This paper investigates the degrees of freedom of the interference channel in the presence of a dedicated multiple-input multiple-output (MIMO) relay. The relay is used to manage the interference at the receivers. It is assumed that all nodes including the relay have channel state information only for their own links and that the relay hasM≥Kantennas in aK-user network. We pose the question: what is the benefit of exploiting the direct links from the source to destinations compared to a simpler two-hop strategy. To answer this question, we first establish the degrees of freedom of the interference channel with an MIMO relay, showing that aK-pair network with an MIMO relay has [(K)/2] degrees of freedom. Thus, appropriate signaling in a two-hop scenario captures the degrees of freedom without the need for the direct links. We then consider more sophisticated encoding strategies in search of other ways to exploit the direct links. Using a number of hybrid encoding strategies, we obtain nonasymptotic achievable sum rates. We investigate the case where the relay (unlike other nodes) has access to abundant power, showing that when sources have powerPand the relay is allowed power proportional toO(P2) , the full degrees of freedomKare available to the network.

In a cognitive (secondary) multiple-access network which is subject to interference power constraints imposed by a primary system, it is desirable to mitigate the interference on the primary and to harvest multiuser diversity gains in the secondary. To simultaneously achieve these goals, a two-step (hybrid) scheduling method is proposed that pre-selects a set of secondary users based on their interference on the primary, and from among them selects the user(s) that yield the highest secondary throughput. The optimal number of active secondary transmitters is characterized as a function of the primary interference constraint, the secondary transmit power, and the number of secondary transmitters n. The secondary sum-rate (throughput) of the proposed algorithm grows optimally (proportional to log n). We investigate the tradeoff between scaling the secondary throughput and reducing interference on the primary, and characterize the optimum tradeoff in the regime of large n. Finally, we study user scheduling under fairness constraints, which is necessary when the channel statistics of secondary nodes are not identical. A modified hybrid scheduling rule is proposed to ensure user fairness, while still achieving the optimal growth rate for the secondary throughput.

This paper investigates the secondary multiuser diversity in spectrum sharing networks. We show that by exploiting the fading nature of interference links, the secondary system to efficiently utilize the spectrum while complying with constraints imposed by the primary system. More precisely, as the number of secondary users increases, the throughput grows logarithmically in a secondary multiple-access channel (MAC) and double-logarithmically in a secondary broadcast channel (BC). The multiuser diversity may also reduce the interference on the primary asymptotically to zero; the tradeoff between throughput enhancement and interference reduction is characterized. Finally, we results show that for the secondary MAC the growth rate of throughput decreases linearly with the number of primary users (constraints), while for the secondary BC the growth rate is unaffected by the number of primary constraints.

Cyclic-prefix (CP) insertion in a single or multi-carrier system transforms the frequency-selective channel into a set of parallel flat channels, thus reducing the equalization complexity considerably. To harness the channel multipath diversity in this parallelized system the use of error control codes and/or linear precoding are proposed in the literature. A more recent result shows that maximum diversity can be achieved by lattice-reduction aided equalization together with precoded OFDM transmission. In this paper, we show that full diversity lattice-reduction is possible {\em without} requiring either precoding or error control codes. In earlier work it was shown that some cyclic-prefix systems have a diversity that is rate-dependent; we show that lattice-reduction diversity does not follow the same pattern of behavior. We also explore and expose important distinctions between diagonal and non-diagonal equalization for cyclic prefix systems.

Protograph-based bit-interleaved coded modulation (BICM) provides an elegant way of designing coded modulation over Rayleigh faded channels, however, to date the available designs have been limited to specific modulations and the corresponding decoding thresholds have not been known for Rayleigh faded channels. In this work, we present a simple method for designing protograph-based BICM that is general and applies to any modulation, and furthermore we calculate the iterative decoding thresholds of the protograph codes while mapped to higher order modulations. This general coding framework can support not only multiple rates but also adaptive modulation. We report that certain families of protograph codes achieve a threshold within a gap of approximately 0.2 - 0.4 dB of BICM capacity limit across a wide range of rates and modulations.

We consider the effective degrees of freedom (DoF) achieved by interference alignment when channel state information (CSI) is acquired by training and feedback. For a flat block- fading K × K interference channel with power P per transmitter and M antennas per node, we show that interference alignment achieves higher DoF than orthogonal transmission (e.g., TDMA) only if the channel coherence time is large and the capacity of feedback link is at least as Θ(log P). Under this condition, to maximize the effective DoF, each receiver needs to feed back CSI via (M2-1)log P bits per coherence interval; smaller growth rate of feedback bits will decrease the effective DoF. We also show that in the presence of training and feedback cost, K = 3 achieves the optimal DoF for a broad range of channel characteristics; with larger number of user pairs, the DoF falls short of its optimum and beyond a certain point becomes a decreasing function of K.

We consider a set of cognitive nodes cooperatively sensing the activities of a primary system. Two cooperative protocols are proposed, where cognitive nodes opportunistically transmit to each others, and finally each node makes a decision based its own observations. In the first protocol (Protocol 1), a node relays the signal received from the primary to the other nodes only if the signal energy is sufficiently large. In the second protocol (Protocol 2), given the knowledge of channel gains to the other nodes, a node transmits only if the channel gains are large. With two cognitive nodes, Protocol 1 improves the average detection probability by up to 50% relative to the protocol studied in. Compared to Protocol 1, while additional channel knowledge is needed, Protocol 2 saves up to 50% transmit power and maintains almost the same detection probability.

It is known that in multiantenna broadcast channels without transmitter-side channel state information (CSIT), time-sharing (orthogonal transmission) achieves the maximum multiplexing gain if perfect receiver-side channel state information (CSIR) is available to all receivers, or if no receiver has CSIR. We show that orthogonal strategies are not optimal in cases where some receivers have more CSIR than others. A superposition signaling is proposed to transmit to two receivers simultaneously on Grassmannians, achieving higher multiplexing gain compared with orthogonal transmissions. The information for the two receivers is conveyed by the row and column spaces of the transmitted matrix, respectively, which is constructed from a product of two matrices that each lie on different Grassmannians. This multiplicative superposition allows the two receivers to be interference-free from the other's signals even without CSIT.

This paper analyzes the MMSE receiver in MIMO frequency-selective channels. This expands our understanding of the MMSE MIMO channel, whose diversity was only recently characterized in the MIMO flat-fading regime. Specifically, in this paper lower and upper bounds on the diversity of the MMSE receiver operating over frequency selective MIMO channel under block transmission with zero-padding (ZP) or cyclic-prefix (CP) are produced. The tightness of the bounds is demonstrated for both ZP/CP for the special case of SIMO channel.

