Media-based modulation (MBM) is a novel technique for embedding information in the channel states via intentional perturbations of the transmission media. This article provides an overview of MBM and its benefits while highlighting relevant challenges and future research directions. We explain how MBM differs from source-based modulation and how it addresses issues in legacy multiple-input multiple-output (MIMO) systems, such as deep fades and MIMO diversity-multiplexing trade-off. We demonstrate how MBM works in harmony with other index modulations and improves upon them by providing similar advantages with a more compact transmitter. Numerical results (simulation and analytical) support these claims and include outage comparison with legacy MIMO systems, comparisons with other state-of-the-art modulation schemes, and a performance example showcasing transmitting 32 bits of information in a single channel use with an excellent symbol error rate of$\mathsf {SER} \simeq 10^{-5}$at “energy per bit to noise power spectral density ratio” of$\mathsf {E_{b}/N_{0}} \simeq -3.5$dB. The article continues with methods to address the issues of receiver training and decoding for large constellation sets. A number of other research questions, such as pulse shaping to limit bandwidth expansion due to the time-varying nature of MBM and the effect of forward error correcting codes on MBM diversity order are discussed. We present an RF transceiver structure that generates independent propagation paths for embedding information. Fabrication and testing of the transceiver structure show close agreement between simulation and measurement. There are inherent connections between MBM and Intelligent Reflecting Surface (IRS). These connections, including the application of MBM in beamforming, are discussed. We present a solution that involves the integration of a filtering radiating patch within the MBM walls to restrict bandwidth expansion. Lastly, we delve into several specific application domains for MBM.

5G, the fifth generation of mobile networks, promises new services, faster speeds, lower latency, and increased network capacity. A 5G network has three main elements: the Radio Access Network (RAN) which can be further divided into a hardware component, called software-defined radio (SDR), a software component, the core network and the User Equipment (UE). Recent years have seen the emergence of an “open” paradigm where the different elements of a 5G network are designed by different developers, and as a result can be separately modified and then integrated to enhance network functionality. This paper presents a framework to compare the impact of different elements on the performance of an end-to-end 5G standalone testbed. In particular, using open5GS as the core and 5G modems as the UE(s), we compare the performance of the recently released “O-RAN native suite, srsRAN-Project” to its srsRAN predecessor for two different SDRs (Ettus USRPs B210 and X410), over wireless and wired channels, in a single cell with one or two UEs. It is concluded that srsRAN-Project, with X410 as the SDR, provides the most stable and consistent performance over wired and wireless channels in both single-UE as well as multi-UE testbeds.

The idea of media-based modulation (MBM) [1] [2] is to embed information in the variations of the transmission media (channel states). Using a single traditional antenna surrounded by a closure with w radio frequency (RF) walls, MBM creates a set of 2wstates for the end-to-end channel, and the data is mapped into the index of these channel states. Each channel state results in an independent complex channel gain to each receive antenna, which specifies an MBM constellation point coordinate. In a rich scattering environment, MBM constellation points are independent of each other, with coordinates that follow an independent identically distributed (i.i.d.) complex Gaussian density. In a 1 ×K MBM, this property mimics the random code-book generation for signaling over K parallel additive white Gaussian noise (AWGN) channels. Accordingly, it is shown in [2] that the capacity of a 1 ×K MBM system with one unit of transmit energy and AWGN variance σ2over each receive antenna is equal to K times the capacity of an AWGN with a signal to noise ratio of snr = 1/σ2. The current article provides an alternative proof based on a novel formulation that reveals several interesting features of MBM. It is shown that the capacity in a 1×K MBM, as a random variable defined over the sample space of MBM constellation of cardinality M, follows a normal distribution with a mean of K log(1 + snr) and variance of (K/M)(snr/(1 + snr))2→ 0 as the M →∞. This entails, in contrast to legacy MIMO where the singularity of the channel matrix governs the outage probability, in MBM the outage is determined by the realized energy of the MBM constellation, and for any multiplexing gain r < K, the outage probability decreases exponentially fast as the number of points increases.

We consider the$K$-user Multiple Input Multiple Output (MIMO) Gaussian interference channel with$M$antennas at each transmitter and$N$antennas at each receiver. It is assumed that channel coefficients are constant real numbers and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the number of Degrees of Freedom (DoF) of this channel. Using the real interference alignment technique introduced in Motahariet al., 2014, we show that$\frac {MN}{M+N} K$degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the DoF of this channel is provided. This upper-bound coincides with our achievable DoF for$K\geq K_{u} \triangleq \frac {M+N}{\gcd (M,N)}$, where$\gcd (M,N)$denotes the greatest common divisor of$M$and$N$. This gives an exact characterization of DoF for$M\times N$MIMO Gaussian interference channel in the case of$K\geq K_{u}$. Since there is no cooperation between transmit (or receive) antennas of each user in our transmission scheme, this result shows that the DoF benefit of joint processing in collocated antennas vanishes when the number of users is greater than a certain threshold.

Most coding schemes proposed for the interference channel take advantage of joint decoding to enlarge rate region. However, decoding complexity escalates considerably when joint decoding is used. This paper studies the achievable sum-rate of the two-user Gaussian interference channel when joint decoding is replaced by successive decoding. First, the strong interference class is examined, and it is proved that if transmitters' powers satisfy certain conditions, successive decoding is optimal and achieves the sum-capacity. The number of the required splits, the amount of power allocated to each split, and the order of decoding at receivers are explicitly determined. Second, the weak interference class is examined. A novel rate-splitting scheme is proposed that does not use joint decoding. The number of required splits and the amount of power allocated to each split are expressed in closed forms. It is shown that, for a wide range of transmitters' powers, this scheme achieves the sum-rate of the Gaussian Han-Kobayashi scheme. Moreover, it is proved that the difference between the sum-rate of this scheme and that of the Gaussian Han-Kobayashi scheme is bounded, for all values of transmitters' powers.

The best-known achievable rate region for the two-user Gaussian interference channel corresponds to the Han-Kobayashi scheme. However, mathematical expressions that characterize the Han-Kobayashi rate region are complicated. This complexity hinders a comprehensive understanding of the rate region. For instance, when interference is weak, the maximum achievable sum-rate of the Han-Kobayashi scheme has been unknown. This paper studies the sum-rate of the Han-Kobayashi scheme with Gaussian inputs and fully characterizes the maximum achievable sum-rate, when no time sharing is used. The optimal power-splitting variables and the corresponding maximum achievable sum-rate are explicitly expressed in closed forms. With the same approach, the maximum weighted sum-rate is expressed that characterizes the boundary of the Han-Kobayashi region without time sharing. Moreover, when time sharing is used, the boundary is expressed in terms of the upper concave envelope of a function of transmitters' powers.