In frequency-selective channels linear receivers enjoy significantly-reduced complexity compared with maximum likelihood receivers at the cost of performance degradation which can be in the form of a loss of the inherent frequency diversity order or reduced coding gain. This paper demonstrates that the minimum mean-square error symbol-by-symbol linear equalizer incurs no diversity loss compared to the maximum likelihood receivers. In particular, for a channel with memory ν, it achieves the full diversity order of (ν+1) while the zero-forcing symbol-by-symbol linear equalizer always achieves a diversity order of one.

The performance of many opportunistic relay networks has been unknown in part because opportunistic analysis relies on independence assumptions that break down in many interesting and useful network topologies. This paper develops techniques that expand opportunistic analysis to a broader class of networks, proposes new opportunistic methods for several network geometries, and analyzes them in the high-SNR regime. For each of the geometries studied in the paper, we analyze the opportunistic DMT of several relay protocols, including amplify-and-forward, decode-and-forward, compress-and-forward, nonorthogonal amplify-forward, and dynamic decode-forward. Among the highlights of the results: In a variety of multi-user single-relay networks, simple selection strategies are developed and shown to be DMT-optimal. It is shown that compress-forward relaying achieves the DMT upper bound in the opportunistic multiple-access relay channel as well as in the opportunistic$n\times n$user network with relay. Other protocols, e.g., dynamic decode-forward, are shown to be near optimal in several cases. Finite-precision feedback is analyzed for the opportunistic multiple-access relay channel, the opportunistic broadcast relay channel, and the opportunistic gateway channel, and is shown to be almost as good as full channel state information.

The performance of relay selection in the presence of a direct source-destination link has been an open problem, essentially because a direct link introduces cross-dependencies in the relay selection that significantly complicate its analysis. Thus, the previous studies of relay selection by and large have been forced to assume that the network geometry is such that the direct link is weak enough to be ignored.This paper addresses and solves this open problem. Several relaying protocols are analyzed with relay selection in the high-SNR regime using the diversity-multiplexing tradeoff, including AF, DF, NAF, DDF, and CF. In several cases, simplified selection criteria are developed.

In this paper, we consider a pair of cognitive radio (CR) users co-existing with a pair of ARQ- based primary users (PU). The secondary user (SU) overhears the ACK/NACK feedback sent from the receiver of the primary system, and then decides to access the spectrum or not. An opportunistic sharing scheme, referred to as Spectrum sHaring with ARQ Retransmission and Probing timeslots (SHARP), is proposed to exploit spectrum opportunities based on the ACK/NACK of PU only. Numerical results show that the analytical outcomes perfectly match those from the Monte Carlo simulation. Moreover, the goodput of SU increases dramatically while the outage probability of the primary remains small.

This work settles a long-standing open problem by providing a complete characterization of the diversity of the MMSE MIMO receiver for all fixed rates (spectral efficiencies). The MMSE MIMO receivers exhibit a complicated behavior in the fixed-rate regime that cannot be obtained via DMT analysis. Specifically, we show that in a system with M transmit antennas, N receive antennas, and rate R, the diversity is given by d = ⌈M2-R/M⌉2+ (N - M)⌈M2-R/M⌉. This verifies and refines earlier results that were obtained only for two extremal operating points: diversity MN at very low rates and diversity N - M + 1 at very high rates.

This paper presents a high-performing LDPC code for the relay channel that addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly optimized for a given channel quality and are not easily adapted, without extensive re-optimization, for various channel conditions. This paper presents a code for the relay channel that combines structured design and easy encoding with rate compatibility to allow adaptation to the three links involved in the relay channel, and furthermore offers very good performance. The proposed code is constructed by synthesizing a bilayer structure with a protograph. In addition to the contribution to relay encoding, we also produce an improved family of protograph codes for the point-to-point AWGN channel whose high-rate members enjoy thresholds that are within 0.07 dB of capacity.

This paper considers the problem of user coexistence in cognitive radio networks operating under fading. The core idea of this work is to exploit the opportunities occurring during retransmissions of a primary system to allow the coexistence of cognitive radios. Several protocols are proposed depending on the amount of the channel knowledge available at the cognitive transmitter about the network links while avoiding the assumption of non-causal knowledge of the primary user data that appears in some existing works. The protocols presented allow the cognitive link to achieve non-trivial throughput while causing minimal effects on the throughput of the primary link. Performance analysis of the protocols is presented and their effectiveness is verified via simulations.

This paper analyzes the diversity gain achieved by single-carrier frequency-domain equalizers (SC-FDE) in frequency selective channels, and uncovers the interplay between diversity gain d, channel memory length ¿, transmission block length L, and the spectral efficiency R. We specifically show that for the class of minimum mean-square error (MMSE) SCFDE receivers, for rates R ¿ log L/¿ full diversity of d = ¿+ 1 is achievable, while for higher rates the diversity is given by d = [2-RL + 1. In other words, the achievable diversity gain depends not only on the channel memory length, but also on the desired spectral efficiency and the transmission block length. A similar analysis reveals that for zero forcing SC-FDE, the diversity order is always one irrespective of channel memory length and spectral efficiency. These results are supported by simulations.

This paper addresses user coexistence in cognitive radio systems by taking advantage of opportunities that arise during ARQ retransmission. It is shown that if these opportunities are properly exploited, nontrivial rates can be made available to a secondary (cognitive) pair while impinging little or no interference on the primary pair. This can be accomplished with an oblivious primary system and without assuming any non-causal information at the secondary about the primary data. Several protocols are devised that work with varying amounts of channel state information about the cognitive and primary links. The protocols are further extended to the scenario where multiple cognitive receivers exist. Performance analysis of the protocols is presented and their effectiveness is verified via simulations.

In this paper we study opportunistic communication in two relay channels, the shared relay channel (SRC) and the X-relay channel (XRC). The shared relay channel consists of multiple non-interfering source-destination pairs sharing one relay. The X relay channel is a multi-source multi-destination network where each source has a message for each destination and the network is assisted by one relay. The diversity multiplexing tradeoff is calculated for these two networks under protocols including non-orthogonal amplify-forward, dynamic decode-forward, and compress-forward. The performance of simpler protocols can be easily deduced from the results in this paper.

This paper introduces a new class of space-time codes that achieve coding gain without a trellis or any form of inter-block dependency. The construction of the new codes starts from an existing (parent) space-time block code (STBC). Then by increasing the constellation size followed by expurgation of the expanded codebook, a better code is obtained at the original transmission rate. This method can be applied to a wide variety of space-time block codes, including orthogonal codes and quasi-orthogonal codes. A multi-stage design algorithm is presented, and for orthogonal parent codes, an efficient decoding algorithm is developed, and its decoding complexity is analyzed. Despite altering the regular structure of the orthogonal code, the decoding complexity is only affected by a constant factor.

Shannon entropy is a powerful tool in image analysis, but its reliable computation from image data faces an inherent dimensionality problem that calls for a low-dimensional and closed form model for the pixel value distributions. The most promising such models are Markovian, however, the conventional Markov random field is hampered by noncausality and its causal versions are also not free of difficulties. For example, the Markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system. A new model, named quadrilateral Markov random field (QMRF) is introduced in this paper in order to overcome these limitations. A property of QMRF with neighboring size of 2 is then used to decompose an image prior into a product of 2-D joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption. In addition, the paper includes an extension of the introduced method to the computation of image spatial mutual information. Comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones.

We consider a relay that simultaneously assists multiple source-destination pairs that do not have a direct link, which we denote the gateway channel, and explore the sum capacity of this network in the presence of quasi-static fading. In the absence of transmitter-side channel state information (CSI), we study superpostion as well as orthogonal channel access. In the presence of transmitter CSI, we consider opportunistic channel access with full CSI, as well as limited CSI via a 1- bit feedback (per user). In each case, the outage capacity and the diversity-multiplexing tradeoff are calculated. It is observed that orthogonal channel access is almost as good as superposition coding, and that opportunistic access provides significant gains. It is shown that a 1-bit feedback per user captures most of the gains available in opportunistic communication.

This paper addresses the problem of lifetime maximization under unequal and time-varying channel conditions, individual battery constraints, and estimation quality requirements at the fusion center. The standard tool for solving this problem (dynamic programming) has exponential complexity with number of sensors and states and needs heavy information exchange with sensors at each iteration. Also errors are introduced via coarse quantization of the parameters, which is forced by complexity concerns. In light of these issues, we propose a pragmatic method via a decomposition: The overall SNR requirement a is "divided" among sensors according to their battery powers and radio link statistics, and then individual sensors transmit powers are carefully controlled to maximize the lifetime. The proposed decomposition drastically reduces the computational requirement, and also allows a semi-distributed control of sensor transmit powers. Simulations verify the viability of this method.

Relay networks face a fundamental challenge in terms of spectral efficiency, because relays must repeat the source information. To address this key problem, this paper presents two relay selection protocols that salvage spectral efficiency by adroitly leveraging the multiple relays. Both protocols have the feature of letting the source transmit all or most of the time. The diversity-multiplexing tradeoff (DMT) of Zheng-Tse is used to show the advantage of our protocols. The proposed protocols require minimal overhead and feedback, and have similar complexity compared to existing protocols.

This paper investigates the degrees of freedom of the interference channel in the presence of a dedicated MIMO relay. The relay is used to manage the interference at the receivers. We pose a fundamental question: What benefits are achieved by exploiting the direct links from the sources to the receivers and whether a two-hop strategy suffices considering the pre- log factor in the capacity formula? Using a number of hybrid encoding strategies and power allocation policies, we obtain non-asymptotic achievable sum-rates, subsequently leading to achievable degrees of freedom. The results are generalized from a two-user to a if-user network. Our main result is that only k/2 degrees of freedom are achievable in an interference channel with MIMO relay, assuming global channel knowledge at the relay but not at other nodes. Thus, appropriate signaling in a two-hop scenario captures the degrees of freedom gains without the need for the direct links. We also investigate the case where the relay (unlike other nodes) has access to abundant power, showing that when sources have power P and the relay is allowed power proportional to O(P2), the full degrees of freedom K are available to the network.

This paper addresses the multiplexing loss that occurs in relay networks due to causality of relays and the half-duplex constraint. We devise relay selection methods to recover the multiplexing loss in decode-and-forward (DF) relay networks, while requiring very little feedback (merely bits/relay). Two network topologies are studied: First the case is considered where a direct link is available between the source and destination, in addition to the relayed links. For this configuration, an incremental transmission scheme is proposed, and comprehensively analyzed, which uses limited feedback to improve both diversity as well as multiplexing gain. Then, the case without a direct link is considered, for which efficient non-orthogonal DF protocols are produced and analyzed. An interesting feature of the latter methods is unequal error protection capability via a family of embedded diversity-multiplexing (DMT) curves, which can be very useful for practical applications. Even considering this method's minimal DMT, a marked improvement over previous DF methods is observed, especially in high spectral efficiencies.

Full packet headers consume valuable bitrate, which is especially costly in satellite links and some terrestrial wireless links. This has motivated the compression of packet headers by exploiting their correlation via using finite-state machines. The drawback is that compression in the presence of channel errors (packet loss) may result in error propagation. We offer several designs by adapting error control codes for the requirements of packet header compression in uni-directional and bi-directional links, and explore the tradeoffs in complexity, delay, and system performance. For the bi-directional link, we propose a new design called predictive hybrid ARQ and evaluate its performance. Experiments show significant gains in link-layer throughput as well as improved application layer performance demonstrated via video transfer experiments.

In this paper we investigate the diversity order of single-carrier frequency domain equalizers (SC-FDE). Specifically, we look at minimum mean square error (MMSE) linear equalizers utilizing block-transmission and cyclic prefix. It is shown that the diversity order in these systems depends on data transmission rate, channel memory length, as well as transmission block length. Analyses reveal that with memory length v and transmission block length L, for the rates Rleslog L/v full diversity of v+1 is achievable. For higher rates the achievable diversity order is degraded and is equal to [2-RL]+1. Therefore MMSE SC-FDE has a diversity that varies between 1 and v+1, and achieves full diversity only for a limited range of data rates.

Opportunistic cooperation is a technique where in each transmission the best relay (or k best relays) are chosen to assist. In a multiuser cooperative network, coordinating the cooperating users requires exchange of channel information between various nodes. As the number of nodes increases, this information exchange can get out of hand. In this work, we propose an opportunistic cooperation technique where at most two bits of information per relay are exchanged for each cooperation period (one bit feedback and one bit feedforward). Our method does not need any carrier sensing technique or any information regarding source-relay channels for its operation. We show that this frugal technique is capable of achieving the same diversity-multiplexing tradeoff (DMT) achieved by distributed space-time-coded cooperation protocols (DSTC) in Laneman and Wornell (2003). Also we show how bandwidth allocation between a user and its partner affects the diversity-multiplexing tradeoff.

This paper investigates the diversity order of single-carrier, symbol-by-symbol linear equalization (LE). It is shown that minimum mean square error (MMSE) linear equalizers achieve full diversity of v + 1 (the number of channel taps) independent of spectral efficiency. Our results also provide a new proof for the full diversity of decision feedback equalization (DFE), which was shown originally in A. Medles and D.T.M Slock (2004).

Various results to date have demonstrated the advantages of one or several relay nodes assisting transmissions in a wireless network. In many practical scenarios, not all nodes in the network are simultaneously involved in every transmission; therefore, protocols are needed to form groups or subsets of nodes for the purposes of cooperation. We consider this problem in the context of regenerative nodes and non-altruistic cooperation (all nodes have data of their own to transmit). For a network-wide diversity advantage, the protocol must provide each transmitting node with enough "partners" that can decode its message with high-enough probability. Assuming that the nodes cannot communicate their control decisions (distributed scenario), and that each node chooses to help n other nodes, we point out a simple, static selection strategy that guarantees diversity n+1 for all transmissions. We then consider centralized control strategies and study the additional gains that arise from a central control, under various amounts of information being available to the central controller.