Delay, guaranteeing causality, is inevitable in cooperative communication systems. Traditionally, delay granularity has been limited to one symbol; however, channel delay is in fact governed by channel memory and can be shorter. For example, the delay requirement in orthogonal frequency-division multiplexing, captured in the cyclic prefix, is typically much shorter than the symbol itself. This perspective is used to study the two-user Gaussian interference channel with full-duplex transmitters. By superimposing the signal from the other node onto its own signal, each transmitter cancels the interference at its receiver. Among other results, it is proved that under a mild condition, the maximum multiplexing gain of this channel is in fact two, rather than the limit of one, previously shown under the traditional constraint of causal delay. Further, the optimal power allocation among orthogonal sub-carriers, which maximizes the achievable sum-rate, is shown to be a generalization of the well-known water filling. Simulation results are included to demonstrate the improvement in the achievable sum-rate when full-duplex transmitters are used.

Capacity bounds for the two-user interference channels with cooperative receivers via conferencing links of finite capacities are investigated. Capacity results known for these communication scenarios are limited to a very few special cases of the one-sided channels. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are established for the interference channels with conferencing receivers. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A fact is that a conferencing link (between receivers) may be utilized to provide one receiver with information about its corresponding signal or its non-corresponding signal (interference signal). As an interesting consequence, it is demonstrated that both strategies can be helpful to achieve capacity. Lastly, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse.

The idea of Media-based Modulation (MBM), introduced in [1] [2], is based on embedding information in the variations of the transmission media (channel states). MBM offers several advantages vs. legacy systems, including “additivity of information over multiple receive antennas”, and “inherent diversity over a static fading channel”. MBM is particularly suitable for transmitting high data rates using a single transmit and multiple receive antennas. However, complexity issues limit the amount of data that can be embedded in channel states using a single transmit unit. To address this shortcoming, the current article introduces the idea of Layered Multiple Input-Multiple Output Media-Based Modulation (LMIMO-MBM). LMIMO-MBM enables forming a high-rate constellation as superposition of constituent vectors due to separate transmit units. Relying on such a layered structure, LMIMO-MBM can significantly reduce both hardware and algorithmic complexities, as well as the training overhead. Simulation results show excellent performance in terms of Symbol Error Rate (SER) vs. Signal-to-Noise Ratio (SNR). For example, a 4 × 16 LMIMO-MBM is capable of transmitting 32 bits of information per (complex) channel-use, with SER 10-5at E /N0≃ -3.5dB (or SER 10-4at E/N0= -4.5dB). This performance is achieved using a single transmission (no extension in time/frequency), and without adding any redundancy for Forward-Error-Correction (FEC). Application of FEC can further improve the performance. For example, applying Reed-Solomon codes enables transmitting 30 bits of information per (complex) channel-use with a Frame Error Rate (FER) 10-5at E/N0≃ -6dB. Under a set of mild conditions, by applying FEC with error correction capability t, the slope of the error rate vs. SNR (with hard decision decoding) will asymptotically increase by a factor of t +1.

The best known achievable rate region for the two-user Gaussian interference channel is due to the Han-Kobayashi (HK) scheme. The HK achievable region includes the regions achieved by all other known schemes. However, mathematical expressions that characterize the HK region are complicated and involve a time sharing variable and two arbitrary power splitting variables. Accordingly, the boundary points of the HK region, and in particular the maximum HK sum-rate, are not known in general. This paper studies the sum-rate of the HK scheme with Gaussian inputs. For the weak interference class, this study fully characterizes the maximum achievable sum-rate and shows that the weak interference class is partitioned into five regions. For each region, the optimal power splitting and the corresponding maximum achievable sum-rate are expressed in closed forms. Moreover, we show that the same approach can be adopted to characterize all boundary points.

This paper presents an outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modeled as a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian code-books and maintain a statistical correlation ρ between the signals transmitted over the underlying sub-channels. When joint decoding (JD) is performed at the receivers, setting ρ = 0 minimizes the outage probability, regardless of the value of the signal-to-noise ratio (SNR). It is shown, however, that if the receivers treat interference as noise (TIN) or cancel interference (CI), the value of optimum ρ approaches 1 as SNR goes to infinity. Motivated by these observations, we let ρ = 0 under JD and ρ = 1 under TIN and CI and compute the outage probability in finite SNR, assuming that the direct and crossover channel coefficients are independent zero-mean complex Gaussian random variables with possibly different variances. In the asymptote of large SNR and assuming the transmission rate per user is r log snr, it is shown that the outage probability scales like snr-(1-r)under both TIN and CI, while it vanishes at least as fast as snr-min{2-r,4(1-r)}log snr under JD. This paper is concluded by extending some of the results to a two-user parallel Gaussian interference channel with an arbitrary number of sub-channels.

A sequence of lower and upper bounds is derived on the differential entropy of a Gaussian mixture where the Gaussian components only differ in mean values. As the sequence index increases, the computational complexity of the bounds increases; however, the gap between the lower and upper bounds becomes vanishingly small. We address the applications of these bounds in several communication scenarios where the transmitters utilize Pulse Amplitude Modulation (PAM) constellations to transmit data.

We address outage analysis for a two-user parallel Gaussian interference channel consisting of two sub-channels. Each sub-channel is modelled by a two-user Gaussian interference channel with quasi-static and flat fading. Both users employ single-layer Gaussian codebooks and maintain a statistical correlation ρ between the signals transmitted over the underlying sub-channels. If the receivers treat interference as noise (TIN) or cancel interference (CI), the value of ρ minimizing the outage probability approaches 1 as the signal-to-noise ratio (SNR) approaches infinity, while ρ = 0 is optimum under joint decoding (JD) regardless of the value of SNR. Motivated by these observations, we let ρ = 1 under TIN and CI and ρ = 0 under JD and compute the outage probability in finite SNR assuming the direct and crossover channel coefficients are independent zero-mean complex Gaussian random variables with possibly different variances. In the asymptote of large SNR and assuming the transmission rate per user is r log snr, we show that the outage probability scales as snr-(1-r)under both TIN and CI, while it vanishes at least as fast as snr-min{2-r;4(1-r)}log snr under JD.

The Gaussian K-user interference and M × K X channels are investigated with no instantaneous channel state information at transmitters (CSIT). First, it is assumed that the CSI is fed back to all nodes after a finite delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode, i.e, they can transmit and receive simultaneously. Achievable results on the degrees of freedom (DoFs) of these channels under the above assumption are obtained. It is observed that, in contrast with no CSIT and full CSIT models, when CSIT is delayed, the achievable DoFs for both channels with the full-duplex transmitter cooperation are greater than the available achievable results on their DoF without transmitter cooperation. Then, K-user interference and K × K X channels are considered with output feedback, wherein the channel output of each receiver is causally fed back to its corresponding transmitter. Our achievable results with output feedback demonstrate strict DoF improvements over those with the full-duplex delayed CSIT when K 5 in the K-user interference channel and K > 2 in the K × K X channel. Next, the combination of delayed CSIT and output feedback, known as Shannon feedback, is studied and strictly higher DoFs compared with the output feedback model are achieved in the K-user interference channel when K = 5 or K 6, and in the K × K X channel when K > 2.