In this paper, we present a new method to analyze the throughput and delay of the selective-repeat (SR) automatic repeat-request (ARQ) protocol. Previous work on SR ARQ has concentrated on reliable feedback or two-state Markovian feedback errors. We solve a wider class of problems by characterizing both the forward and reverse channels by general hidden Markov models (HMMs). The moment-generating function (MGF) technique is used to find throughput and delay. To calculate the MGF, we construct matrix signal-flow graphs for the hidden Markov process. This procedure can be useful for a variety of other HMM problems, and is of interest by itself. Practical issues such as erasure errors and timeouts are included in our analyses, which are verified by extensive simulations

Concatenation of orthogonal space-time block codes (OSTBC) with an outer trellis has led to simple and powerful codes, known as superorthogonal codes or space-time block trellis-coded modulation. In this letter, we generalize these codes by finding new code supersets and corresponding set partitioning, resulting in improved coding gain. We provide design guidelines for the labeling of the generalized code trellises and demonstrate the gains by several example designs for two and four transmit antennas

This letter presents two results for antenna selection under keyhole condition. First, we analyze the capacity of the antenna-selection keyhole channel. We show that in an MtimesN system a small number of selected antennas can match the capacity of a baseline full-antenna system (baseline system has no feedback). Second, we formally prove the intuitive result, until now unproven, that antenna selection in the keyhole multiple-input multiple-output channel preserves the available diversity of the channel

This correspondence studies the capacity of multiple-input-multiple-output (MIMO) channels in the presence of antenna selection. Antenna selection reduces the complexity of the radio devices and requires only a small amount of channel state feedback. For high signal-to-noise ratio (SNR), we define excess rate as the constant term in the expansion of the ergodic capacity in terms of SNR. It is shown that this value is representative of the channel state information (CSI) at the transmitter. The asymptotic behavior of the excess rate is then analyzed for three cases: complete CSI, no CSI, and partial CSI at transmitter (antenna selection). While water-filling provides a excess rate that increases logarithmically in M (the number of transmit antennas), the excess rate of transmit antenna selection behaves only like log(log M). For the low SNR case, we use the concept of channel gain, a measure introduced by Verdu. We show that channel gain for antenna selection increases only logarithmically in M as opposed to water-filling channel gain which increases linearly in M. The same techniques are also applied to the receive selection, and corresponding results are noted in high- and low-SNR regimes. The methodology developed in this correspondence, although motivated by antenna selection, is fairly general and can be used for any system where partial CSI is available at the MIMO transmitter.

Opportunistic scheduling provides attractive sum-rate capacities in a multiuser network when the base-station has transmit-side channel state information (CSI), which is often estimated at the mobiles and provided to the base station via a feedback channel. This correspondence investigates opportunistic methods in the presence of limited feedback. For flat Rayleigh-fading channels, strategies with only one-bit feedback per user are demonstrated that capture the double-logarithmic capacity growth (with number of users) of full-CSI systems. Furthermore, for a given system configuration, it is shown that if the one-bit feedback is chosen judiciously, there is little to be gained by increasing the feedback rate. Our results provide optimal methods of calculating the one-bit feedback, as well as expressions for the sum-rate capacity in the one-bit feedback regime. It is shown that one may achieve proportional fairness of scheduling in this regime with no loss of throughput. For OFDM multiuser systems, the motivation for limited feedback is even more pronounced. An extension of the one-bit technique is presented for subchannel/user selection under both correlated and uncorrelated subchannel conditions, and optimal growth in capacity is demonstrated.

The relay channel with private messages (RCPM) is a generalized relay channel model where in addition to the traditional communication from source to destination (assisted by relay), the source has a private message for the relay, and the relay has a private message for the destination. This paper develops coding strategies for this channel based on decode-and-forward and compress-and-forward schemes. Achievable rate regions as well as outer bounds on the capacity region are obtained for the discrete memoryless relay channel with private messages. Then, the Gaussian versions of this channel are studied and achievable rate regions are characterized. Numerical results are provided that give insights into the trade-offs between private messaging and relayed messaging in this hybrid three-node network.

This work analyzes the throughput of Go-Back-N (GBN) in block fading, a model frequently used for slow fading wireless channels. We devise hidden Markov models and block transition probabilities for the block fading channel, allowing us to calculate the throughput of GBN with reliable feedback, as well as unreliable feedback. The advantages of this approach include generality: it applies to two-state as well as multi-state models for forward and reverse channels. Also, the results for both reliable and unreliable feedback are expressed in terms of probability matrices, which can be used as convenient building blocks in the analysis and simulation of larger systems. Simulations verify our analysis.

We propose a new class of block codes that outperforms known space-time block codes at low rates. The new codes are designed by using appropriate rotations and set partitioning on two quasi-orthogonal codes, and combining subsets of their codewords. Using these techniques we are able to obtain higher coding gain at a given rate and improve performance. Simulations confirm the advantages of this code compared to other codes operating at the same rate and signal-to-noise ratio (SNR). We also provide an efficient maximum likelihood (ML) decoding algorithm for the new code

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. Thus, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). This work provides pairwise error probabilities for general space-time codes in keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. Also included is the proof of the intuitive result that the diversity under keyhole condition is min (M, N), where M and N are the number of transmit and receive antennas, with a slightly unexpected twist in the case of M=N.

This work investigates the following question: subject to strictly limited (finite-rate) feedback in a multi-user multi-antenna system, what channel state information (CSI) should we send back to the transmitter, and how should it be used? Considering the class of single-beam systems, we suggest a combination of beamforming (array gain) and multi-user diversity. It has been shown that in single antenna systems, one bit of feedback per user can capture almost all gains available due to multi-user diversity, therefore we propose and analyze a compound strategy that uses one bit for multi-user diversity and any further feedback bits for beamforming. We obtain the scaling laws of this compound strategy, showing that it scales as well as any single-beam system with full transmit-CSI.

In this paper we investigate the effect of asymmetric side information in discrete memoryless relay channels. The capacity of the degraded relay channel is known when side information at both the source and relay is identical. However, in many naturally interesting cases the source and relay may not have, or may not be able to exploit, exactly the same side information. This may occur either when side information is privileged information that is available only at one of the nodes (e.g. watermarking problems) or when the relay does not have the ability to collect or utilize full information about channel state and/or interference. In this paper we calculate capacity expressions for degraded discrete memoryless relay channels where the source and relay do not have identical side information. As a special case we consider the case where the relay has no side information. We consider causal as well as non-causal side information, and show an upper bound for the difference between capacities for various cases.