This paper addresses the following question regarding Gaussian networks: Is there an alternative to decoding interference or treating interference as Gaussian noise? To state our result, we study a decentralized network of one primary user (PU) and one secondary user (SU) modeled by a two-user Gaussian interference channel. In one scenario, the primary transmitter is constellation-based and PUs codebook is constructed over its modulation signal set. Assuming SU is aware of the constellation points of PU, the interference plus noise at the secondary receiver is modeled by a mixed Gaussian process. We show that SU can achieve larger rates by matching its decoder to the actual interference plus noise compared with the case where the secondary receiver performs nearest neighbor decoding (NND). In another scenario, we assume that PU utilizes a predetermined point-to-point code. We ask if SU can utilize its knowledge about PUs codebook without decoding PUs codewords. The proposed strategy assumes each transmitted codeword of SU overlaps with infinitely many transmitted codewords of PU, referred to as the unequal codeword-length (UCL) strategy. The secondary receiver views PU as a virtual user that is constellation-based and its modulation signal set is the codebook of the actual PU. UCL is compared with other strategies, namely, interference cancellation (IC), joint decoding, and NND. It is shown that UCL can outperform both IC and NND simultaneously.

This paper studies a decentralized wireless network of asynchronous transmitter-receiver pairs with burst transmissions. Each receiver learns about the number of active users, channel coefficients, and mutual delays based on locally available measurements. The estimates for the mutual delays are not perfect, however, they are reliable enough to guarantee successful decoding. Two signalling schemes are addressed, namely, randomized masking (RM) and reduced cycle transmission (RCT). Under RM, the n symbols of a codeword are generated according to a Bernoulli-Gaussian distribution with activity factor 0 <; θ ≤ 1. This is in contrast to RCT where each codeword consists of ⌈θn⌉ Gaussian symbols followed by n-⌈θn⌉ zeros. Assuming the transmitters are unaware of the number of users, channel coefficients, and mutual delays, the probability of outage under RM is considerably lower compared with RCT if the signal-to-noise ratio (SNR) is sufficiently large. A generalized RCT scheme is also examined where the n - ⌈θn⌉ zero symbols are not necessarily located at the end of a codeword. In the asymptote of large SNR, the outage probability becomes vanishingly small under RM, however, it is bounded away from zero for generalized RCT regardless of the value of SNR.

The achievable region of parallel Gaussian interference channels is investigated. The known coding schemes proposed for the the two-user Gaussian interference channel are extended to parallel Gaussian interference channels. The optimality of separate coding for two coding schemes namely, time division with power control and treat as noise, is proved. Moreover, the necessity of joint coding for simultaneous non-unique decoding and Han-Kobayashi coding is demonstrated. For all mentioned schemes, the optimal covariance matrix is shown to be diagonal. In addition, the ergodic fading interference channel is studied. The ergodic achievable sum-rate is investigated for different coding schemes and the optimality of diagonal covariance matrices is shown. It is proved that for time division with power control and simultaneous non-unique decoding, uniform power allocation over all sub-channels is sum-rate optimal.

This paper addresses a hybrid setup for cognitive radio based on Gaussian interference channel where the secondary user can use both interweave and underlay strategies. The primary user does not cooperate or adapt since it is using legacy hardware. We show that these assumptions lead to a non-convex achievable rate region for various types of hybrid interweave-underlay strategies and that the rate optimization problem for the secondary user is in general non-convex and non-smooth. We analyze the structure of this optimization problem to reduce it to a number of tractable subproblems in various interference regimes. Numerical simulations are also presented to give insight into the performance of the proposed schemes.

It is shown in [1] that embedding information in the (intentional) variation of the transmission media (end-to-end channel) can offer significant gains vs. traditional SISO, SIMO and MIMO systems. In particular, it is shown that using a single transmit antenna and K receive antennas; significant savings in energy vs. a K×K MIMO can be achieved [1]. This article proves that, a 1 × K media-based modulation over a static multi-path channel asymptotically achieves the capacity of K parallel AWGN channels, where for each unit of energy over the single transmit antenna, the effective energy for each of the K AWGN channels is the statistical average of channel fading. The rate of convergence is computed. Significant gains can be realized even in a SISO media-based setup. An example for the practical construction of the system and its realistic RF simulation are presented. Issues of equalization and selection gain are discussed.

The diamond channel is a dual-hop communication system composed of a source, and a destination connected through two noninterfering relays. Operating in the half-duplex mode, relays are not capable of simultaneous transmission and reception of signals. This paper studies coding and scheduling schemes achieving within constant gap from the maximum achievable rate possible assuming the scheduling is fixed for all messages and known to all nodes prior to transmission. It is shown that under constant power constraints, a simple transmission scheme for relays is within 0.71 bits of the optimum rate. It is also demonstrated that the proposed scheme can attain the optimum rate, when channels satisfy a certain property. Furthermore, it is proved that under average power constraints, the same scheme can be used to achieve within 3.6 bits of the optimum rate.

This paper addresses a two-user Gaussian multiple access channel (MAC) under peak power constraints at the transmitters. It is shown that generating the code-books of both users according to discrete distributions with a finite number of mass points achieves the largest weighted sum-rate in the network. This verifies that any point on the boundary of the capacity region of a two-user MAC under peak power constraints at both transmitters is achieved by discrete distributions with a finite number of mass points. Although the capacity-achieving distributions are not necessarily unique, it is verified that only discrete distributions with a finite number of mass points can achieve a point on the boundary of the capacity region. It is shown that there exist an infinite number of sum-rate-optimal points on the boundary of the capacity region. In contrast to the Gaussian MAC with average power constraints, we verify that time division (TD) cannot achieve any of the sum-rate-optimal points in the Gaussian MAC with peak power constraints. Using the so-called I-MMSE identity of Guo et al., the largest achievable sum-rate by orthogonal code division (OCD) is characterized where it is shown that Walsh-Hadamard spreading codes of length 2 are optimal. In the symmetric case where the peak power constraints at both transmitters are identical, we verify that OCD can achieve a sum-rate that is strictly larger than the highest sum-rate achieved by TD. Finally, it is demonstrated that there are values for the maximum peak power at the transmitters such that OCD can not achieve any of the sum-rate-optimal points on the boundary of the capacity region.

This paper addresses a decentralized wireless networks of K separate transmitter-receiver pairs. Users treat each other as noise and there is no central controller to assign the resources to the users. Each user randomly spreads the symbols in its Gaussian codewords by the so-called signatures of spreading gain N. Any receiver is aware of the signatures of its affiliated transmitter, however, it is unaware of the signatures of other users. This makes the interference plus noise at each receiver be mixed Gaussian, and hence, there is no closed expression for the achievable rates of users. Invoking conditional entropy power inequality and a key upper bound on the differential entropy of a mixed Gaussian random vector, we develop a lower bound on the achievable rates of users. This lower bound has the same signal-to-noise ratio (SNR) scaling as that of the exact achievable rate. It is shown that the sum multiplexing gain (SMG) in the network can be made arbitrarily close to (K/N) for any finite values of K and N where K ≤ N. The effect of matched filtering is studied in the particular case where the signatures are constructed over a binary alphabet. It is established that the SMG of the network is larger than (1/2e) regardless of the value of K as long as N = 2 and the signatures are generated according to a proper nonuniform distribution. This paper is concluded by a section on signature design in the finite SNR regime. The main observation is that for any two different methods A and B of designing the signatures, if method A results in a larger achievable rate per user for sufficiently large SNR values, then construction B is likely to yield larger achievable rates for sufficiently small values of SNR. This behavior is attributed to the interplay between two critical factors, namely, the multiplexing gain per user and what we refer to as the interference entropy factor.

In this paper, we develop the machinery of real interference alignment. This machinery is extremely powerful in achieving the sum degrees of freedom (DoF) of single antenna systems. The scheme of real interference alignment is based on designing single-layer and multilayer constellations used for modulating information messages at the transmitters. We show that constellations can be aligned in a similar fashion as that of vectors in multiple antenna systems and space can be broken up into fractional dimensions. The performance analysis of the signaling scheme makes use of a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on nondegenerate manifolds. Using real interference alignment, we obtain the sum DoF of two model channels, namely the Gaussian interference channel (IC) and the X channel. It is proved that the sum DoF of the K-user IC is (K/2) for almost all channel parameters. We also prove that the sum DoF of the X-channel with K transmitters and M receivers is (K M/K + M - 1) for almost all channel parameters.

The problem of dual-hop transmission from a source to a destination via two parallel full-duplex relays in block Rayleigh fading environment is investigated. All nodes in the network are assumed to be oblivious to their forward channel gains; however, they have perfect information about their backward channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. The focus of this paper is on simple, efficient, and practical relaying schemes to increase the expected-rate at the destination. For this purpose, various combinations of relaying protocols and the broadcast approach (multi-layer coding) are proposed. For the decode-forward (DF) relaying, the maximum finite-layer expected-rate as well as two upper-bounds on the continuous-layer expected-rate are obtained. The main feature of the proposed DF scheme is that the layers being decoded at both relays are added coherently at the destination although each relay has no information about the number of layers being successfully decoded by the other relay. It is proved that the optimal coding scheme is transmitting uncorrelated signals via the relays. Next, the maximum expected-rate of ON/OFF based amplify-forward (AF) relaying is analytically derived. For further performance improvement, a hybrid decode-amplify-forward (DAF) relaying strategy, adopting the broadcast approach at the source and relays, is proposed and its maximum throughput and maximum finite-layer expected-rate are presented. Moreover, the maximum throughput and maximum expected-rate in the compress-forward (CF) relaying adopting the broadcast approach, using optimal quantizers and Wyner-Ziv compression at the relays, are fully derived. All theoretical results are illustrated by numerical simulations. As it turns out from the results, when the ratio of the relay power to the source power is high, the CF relaying outperforms DAF (and hence outperforms both DF and AF relaying); otherwise, DAF scheme is superior.

It is well-known that the so-called Shannon Achievable Region (SAR) in a collocated two-user Gaussian Two-Way Channel (GTWC) does not depend on the self-interference that is due to the leakage of the signal transmitted by each user at its own receiver. This is simply because each user can completely remove its self-interference. In this paper, we study a class of GTWCs where each user is unable to cancel the self interference due to random erasures at its receiver. The mixture of the intended signal for each user and its self-interference is erased independently from transmission slot to transmission slot. It is assumed that both users adopt PAM constellations for transmission purposes. Due to the fact that both users are unaware of the erasure pattern, the noise plus interference at each user is mixed Gaussian. To analyze this setup, a sequence of upper and lower bounds are developed on the differential entropy of a general mixed Gaussian random variable where it is shown that the upper and lower bounds meet as the sequence index increases. Utilizing such bounds, it is shown that the achievable rate for each user is monotonically increasing in terms of the level of self-interference and eventually saturates as self-interference grows to infinity. This saturation effect is justified analytically by showing that as self-interference increases, each user is enabled to extract the erasure pattern at its receiver. Treating the erasure pattern as side information, both users are able to cancel self-interference and decode the useful information at higher transmission rates.

It is shown that embedding part or all of the information in the (intentional) variations of the transmission media (end-to-end channel) can offer significant performance gains vs. traditional SISO, SIMO and MIMO systems, at the same time with a lower complexity. This is in contrast with the traditional wireless systems where the information is entirely embedded in the variations of an RF source prior to the antenna to propagate via the channel to the destination. In particular, it is shown that using a single transmit antenna and D receive antennas; significant savings in energy with respect to a D×D traditional MIMO are achieved. Similar energy savings are possible in SISO, and SIMO setups.

A point-to-point communication system with an AWGN channel is considered. It is assumed that data randomly arrive at the system and the transmitter has a finite buffer. Supposing that, to save energy, the transmitter is able to adapt the rate depending on the number of bits existing in the buffer, the stationary probability distribution of the number of bits in the buffer is obtained and an approximate relation for the average of saving in energy is found.

This paper is a follow up to [1] on the two-user Gaussian Multiple Access Channel (MAC) with peak constraints at the transmitters. It is shown that there exist an infinite number of sum-rate-optimal points on the boundary of the capacity region. In contrast to the Gaussian MAC with power constraints, we verify that Time Division (TD) can not achieve any of the sum-rate-optimal points in the Gaussian MAC with peak constraints. Using the so-called I-MMSE identity of Guo et.al, the largest achievable sum-rate by Orthogonal Code Division (OCD) is characterized where it is shown that Walsh-Hadamard spreading codes of length 2 are optimal. In the symmetric case where the peak constraints at both transmitters are similar, we verify that OCD can achieve a sum-rate that is strictly larger than the highest sum-rate achieved by TD. Finally, it is demonstrated that there are values for the maximum peak at the transmitters such that OCD can not achieve any of the sum-rate-optimal points on the boundary of the capacity region.

This paper addresses the problem of decoding and precoding in the K-user MIMO interference channels. At the receiver side, a joint decoding of the interference and the desired signal is able to improve the receive diversity order. At the transmitter side, we introduce a joint linear precoding design that maximizes the joint cut-off rate, known as a tight lower bound on the joint mutual information for high signal-to-noise ratio (SNR). We also derive a closed-form solution of the precoding matrices that maximizes the mutual information when the SNR is close to zero. This solution is characterized by its low computational complexity, and only requires a local channel state information knowledge at the transmitters. Our simulation results show that decoding interference jointly with the desired signal results in a significant improvement of the receive diversity order. Also a substantial bit error rate and sum-rate improvements are illustrated using the proposed precoding designs.