This paper introduces broadcasting relay nodes for orthogonal multiuser channels. The underlying idea is that a single relay node is shared by multiple source-destination pairs. In this scheme, the relay node receives the messages of multiple independent sources, and broadcasts a single superimposed signal to multiple destinations. Compared to dedicated relay scenarios, large gains in capacity region and outage capacity is possible with the shared relay scenario. We consider the special case of two pairs, and examine discrete memoryless channels and Gaussian channels assuming degradedness for the relay channels and physically degradedness for the broadcast channel. Upper bounds on capacity are obtained and shown to be achievable. The analysis is also extended to Rayleigh fading channels, where outage regions are investigated.

We introduce a relay channel with private messages, where three concurrent communication tasks take place: in addition to the traditional communication from source to destination (assisted by relay), the source has a private message for the relay, and the relay has a private message for the destination. We develop coding strategies for this channel based on decode-and- forward and compress-and-forward schemes. Achievable rate regions are obtained for the discrete memoryless and Gaussian versions of this channel. Our work generalizes some of the results obtained in the original relay channel introduced by Cover and El-Gamal and in the recent works on relay broadcast channels.

We propose a new class of block codes that outperforms known space-time block codes at low rates. The new codes are designed by starting with a quasiorthogonal structure, and then making certain modifications to increase the coding gain distance. By using appropriate rotations and set partitions for two quasi-orthogonal codes, and combining subsets of their codewords, we are able to obtain higher coding gain distance at a given rate, and thus improve performance. Simulations confirm the advantages of this code compared to other codes operating at the same rate and SNR. We also provide an efficient ML decoding algorithm for the new code.

This paper presents a method for increasing the coding gain of all varieties of space-time block codes (STBC), without using a trellis or introducing dependency between successive transmission blocks, using ideas from block-coded modulation (BCM). For a given STBC, we first increase the constellation size, then prune the codewords of the expanded codebook according to distance criteria, so that we arrive at the original transmission rate. We show that it is possible to improve the performance of a wide variety of space-time signalings, including orthogonal codes, quasi-orthogonal codes. An algorithm for the code design is presented. In the case of orthogonal codes, a decoding algorithm for the modified orthogonal codes is presented, showing that despite altering the regular structure of the orthogonal code, the complexity of decoding is only affected by a small constant. The same principle also applies to a wide variety of codes such as LD and TAST codes, whose design examples are under construction at the time of writing of this manuscript

Cooperative communication is an emerging paradigm where multiple mobiles share their resources (bandwidth and power) to achieve better overall performance. Coded cooperation is a mechanism where cooperation is combined with-and operates through-channel coding, as opposed to the repetition-based methods. This work develops expressions for outage probability of coded cooperation. In this work, each node acts as both a data source as well as a relay, i.e., only active (transmitting) nodes are available to assist other nodes, and each node operates under overall (source + relay) power and bandwidth constraints. Outage expressions confirm that full diversity is achieved by coded cooperation. This shows that despite superficial similarities, coded cooperation is distinct from decode-and-forward, which has been shown to have diversity one. The outage probability expressions developed in this work characterize coded performance at various rates. Furthermore, outage probabilities yield bounds that are arguably more insightful than the bit-error rate (BER) results previously available for coded cooperation. Numerical comparisons shed light on the relative merits of coded cooperation and various repetition-based methods, under various inter-user and uplink channel conditions.

Motivated by the recent works on the relay channel and cooperative diversity, this letter introduces coded cooperation, where cooperation is achieved through channel coding methods instead of a direct relay or repetition. Each codeword is partitioned into two subsets that are transmitted from the user's and partner's antennas, respectively. Coded cooperation achieves impressive gains compared to a non-cooperative system while maintaining the same information rate, transmit power, and bandwidth. We develop bounds on BER and FER and illustrate the advantage of coded cooperation under a number of different scenarios.

In this paper we analyze the performance of an important class of MIMO systems that of orthogonal space-time block codes concatenated with channel coding. This system configuration has an attractive combination of simplicity and performance. We study this system under spatially independent fading as well as correlated fading that may arise from the proximity of transmit or receive antennas or unfavorable scattering conditions. We consider the effects of time correlation and present a general analysis for the case where both spatial and temporal correlations exist in the system. We present simulation results for a variety of channel codes, including convolutional codes, turbo codes, trellis coded modulation (TCM), and multiple trellis coded modulation (MTCM), under quasi-static and block-fading Rayleigh as well as Rician fading. Simulations verify the validity of our analysis

It is well-known that diversity, despite being widely used as a design criterion, may not be enough to ensure good performance of a wireless system, because the diversity factor may "kick in" at unrealistically high values of SNR. This paper proposes a new class of layered space-time codes with a new design criterion that works well in moderate SNR's. Specifically, we propose to relax some of the constraints of threaded algebraic space-time (TAST) codes, leading to a class of codes with better error performance, which we call relaxed threaded space time (RTST) codes. We also propose a modified design criterion, the average union bound (AUB), which ensures good performance at medium SNR. For a 2 times 2 system operating at 6 b/s/Hz, improvements of more than 1.5 dB have been observed

This paper proposes a system using convolutional codes to mitigate error propagation in packet header compression. Convolutional codes are a class of forward error correction (FEC) codes, and their use is motivated because on uni-directional links loss of even one packet can render subsequent packets useless. A combination of two interleavers is used to address channel memory and increase the power of the code, and the optimum yet computationally efficient Viterbi algorithm is used for decoding at the receiver. Simulation results demonstrate the advantages of the proposed scheme.

We consider linear detectors for MIMO systems, i.e., multi-antenna systems where linear equalizers are employed to remove spatial interference. We analyze the behavior of linear equalizers through outage probability. The MMSE equalizer was found to behave in unexpected ways. Contrary to the usual intuition, the performance of MMSE and zero-forcing equalizers may not coincide at high-SNR. This is especially true at low spectral efficiencies, where the MMSE equalizer may achieve full spatial diversity.

At high SNR the capacity of a point-to point MIMO system with NTtransmit antenna and NRreceive antenna is min{NT, NR} log(SNR) + O(1). The factor in front of the log is called the multiplexing gain. In this paper we consider a network with 2N nodes (N source destination pairs) that each have only a single antenna. These single antenna nodes could cooperate to form larger virtual arrays, usually called cooperative diversity, user cooperation, or coded cooperation. The question we ask is: how large a multiplexing gain is possible. We prove that for N = 2 the multiplexing gain is 1, and consider generalizations to larger networks

The performance of space-time codes under channel correlation has been studied in detail recently, and a variety of results have been produced. In this work, we simplify some of the existing derivations as well as present some new results. One of the novel issues raised in this investigation is the loss of the uniform error probability (UEP) property of many codes in the presence of transmit side correlation. Also our error expressions for the general case of jointly spatio-temporally correlated Rayleigh and Rician fading are new, to the best of our knowledge. We also apply our analysis to some of the more recently developed codes for the MIMO channel, including the super-orthogonal codes and the linear dispersion codes.