A decentralized network of one Primary User (PU) and several Secondary Users (SU) is studied. PU is licensed to exploit the resources, while the party of SUs intend to share the resources with PU. Each SU must guarantee to not disturb the performance of PU beyond a certain level, while maintaining a satisfactory quality of service for itself. It is proposed that each secondary transmitter adopts a Randomized Masking (RM) strategy with full average transmission power where it remains silent or transmits a symbol in its codeword independently from transmission slot to transmission slot. We consider a setup where the primary transmitter is unaware of channel coefficients, code-books of secondary users and the number of secondary users. SUs are anonymous to each other, i.e, they are unaware of each others' code-books, however, each SU is smart in the sense that it is aware of the code-book of PU, channel coefficients and the number of active SUs. Invoking the concept of ε-outage capacity, we define the (ε,ν)-admissible region as the set of masking probabilities for each SU such that the probability of outage for PU is maintained under a threshold \varepsilon in a case where PU sets its transmission rate at a fraction ν of its ε-outage capacity as if there were no SUs in the network. The masking probability of SUs is designed through maximizing the average (with respect to channel coefficients) achievable rate per SU over the (ε,ν)-admissible region. In our analysis, the primary receiver treats interference as noise, however, each secondary receiver has the option to decode and cancel the interference caused by PU, while treating the signals of other SUs as noise. In another approach, referred to as Continuous Transmission with Power Control (CTPC), each SU transmits continuously (no masking is applied), however, it adjusts its transmission power in order to yield the largest value for average achievable rate per SU. The schemes RM and CTPC are compared for different values of transmission power for each SU and PU and distance between different users. It is observed that neither of RM or CTPC always outperforms the other in various scenarios in terms of the underlying system parameters. A combination of RM and CTPC referred to as Randomized Masking with Power Control (RMPC) is also investigated where each SU controls both its probability of masking and average transmission power. It is demonstrated through simulations that RMPC can outperform both RM and CTPC.

A number of recent source coding techniques compress the source signal into multiple layers such that a destination is able to reconstruct the original signal (with some distortion) even if it has not received all the layers. Implementation of such source coding techniques in wireless networks requires the application of coding mechanisms (such as multilayer coding) which allow unequal error protection for different layers of the transmitted data. In this paper, we study the performance of multilayer coding for quasi-static fading channels where the source and the destination are equipped with multiple antennas and the Channel-State-Information (CSI) is only known at the destination. We limit the study to the scenarios where the destination is only able to perform successive-decoding (joint-decoding is not possible) and the objective is to find the design of a multilayer code which maximizes the average data rate received at the destination. To this end, we first propose a design rule for constructing a proper multilayer code for Multiple-Input-Multiple-Output (MIMO) networks. Furthermore, the paper presents a procedure which uses the proposed design rule to determine the parameters of the multilayer code. The performance of the designed multilayer coding scheme is then studied for different network setups.

A distributed random access network with K users and one Access Point (AP) is considered. It is assumed that users and the AP are equipped with M and N antennas, respectively. Each user independently decides whether to transmit in a time slot or not. We initially focus on two-user random access networks and characterize the network average Degrees of Freedom (DoF)1. For the K-user networks, an upper-bound on the network average DoF is first proposed. Then, it is shown that the proposed upper-bound can be achieved using single stream data transmission for many network configurations. Finally, we show through a few examples that there exist some network configurations where multi-stream data transmission in conjunction with interference alignment is necessary in order to achieve the upper-bound.

The K-user single-input single-output (SISO) additive white Gaussian noise (AWGN) interference channel and 2×K SISO AWGN X channel are considered, where the transmitters have delayed channel state information (CSI) through noiseless feedback links. Multiphase transmission schemes are proposed for both channels which possess novel ingredients, namely, multiphase partial interference nulling, distributed interference management via user scheduling, and distributed higher order symbol generation. The achieved degree-of-freedom (DoF) values are greater than the best previously known DoFs for both channels with delayed CSI at the transmitters.

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian multiple-input multiple-output (MIMO) broadcast channel. An eavesdropper also receives the transmitted signal via another MIMO channel. We first consider the discrete memoryless channel and obtain the capacity region of the degraded channel. The secret dirty paper coding (SDPC) region as an achievable rate region for the general discrete channel is introduced. Relying on the results for the discrete channel, we fully characterize the secrecy capacity region of MIMO broadcast channel. It is shown that the SDPC scheme is optimal. The converse part of the proof relies on the generalized Costa's entropy power inequality and a new channel enhancement strategy in which we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.

This paper investigates the benefits of amplify-and-forward (AF) relaying in the setup of multiantenna wireless networks. For this purpose, random sequential (RS) relaying is studied. It is shown that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better diversity-multiplexing tradeoff (DMT) as compared to the traditional AF relaying. First, the RS scheme is proved to achieve the optimum DMT for a multiantenna full-duplex single-relay two-hop network. Applying this result, a new achievable DMT is derived for the case of multiantenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multiantenna two parallel noninterfering half-duplex relays. Furthermore, random unitary matrix multiplication is shown to also improve the DMT of the nonorthogonal AF relaying scheme for the case of a multiantenna single relay channel. Finally, the general case of multiantenna full-duplex relay networks is studied. First, a new lower-bound is derived on its DMT using the RS scheme. Furthermore, maximum multiplexing gain of the network is also shown to be achievable by traditional amplify-forward relaying. The gain value is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes.

The Gaussian single-input single-output (SISO) K-user interference and M × K X channels are investigated in i.i.d. fading environment with no instantaneous channel state information (CSI) at transmitters. First, it is assumed that the CSI is fed back to all nodes after some delay (delayed CSIT), and furthermore, the transmitters operate in full-duplex mode. Achievable results on the degrees of freedom (DoF) of these channels under the above assumption are obtained. Then, achievable DoFs are obtained for the K-user interference and K × K X channels with output feedback and also Shannon feedback, which is a combination of output feedback and delayed CSIT, and compared with the achievable DoFs under the full-duplex delayed CSIT assumption.

The multiple-input multiple-output (MIMO) Gaussian X channel in i.i.d. fading environment and with delayed channel state information at transmitters (delayed CSIT) is considered. It is assumed that each transmitter has M antennas and each receiver has N antennas. New achievable results on the sum degrees of freedom (DoF) of this channel are provided and shown to be tight for all possible values of M and N except for 1/2 <; N/M <; 4/3. It is noteworthy that for certain values of M and N, the channel DoF coincides with the DoF of the broadcast channel obtained by assuming perfect transmitter cooperation.

We study a 2-user symmetric X channel with random access capability for transmitters from a deterministic point of view. Transmitters can work in two modes of operation independent of each other, either active or inactive. There is an independent message from each transmitter to each receiver. It is aimed in this study at maximizing the throughput of this network over the set of rates which can be reliably communicated. To characterize this rate region, an information theoretic outer-bound is derived. Achievability is based on opportunistic signal transmission along with a linear pre-coding scheme. Once the rate region is exactly determined, throughput maximization can be solved as a linear programming problem.

This paper addresses a two-user Gaussian Multiple Access Channel (MAC) under peak constraints at the transmitters. It is shown that generating the code-books of both users according to discrete distributions achieves the largest sum-rate in the network. In other words, sum-capacity achieving input distributions for this channel are discrete with a finite number of mass points. We also demonstrate uniqueness of the input distributions which achieve rates at any of the corner points of the capacity region of the channel.

A random access interference channel in which transmitters are active with a certain probability is considered. By adopting the deterministic channel model, the optimum transmission strategy which yields the maximum achievable expected sum-rate, or channel throughput, is characterized for the symmetric case. The optimal transmission strategy achieves the sum-capacity of the deterministic interference channel when both users are active, and opportunistically increases the expected sum-rate when transmitters may not always be active.

This paper studies the problem of dual-hop transmission from a source to a destination via two parallel full-duplex relays in block Rayleigh fading environment. All nodes in the network are assumed to be oblivious to their forward-channel gains, however, they have perfect information about their backward-channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. Hence, we adopt the broadcast approach to increase the expected-rate received at the destination. The focus of this paper is on simple, efficient, and practical relaying schemes to increase the average achievable rate at the destination. The maximum expected-rate of ON/OFF based amplify-forward relaying is analytically derived. For further performance improvement, a hybrid decode-amplify-forward relaying strategy, adopting the broadcast approach at the source and relays, is proposed and its maximum throughput and expected-rate are presented. Finally, two different upper-bounds, based on the full cooperation between the relays, are obtained. All theoretical results are illustrated by numerical simulations. As it turns out from the numerical results, when the ratio of the relay power to the source power is low, the proposed hybrid decode-amplify-forward relaying scheme meets the obtained upper-bound.

The point-to-point multiple-input single-output (MISO) channel is investigated in uncorrelated block fading environment with Rayleigh distribution. The maximum throughput and maximum expected-rate of this channel are obtained under the assumption that the transmitter is oblivious to the channel state information (CSI), however, the receiver has perfect CSI. First, we prove that the optimum transmission strategy maximizing the throughput is to use all available antennas and perform equal power allocation with uncorrelated signals. Furthermore, to increase the expected-rate, multi-layer coding is applied. Analogously, we establish that sending uncorrelated signals and performing equal power allocation across all available antennas at each layer is optimum. Finally, a closed form expression for the maximum continuous-layer expected-rate of MISO channels is also obtained.

This paper deals with the delay-throughput analysis of a single-hop wireless network with n transmitter/receiver pairs. All channels are assumed to be block Rayleigh fading with shadowing, described by parameters (α, ω̅), where α denotes the probability of shadowing and ω̅ represents the average cross-link gains. The analysis relies on the distributed on-off power allocation strategy (i.e., links with a direct channel gain above a certain threshold transmit at full power and the rest remain silent) for the deterministic and stochastic packet arrival processes. It is also assumed that each transmitter has a buffer size of one packet and dropping occurs once a packet arrives in the buffer while the previous packet has not been served. In the first part of the paper, we define a new notion of performance in the network, called effective throughput, which captures the effect of arrival process in the network throughput, and maximize it for different cases of packet arrival process. It is proved that the effective throughput of the network asymptotically scales as (log n)/α̂, with α̂=△ αω̅, regardless of the packet arrival process. In the second part of the paper, we present the delay characteristics of the underlying network in terms of the packet dropping probability. We derive the sufficient conditions in the asymptotic case of n → ∞ such that the packet dropping probability tend to zero, while achieving the maximum effective throughput of the network. Finally, we study the trade-off between the effective throughput, delay, and packet dropping probability of the network for different packet arrival processes. In particular, we determine how much degradation will be enforced in the throughput by introducing the aforementioned constraints.

In this paper, we consider a downlink communication system in which a base station (BS) equipped with M antennas and power constraint P communicates with N users each equipped with K receive antennas. It is assumed that the users have perfect channel state information (CSI) of their own channels, while the BS only knows the partial CSI provided by the receivers via a feedback channel. We study the fundamental limits on the amount of feedback required at the BS to achieve the sum-rate capacity of the system (when BS has perfect CSI for all users) in the asymptotic case of N →∞, considering various signal to noise ratio (SNR) regimes. The main results of this paper can be expressed as follows. 1) In the fixed-SNR regime (where the SNR does not scale with N) and low-SNR regime (where the SNR is much smaller than 1/In(N) ), to achieve the (1 - ε)-portion of the sum-rate capacity, the total amount of feedback should scale at least with (ε-1). In the fixed-SNR regime, to reduce the gap between the achievable sum rate and the sum-rate capacity of the system (which is defined as the sum-rate gap) to zero, the amount of feedback should scale at least logarithmically with the sum-rate capacity, which is achievable by using the random beam-forming (RBF) scheme proposed by Sharif and Hassibi. In the low-SNR regime, we propose an opportunistic beam-forming (OBF) scheme, which is shown to be asymptotically feedback optimal. 2) In the high-SNR regime (where the SNR grows to infinity as N → ∞), the total amount of feedback depends on the number of receive antennas. In particular, to reduce the sum-rate gap to zero in the case of K; 1/M - 1, should scale at least logarithmically with the SNR. In the case of K ≥ M , the amount of feedback does not need to scale with the SNR. Moreover, we show that RBF is asymptotically feedback optimal in the high-SNR regime.

In this paper, the optimum tradeoff between diversity and multiplexing gains in a two-user quasi-static Rayleigh fading interference channel (IC) is studied. The diversity and multiplexing gains are two basic performance measures in wireless networks which characterize the transmission reliability and the data rate, respectively. It would be of interest to investigate the optimal tradeoff between these two measures. First, we develop a coding scheme for the two-user quasi-static Rayleigh fading Gaussian IC with interference level α := log INR/log SNR ≥ 1. Then, for this coding scheme the achievable diversity-multiplexing tradeoff (DMT) is characterized. Our achievable DMT coincides with its outer bound. In the low and high rate regions (to be defined later), the proposed coding scheme is a one-level Gaussian code, independent of the channel state information (CSI). In the middle rate region (to be defined later), the proposed coding scheme, depending on the partial CSI, can be a one-level or a two-level Gaussian code. We show that the relevant partial CSI can be represented by only one bit determined by the absolute value of the channel gain. In the middle rate region, we assume that the single-bit partial CSI for all the four channel gains of the Gaussian IC are available at both transmitters.

For a multicast network, in which a common source is transmitted to$N$users, the problem of maximizing the average rate subject to a coverage constraint (minimum quality of service) is studied. Considering such a network with single-antenna nodes and assuming that the channel state information is available only at the receiver side, the highest expected rate achievable by a random user in the network, called the expected typical rate, is derived in two scenarios: hard coverage constraint and soft coverage constraint. In the first case, the coverage is expressed in terms of the outage probability, while in the second case, the expected rate should satisfy a certain minimum requirement. It is shown that the optimum solution (achieving the highest expected typical rate for given coverage requirements) in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived. The analysis is extended to a scenario with multiple transmit antennas. For the MISO case, a suboptimal coding scheme is proposed, which is shown to be asymptotically optimal, when the number of transmit antennas grows at least logarithmically with the number of users in the network.