We develop algorithms to efficiently build trellises for various full-rate MIMO codes. By full-rate, we refer to codes for multiple antenna systems whose rate scales with the minimum of the number of transmit and receive antennas, e.g., BLAST and the linear dispersion codes of Hassibi and Hochwald. This is in part inspired by the so-called super-orthogonal codes, which build efficient trellises on orthogonal block space-time codes (e.g. the Alamouti code). Unfortunately that approach cannot be directly transferred to a code with insufficient structure, because set partitioning over an irregular set, such as the one represented by an arbitrary space-time code, is not straightforward. The central contribution of this paper is an efficient set partitioning algorithm for an arbitrary set. We then built trellises for the resulting set partitions and demonstrate via simulations the gains obtained by such trellis codes.

Orthogonal space-time block codes (OSTBC) are among the most practical space-time codes due to their simplicity and optimal decoding. When information about the channel is available at the transmitter, the performance of OSTBC can be significantly improved by exploiting the array gain. However, providing full knowledge of channel state at the transmitter may not he affordable in many practical cases. Thus exploiting partial channel knowledge to improve the performance of OSTBC seems to be attractive. In this work we investigate the design of linear precoders with partial channel knowledge at the transmitter combined with an orthogonal space time code. We derive the condition for optimal precoder subject to a power constraint on the whole transmission block. We also propose a technique for precoder codebook design with limited feedback.

In a system with n users, the sum-rate capacity of the downlink channel grows as log log n, assuming optimal scheduling. However, optimal scheduling requires that the downlink channel state information (CSI) for all users be fully available at the base station. We show that the same capacity growth holds even if the feedback rate from the mobiles to the base station is reduced to one bit. We propose a simple scheduling method to achieve this multiuser capacity and, furthermore, we show that, by a judicious choice of the one-bit quantizer, not only the growth rate, but also most of the capacity of a fully informed system can be preserved.

Antenna spacing and the properties of a scattering environment can create correlation between channel coefficients. Temporal correlation between fading coefficients may also be present, because one may be unable or unwilling to fully interleave the channel symbols. This paper presents a comprehensive analysis of multiple-input multiple-output systems under correlated fading. We calculate pairwise-error-probability (PEP) expressions under quasi-static fading, fast fading, block fading, as well as arbitrarily temporally correlated fading, under Rayleigh and Rician conditions. We use the PEP expressions to calculate union bounds on the performance of trellis space-time codes, super orthogonal space-time codes, linear-dispersion codes, and diagonal algebraic space-time codes.

Cooperative communication has recently emerged as an effective form of signaling in wireless fading channels. This work examines cooperative communication in multi-user networks, where the geometry of information flow becomes an issue, i.e. who should cooperate with whom? In particular, one is interested in algorithms that do not require global network information, which is often unavailable due to latency, limited memory, or other constraints. In this work we propose and study distributed protocols for partner selection in cooperative networks. In this class of protocols, wireless users act individually and independently in establishing cooperative communication, without the aid of a central authority. Such a setup is especially of interest in ad-hoc networks, or networks of wireless sensors. We perform outage analysis for the proposed protocols, showing that full diversity in the number of cooperating users is achieved. The cooperative network with the proposed protocols performs significantly better than the non-cooperative counterpart.

Orthogonal space-time block codes (OSTBC) enjoy simple decoding, but have limited coding gain, if any. By concatenating OSTBC with an outer trellis, simple and powerful codes have been constructed, known as super-orthogonal codes or STB-TCM. In this work, we generalize these codes by exploring new code supersets, through mappings that do not induce any instantaneous modulation constellation expansion. By finding new mappings and establishing the properties of the resulting set partitions, we provide design guidelines for the labeling of the generalized code trellises. Simulations demonstrate significant coding gains resulting from our codes.

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. In cases that this condition is likely, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). In this work, we provide pairwise error probabilities for general space-time codes in the keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. We also prove the intuitive result that the diversity under the keyhole condition is min(M,N), with a slightly unexpected twist in the case of M=N.

Header compression saves bandwidth, but it also introduces error propagation whenever packets are lost. We propose to use error correcting codes on the compressed packet headers. The result is an overall system that maintains most of the bandwidth savings of header compression and yet is robust with respect to errors. The key to achieving this tradeoff is appropriate distribution of parity symbols across the packets. The proposed system performs better than ordinary header compression and as well as the TWICE algorithm. In most cases, the effects of the error propagation can be almost removed, such that the end-to-end packet loss rate is similar to a system with no header compression, while the bitrate savings are largely maintained.

Coded cooperation is a new framework recently proposed for cooperative communication. In this work, we present outage probability results for coded cooperation, and demonstrate that full diversity is achieved. In addition, we compare the outage behavior of coded cooperation with other repetition-based cooperative schemes.

In this work we investigate the asymptotic behavior of the capacity of transmit antenna selection, in the limit of large number of transmit antennas, under both low and high SNR regimes. Antenna selection provides a low-cost low complexity solution for MIMO systems.

In this paper we present a simple scheme for subchannel allocation in OFDM multiuser networks in the presence of limited feedback, in particular, when only one bit of information per subchannel is available at the base station. Our objective is to maximize the sum rate capacity of the network in the downlink transmission. We show that even with very limited feedback the sum rate capacity growth is the same as the fully informed transmission. We also extend this result to the case when subchannels are correlated.

Efficient compression of finite-alphabet sources requires variable-length codes (VLCs). However, in the presence of noisy channels, error propagation in the decoding of VLCs severely degrades performance. To address this problem, redundant entropy codes and iterative source-channel decoding have been suggested, but to date, neither performance bounds nor design criteria for the composite system have been available. We calculate performance bounds for the source-channel system by generalizing techniques originally developed for serial concatenated convolutional codes. Using this analysis, we demonstrate the role of a recursive structure for the inner code and the distance properties of the outer code. We use density evolution to study the convergence of our decoders. Finally, we pose the question: Under a fixed rate and complexity constraint, when should we use source-channel decoding (as opposed to separable decoding)? We offer answers in several specific cases. For our analysis and design rules, we use union bounds that are technically valid only above the cutoff rate, but interestingly, the codes designed with union-bound criteria perform well even in low signal-to-noise ratio regions, as shown by our simulations as well as previous works on concatenated codes.

We propose a general class of concatenated error-correcting entropy codes and channel codes. In this way we extend and generalize the existing body of work on iterative decoding of entropy and channel codes. Using the structure and properties of serial concatenated codes, we employ error-correcting entropy codes as the outer code, and a convolutional codes as the inner code. The generalization from entropy codes to redundant entropy codes allows powerful error correction similar to turbo codes. We provide upper bounds for the concatenated entropy code and channel code. We also show that iterative decoding of the proposed concatenated code outperforms iterative decoding of previously reported entropy and channel codes that operate at the same overall rate.