This paper considers a two-hop network in which information is transmitted from a source via a relay to a destination. It is assumed that channels are quasi-static fading with additive white Gaussian noise and that all nodes are equipped with a single antenna. The channel state information (CSI) of each hop is available only at the corresponding receiver and relay is not capable of data buffering over multiple coding blocks. One commonly used design criterion in such configurations is the maximization of the average received rate at the destination. Considering infinite-layer coding at both the source and the relay, in conjunction with decode and forward strategy at the relay, we present a procedure to optimally distribute the available source and relay powers to different layers of their corresponding codes. Next, we demonstrate how this transmission technique can be generalized to a multihop setting. Assuming Rayleigh fading, the performance of the proposed coding scheme is evaluated for a two-hop network and compared with the performance of previously known strategies.

In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously known coding schemes, achieves the optimal scaling of the source signal-to-distortion ratio (SDR) versus channel signal-to-noise ratio (SNR). Also, we propose a family of robust codes, which together maintain a bounded gap with the optimum SDR curve (in terms of decibel). To show the importance of this result, we derive some theoretical bounds on the asymptotic performance of a widely used class of delay-limited hybrid digital-analog (HDA) coding schemes based on superposition of analog and digital components. We show that, unlike the delay-unlimited case, for this class of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of decibels). Although the main focus of this paper is on uniform sources, it is also shown that the results are also valid for a more general class of well-behaved distributions.

We investigate the three-user MIMO Gaussian broadcast channel with i.i.d. fading and the same number of antennas at each receiver, and with the delayed channel state information at the transmitter (CSIT). We obtain achievability results on the degrees of freedom (DoF) of this channel and also show that our achievable DoF is tight for some ranges of transmit-receive antenna ratio. It is observed that when the number of antennas at the transmitter is strictly greater than that at each receiver, the DoF with delayed CSIT lies strictly between the DoF with perfect CSIT and DoF with no CSIT.

We consider the X channel and the 3-user X network with independent and identically distributed fading across antennas and channel uses and with the delayed channel state information at the transmitters (CSIT). We provide new results for degrees of freedom of these channels. Specifically, we show that the single antenna X channel with delayed CSIT can achieve 6/5 degrees of freedom while the 3-user X network can achieve 5/4 degrees of freedom.

This paper addresses the following question regarding Gaussian networks: Is there an alternative to decoding interference or treating interference as Gaussian noise? By answering this question we aim to establish a benchmark for practical systems where multiuser decoding is not a common practice. To state our result, we study a decentralized network of one Primary User (PU) and one Secondary User (SU) modeled by a two-user Gaussian interference channel. The primary transmitter is constellation-based, i.e., PU is equipped with a modulator and its code-book is constructed over a modulation signal set. SU utilizes random Gaussian codewords with controlled transmission power that guarantees a certain level of Interference-to-Noise Ratio (INR) at the primary receiver. Both users are unaware of each other's code-book, however, SU is smart in the sense that it is aware of the constellation set of PU. While interference at the primary receiver is modeled as additive Gaussian noise, the secondary receiver can utilize the structure of PU's modulator as side information to decode its message without decoding the message of PU. The instantaneous realizations of symbols in a codeword transmitted by PU are unknown to both ends of SU's direct link, however, the sample space of such symbols is available to SU. This makes the interference plus noise at the secondary receiver be a mixed Gaussian process. Invoking entropy power inequality and an upper bound on the differential entropy of a mixed Gaussian vector, we develop an achievable rate for SU that is robust to the structure of PU's modulation signal set and only depends on its constellation size and the dimension of the euclidean space that the constellation points lie in. Moreover, we obtain an achievable rate for PU using Fano's inequality in conjunction with a Gallager-type upper bound on the probability of error in decoding constellation points at the primary receiver. The developed achievable rates for PU and SU enable us to show that the sum rate can be improved compared to a scenario where both users employ Gaussian codewords and treat each other as Gaussian noise.

This paper studies a multiple access network with two users and one Access Point (AP). It is assumed that the users and the AP are equipped with M and N antennas, respectively. To access the network, each user independently decides whether to transmit in a time slot or not (no coordination between users). Focusing on the high SNR behavior of the system, this paper presents the optimal value of the network average Degrees of Freedom (DoF) in different network settings. To this end, after finding an upper-bound for the network average DoF, we propose a transmission scheme (based on interference alignment) which achieves this upper-bound. Some illustrative examples are also presented in the paper.

This paper studies the problem of two-hop transmission from a single-antenna source to a single-antenna destination via two single-antenna relays. The relays operate in a full-duplex mode and they are not capable of buffering data. The links from the source to the relays and from the relays to the destination are considered to be Rayleigh block fading and there is no direct link between the source and the destination. There is also no link between the relays. Consequently, the half-duplex mode is a direct result of the full-duplex mode with frequency or time division. All nodes are assumed to be oblivious to their forward-channel gains, however, they have perfect information about their backward-channel gains. We also assume a stringent decoding delay constraint of one fading block that makes the definition of ergodic (Shannon) capacity meaningless. Hence, we adopt the broadcast approach (multi-layer coding) to maximize the expected-rate received at the destination. For this purpose, the decode-forward (DF) relaying adopting the broadcast approach is proposed. The main feature of the proposed scheme is that the layers being decoded at both relays are added coherently at the destination although each relay has no information about the number of layers being successfully decoded by the other relay. It is proved that the optimum strategy maximizing the throughput and expected-rate is to send uncorrelated signals over the relays. The maximum throughput is analytically formulated. An achievable rate as well as upper-bounds are presented for the maximum expected-rate of the channel.

A network of n wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant powerPor remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate λ. In a Rayleigh fading environment, an upper bound is derived that shows the number of active links scales at most like 1/λ log n. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of λ, the number of supported links by this strategy meets the upper bound; however, as λ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is asymptotically almost surely optimum when λ approaches ∞ or 0. It turns out that the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of loglogn. Finally, both decentralized and centralized schemes are evaluated in a distance-dependent fading environment with a path loss exponent of m and are shown to achieve throughput that scale like Θ( n(m/m+2)log n ) and Θ(n[(m(2)+2m)/( m(2)+2m+4)]), respectively.

This paper studies the setup of a parallel MIMO relay network in which K relays, each equipped with N antennas, assist in transmitting data between a source and a destination, each equipped with M antennas (M ≤ N), in the half-duplex mode. It is assumed that there is no direct source-destination link and the communication is performed in two hops. An amplify-and-forward relaying scheme called Incremental Cooperative Beamforming Scheme (ICBS) is introduced and shown to achieve the capacity of the network in the asymptotic case of K → ∞ with a gap scaling of at most [(log(K))/({4}√{K})]. This result is shown to hold as long as the power of each relay is significantly larger than [(log3(K) log(log(K)))/(K)]. In addition, in the case that the source power is equal to the relays' power and both tend to infinity, the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays. Simulation results confirm the validity of analytical arguments.