In a multi-user environment, coded cooperation creates transmit diversity for small mobiles (e.g. handsets) that cannot support more than one antenna. Coded cooperation allows these mobiles to share their antennas via a simple and effective coding method. In this work we present an analytical methodology for evaluating the performance of coded cooperation. We develop tight bounds for bit and block error capabilities, showing in the process that coded cooperation achieves maximal diversity. We demonstrate the validity of these bounds via simulations.

Motivated by error concealment applications, this letter proposes a method for the postprocessing of JPEG-2000 compressed images at very low bitrates. The proposed method counter-intuitively employs further compression to achieve image enhancement. This approach, although not widely known, is not entirely new: it is an adaptation of a technique originally designed for the removal of block-transform coding artifacts. The contribution of this work is to demonstrate its applicability to wavelet coders. In its simplest form, this algorithm uses existing system components with little or no additional hardware or software. Experimental results show a distinct reduction of ringing artifacts at very low bitrates.

Progressive image transmission is difficult in the presence of a noisy channel, mainly due to the propagation of errors during the decoding of a progressive bitstream. Excellent results for this problem are made possible through combined source-channel coding, a method that matches the channel code to the source operational rate distortion as well as channel conditions. This paper focuses on the key component of combined source-channel coding: rate allocation. We develop a parametric methodology for rate allocation in progressive source-channel coding. The key to this technique is an empirical model of decoded bit-error rate as a function of the channel code rate. We investigate several scenarios. In the case of the memoryless channel, we present closed-form expressions. For the fading channel and channels with feedback, where closed-form results are elusive, our analysis leads to low-complexity algorithms. The results presented are applicable to any progressive source code, and any family of channel codes.

Summary form only given. Forward error correction (FEC) based schemes are use widely to address the packet loss problem for Internet video. Given total available bandwidth, finding optimal bit allocation is very important in FEC-based video, because the FEC bit rate limits the rate available to compress video. We want to give proper protection to the source, but also prevent unwanted FEC rate expansion. The rate of packet headers is often ignored in allocating bit rate. We show that this packetization overhead has significant influence on system performance in many cases. Decreasing packet size increases the rate of packet headers, thus reducing the available rate for the source and its FEC codes. On the other hand, smaller packet size allows a larger number of packets, in which case it can be shown that the efficiency of FEC codes improves. We show that packet size should be optimized to balance the effect of packet headers and the efficiency of FEC codes. We develop a probabilistic framework for the solution of rate allocation problem in the presence of packet overhead. We implement our solution on the MPEG-4 fine granularity scalability (FGS) mode. To show the flexibility of our technique, we use an unequal error protection scheme with FGS. Experimental results show that our overhead-constrained method leads to significant improvements in reconstructed video quality.

The packet header is often ignored in the bit allocation problem of forward error correction (FEC) based packet video transmission schemes. In this paper, we show that the packet header has significant influence on the system performance. We balance the effect of the packet header and the efficiency of FEC codes via a probabilistic formulation. Optimal bit allocation is achieved in both nonscalable video and scalable video. Experiments show that the reconstructed video quality is improved significantly by our algorithm. Finally, we also study the effect of parameter mismatch on the performance of our algorithm.

Digital watermarking is equivalent to bandlimited, power-limited digital communication. The power limit is due to the requirement of imperceptible watermarks, and has long been recognized. The bandwidth limit is due to the lowpass spectrum of images and possible lowpass attacks (malicious or unintentional). This is related to the concept of channel capacity, and has only recently been addressed in the context of watermarking. To achieve high reliability without loss of watermark data rates, we propose an adaptation of trellis coded modulation (TCM). Our method is applicable to a wide class of watermarking algorithms. The objective is to maintain the data rate while improving reliability of watermark detection, in terms of bit error rates (BER). Alternatively, higher data rates can be achieved while maintaining watermark BER. We conduct experiments for blind as well as. informed detection. Simulation results show significant improvement compared to conventional methods over a wide-range of channel (attack) signal-to-noise ratios.

In progressive joint source-channel coding of images, experiments show that optimizing rate allocation according to PSNR criteria and according to rate criteria produce essentially similar results-a very important observation because optimization by rate is often much easier. This paper presents analysis to uncover the reason for-and the generality of-these empirical results. We first examine the typical shape of the distribution of PSNR in light of the distribution of the first uncorrectable error in the bitstream. Then we analyze the sensitivity of rate allocation to the operational R-D curve, via parametric modeling of the source and the channel. We demonstrate that rate allocation is locally insensitive to variations in the R-D characteristics. This analysis provides a justification for low-complexity rate allocation algorithms, such as the one by Chande and Farvardin (2000), that work independently of the operational R-D curve.

Mesh-based motion estimation-also known as control grid interpolation or warping-provides a smoother estimated intensity field compared to the traditional block-matching algorithm (BMA), resulting in most cases in a more realistic motion field and smaller estimation error. In mesh-based motion, unlike BMA, the computation of a motion vector is affected by its neighboring vectors. This interdependence necessitates a costly, iterative computation of motion vectors. The computational cost of mesh-based motion has been a main drawback of this otherwise powerful technique. We propose to use noniteratively computed motion vectors, such as BMA motion vectors, for node motions in the mesh model. However, we found that a straightforward insertion of BMA motion vectors in the deformable mesh leads to unpredictable and erratic results, and were thus motivated to carefully analyze the interaction of motion vectors and interpolation kernels in mesh models. This analysis leads to a methodology for computing optimal motion interpolation kernels for a given set of motion vectors (e.g., BMA motion vectors). We find a generalized orthogonality condition for these kernels; optimality is achieved only if the projections of vertex motions on the local intensity gradients are statistically orthogonal to mesh-based estimation errors. Experiments show that optimal kernels are often very different from the traditional bilinear kernels, and exhibit interesting variations. The new kernels benefit a variety of applications, including motion estimated interpolation, denoising, and compression.

Wavelet domain denoising has recently attracted much attention, mostly in conjunction with the coefficient-wise wavelet shrinkage proposed by Donoho (see IEEE Trans. Inform. Theory, vol.41, no.3, p.613-27, May 1995). While shrinkage is asymptotically minimax-optimal, in many image processing applications a mean-squares solution is preferable. Most MMSE solutions that have appeared so far are based on an uncorrelated signal model in the wavelet domain, resulting in scalar (pixel-wise) operations. However, the coefficient clustering often observed in the wavelet domain indicates that coefficients are not independent. Especially in the case of undecimated discrete wavelet transform (UDWT), both the signal and noise components are non-white, thus motivating a more powerful model. This paper proposes a simple yet powerful extension to the pixel-wise MMSE wavelet denoising. Using an exponential decay model for autocorrelations, we present a parametric solution for FIR Wiener filtering in the wavelet domain. This solution takes into account the colored nature of signal and noise in UDWT, and is adaptively trained via a simple context model. The resulting Wiener filter offers impressive denoising performance at modest computational complexity.

The undecimated discrete wavelet transform (UDWT) is a powerful image denoising tool, well-known to perform better than orthogonal wavelets. Unlike the case of orthogonal wavelets, noise as well as signal in the UDWT domain are non-white. Because of this inter-pixel correlation, scalar operations such as thresholding do not take full advantage of the power of UDWT. In this paper, we present a model for autocorrelations in the UDWT domain, and use it in a Wiener-type denoising algorithm. This algorithm accounts for colored signal and noise, and also aims to implicitly match the directional information due to the local edges in the image.

It is well known that Shannon's separation result does not hold under finite computation or finite delay constraints, thus joint source-channel coding is of great interest for practical reasons. For progressive source-channel coding systems, efficient codes have been proposed for feed forward channels [1] and the important problem of rate allocation between the source and channel codes has been solved [2]. For memoryless channels with feedback, the rate allocation problem was studied in [3]. In this paper, we consider the case of the fading channels with feedback. Feedback routes are provided in many existing standard wireless channels, making rate allocation with feedback a problem of considerable practical importance. We address the question of rate allocation between the source and channel codes in the forward channel, in the presence of feedback information and under a distortion cost function. We show that the presence of feedback shifts the optimal rate allocation point, resultin...

This paper presents a simple and effective post-processing method for compressed images. This work focuses on the cyclic time-variance introduced by block-based and subband transform coders. We propose an algorithm to (almost) restore stationarity to the cyclo-stationary output of the conventional transform coders. Despite a simple, non-iterative structure, this method outperforms other methods of image enhancement known to us, e.g. linear and nonlinear filtering, projection on convex sets (POCS), wavelet-based and optimization-based methods. In particular, the proposed method performs very well in suppressing both blocking and ringing artifacts. Furthermore, it admits a solution with successive approximation. The resulting embeddedness is very useful for multimedia applications such as image browsing on the World Wide Web.

Transmission of compressed image data over noisy channels is an important problem and has been investigated in a variety of scenarios. In this paper, we propose a progressive time-varying source-channel coding system for transmitting images over wireless channels. The core result of this paper is a systematic method of instantaneous rate allocation between the progressive source coder and channel coder. We develop closed form expressions for end-to-end distortion, as well as rate allocation, in memoryless channels. We extend the memoryless results to an algorithm for fading channels. Experimental results demonstrate the performance of this method.

A novel method is proposed for post-processing of JPEG-encoded images, in order to reduce coding artifacts and enhance visual quality. Our method simply re-applies JPEG to the shifted versions of the already-compressed image, and forms an average. This approach, despite its simplicity, offers better performance than other known methods, including those based on nonlinear filtering, POCS, and redundant wavelets.

This paper addresses the question of optimal subband decoding, given a system of subband analysis filters and a predetermined quantization strategy. Optimal analysis-synthesis pairs are of great interest, but have been characterized only under very strong (and impractical) conditions. Limiting our attention to the decoder, we find optimal synthesis filters by solving a system of regression equations. Neither high-rate quantization, whiteness of the quantization noise, nor optimality of the quantizer is assumed. Optimal coefficients are independent of the internal machinery of the quantizers, and can therefore be used with "canned" software packages. Only knowledge of the analysis filter bank is assumed. Preliminary experiments show modest gains, on the order of 0.1-0.3 dB, by applying this method to one-stage reproduction of natural images from zerotree quantizers.

Warping, also known as control grid interpolation, estimates intensities in the present frame through an interpolation of motion vectors-typically with bilinear interpolation. This paper presents a method for computing optimal interpolation parameters for warping prediction. Conventional bilinear warping, while mostly effective, has been known to exhibit unreliable performance in certain situations. Since both block-matching (BMA) and bilinear warping are candidate solutions for optimal warping, the performance of optimal warping is lower bounded by both bilinear warping and BMA, therefore vastly reducing the inconsistency problem. Furthermore, this optimality criterion is applicable to any category of motion vector, including that of block-matching. Thus we are able to demonstrate the optimal usage, under linear operations in the motion domain, of BMA motion vectors.

Presents a new interframe coding method for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using interframe redundancies for coding MR images have been unsuccessful. The authors believe that the main reason for this is twofold: unsuitable interframe estimation models and the thermal noise inherent in magnetic resonance imaging (MRI). The interframe model used here is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. The residue frames are quantized with a zero-tree wavelet coder, which includes arithmetic entropy coding. This particular method of quantization allows for progressive transmission, which aside from avoiding buffer control problems is very attractive in medical imaging applications.

The transmission and storage of digital video at reduced bit rates requires a source coding scheme, which generally contains motion compensated prediction as an essential part. The class of motion estimation algorithms known as backward methods have the advantage of dense motion field sampling, and in coding applications the decoder needs no motion information from the coder. In this paper, we first present an overview of operator based motion compensators with interpolative and non-interpolative kernels. We then proceed with two new results. The first offers a new perspective on the classical pel-recursive methods; one that exposes the weaknesses of traditional approaches and offers an explanation for the improved performance of operator-based algorithms. The second result introduces a minimum norm intra-frame operator and establishes an equivalence relationship between this and the original (least squares) operator. This equivalence induces interesting duality properties that, in addition to offering insights into operator-based motion estimators, can be used to relax either the maximum needed computational power or the frame buffer length.

Hierarchical decomposition of images and their relationship with motion fields continues to be a hotly pursued topic, and the role of backward motion information in coding is beginning to capture the interest of video coding community. This paper simultaneously addresses some of the fundamental issues in multi-resolution and backward motion systems. From a coding viewpoint, a multi-resolution motion hierarchy should be coupled with an estimation system that deals with a maximally subsampled wavelet decomposition of the frames, to avoid redundancy of representation. Given the known difficulties of band-to-band motion compensated estimation in a wavelet domain, we use an alternative approach for estimation of detail bands, using lowpass bands of the anchor frames at higher resolutions. The resulting estimation errors are coded through a zerotree quantizer. Simulations show that a prototype coder of this type is very competitive, with a performance better than conventional forward (block-based) coders.

Volumetric medical imaging data presents a special challenge in terms of storage and communication. Even the smallest sets of volumetric data are many times larger than most single medical images, and the onset of new applications that link data-sharing with video conferencing and multi-media make efficient and flexible coding of volumetric data an important task. Here the authors explore motion-like models for the coding of volumetric data. They first visit the affine interframe model, which was recently used to code MRI sequences effectively. Motivated by the encouraging results from the affine coder, the authors performed a comparative study of motion vs. 3-D spatial optimal autoregressive predictors. The results of this study indicate that motion analysis indeed leads to improved predictor performance in volumetric medical images, compared to the optimal 3-D predictor.

We present a new inter-frame coding for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using inter-frame redundancies for coding MR images have been unsuccessful. We contend that the main reason for this is twofold: bad inter-frame estimation models and ignoring the thermal noise inherent in MRI. Our inter-frame model is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. Simulations demonstrate the viability of this algorithm.>