In this paper, we consider a decentralized wireless communication network with a fixed numberuof frequency subbands to be shared amongNtransmitter-receiver pairs. It is assumed that the number of active users is a realization of a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized frequency hopping (FH) scheme in which each transmitter randomly hops over a subset ofusubbands from transmission slot to transmission slot. Assuming all users transmit Gaussian signals, the distribution of the noise plus interference is mixed Gaussian, which makes calculation of the mutual information between the transmitted and received signals of each user intractable. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large signal-to-noise ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system to that of the frequency division (FD) system in terms of the following performance measures: average sum multiplexing gain (η(1)) and average minimum multiplexing gain per user (η(2)). We show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement in terms of η(1)and η(2)(implying a more efficient usage of the spectrum). In the sequel, we consider a scenario where the transmitters are unaware of the number of active users in the network as well as the channel gains. Developing a new upper bound on the differential entropy of a mixed Gaussian random vector and using entropy power inequality, we obtain lower bounds on the maximum transmission rate per user to ensure a specified outage probability at a given SNR level. We demonstrate that the so-called outage capacity can be considerably higher in the FH scheme than in the FD scenario for reasonable distributions on the number of active users. This guarantees a higher spectral efficiency in FH compared to FD.

In this paper, the impact of noncoordinated interfering signals on a point to point communication is addressed. While the transmitter has no information about the other users' messages, the receiver has full knowledge of the codebooks of the interfering users and can potentially decode some part of the interference. A simple coding strategy is proposed for this channel. Assuming its own data is decoded successfully, the receiver partitions the set of interfering users into two disjoint subsets, namely the set of decodable users and the set of nondecodable users. Then the transmitter's rate is chosen such that the intended signal can be jointly decoded with the set of decodable users. It is proved that the proposed strategy achieves the capacity of the additive Gaussian channel with Gaussian interfering users. A polynomial time algorithm is proposed to compute the achievable rate of the scheme. This algorithm is based a subroutine which separates the set of interfering users into decodable and nondecodable users in polynomial time. The proposed scheme is also applied to the case of -user interference channel and some achievable points are characterized by successive maximization of users' rates.

It is known that the achievable data rate per user can be increased when relays are deployed in wireless networks. However, the drawback of this solution is that some of the network's resources should be allocated to the relays. In this paper, we consider a two-tier network in which all users send or receive data in two hops. By applying vector quantization, we compute the relays' locations to improve network's average transmission rate. These locations are also computed analytically when the number of relays is less than six. Having determined the relays' locations, the network's average transmission rate is evaluated. Subsequently, we define the "neutrality-surface" such that the performance of any relay network operating below this surface is inferior to that of the same network without relays. Finally, we study the relative relaying gain for different network configurations.

This paper addresses a fundamental trade-off between rate and the diversity gain of an end-to-end connection in an erasure network. The erasure network is modeled by a directed graph whose links are orthogonal erasure channels. Furthermore, the erasure network is assumed to be non-ergodic, meaning that the erasure status of the links are assumed to be fixed during each block of transmission and change independently from block to block. The erasure status of the links is assumed to be known only by the destination node. First, we study the homogeneous erasure networks in which the links have the same erasure probability and capacity. We derive the optimum trade-off between diversity gain and the end-to-end rate and prove that a variant of the conventional routing strategy combined with an appropriate forward error correction at the end-nodes achieves the optimum diversity-rate trade-off. Next, we consider the general erasure networks in which different links may have different values of erasure probability and capacity. We prove that there exist general erasure networks for which any conventional routing strategy fails to achieve the optimum diversity-rate trade-off. However, for any general erasure graph, we show that there exists a linear network coding strategy which achieves the optimum diversity-rate trade-off. Unlike the previous works which suggest the potential benefit of linear network coding in the error-free multicast scenario (in terms of the achievable rate), our result introduces the benefit of linear network coding in the erasure single-source single-destination scenario (in terms of the diversity gain). Finally, we study the diversity-rate trade-off through simulations. The erasure graphs are constructed according to the Barabasi-Albert random model which is known to capture the scale-free property of the practical packet switched networks like the Internet. The error probability is depicted for different network strategies and different rate values. The depicted results confirm the trade-off between the rate and the diversity gain for each network strategy. Moreover, the diversity gain is plotted versus the rate for different conventional routing and the linear network coding strategies. It is observed that linear network coding outperforms all conventional routing strategies in terms of the diversity gain.

A two-user Gaussian Interference Channel (GIC) is considered in which encoders are connected through noiseless links with finite capacities. New genie-aided upper bounds on the sum-capacity are developed which incorporate the capacities of the cooperative links. When the GIC is symmetric, with possibly different cooperation link capacities, the sum-capacity is characterized within 2.13 bits gap for all values of the channel parameters. In the achievable scheme, each transmitter sends a private and a common message, and zero-forces the part of the other transmitter's private message, communicated over the conference between the encoders.

In this paper, a dual-hop communication system composed of a source S and a destination D connected through two non-interfering half-duplex relays, R1and R2, is considered. In the literature of Information Theory, this configuration is known as the diamond channel. In this setup, four transmission modes are present, namely: 1) S transmits, and R1and R2listen (broadcast mode), 2) S transmits, R1listens, and simultaneously, R2transmits and D listens. 3) S transmits, R2listens, and simultaneously, R1transmits and D listens. 4) R1, R2transmit, and D listens (multiple-access mode). Assuming a constant power constraint for all transmitters, a parameter Δ is defined, which captures some important features of the channel. It is proven that for Δ=0 the capacity of the channel can be attained by successive relaying, i.e, using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when Δ≠0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of Δ >0 and Δ0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel.

A new achievability rate region for the secure discrete memoryless Multiple-Access-Channel (MAC) is presented. Thereafter, a novel secure coding scheme is proposed to achieve a positive Secure Degrees-of-Freedom (S-DoF) in the single-antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. Tools from the field of Diophantine Approximation in number theory are used to analyze the probability of error in the coding scheme.

This paper studies the general multi-antenna multiple-relay network. Every two nodes of the network are either connected together through a Rayleigh fading channel or disconnected. We study the ergodic capacity of the network in the high SNR regime. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

We consider the K user Multiple Input Multiple Output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver. It is assumed that channel coefficients are fixed and are available at all transmitters and at all receivers. The main objective of this paper is to characterize the total Degrees Of Freedom (DOF) for this channel. Using a new interference alignment technique which has been recently introduced in, we show that MN/M+N K degrees of freedom can be achieved for almost all channel realizations. Also, a new upper-bound on the total DOF for this channel is derived. This upper-bound coincides with our achievable DOF for K ≥ Ku=ΔM+N/gcd(M,N) where gcd(M,N) denotes the greatest common divisor of M and N. This gives an exact characterization of DOF for MIMO Gaussian interference channel in the case of K ≥ Ku.

The K × 2 multiple input multiple output (MIMO) X-channel with constant channel coefficients available at all transmitters and receivers is considered. A new alignment scheme, named layered interference alignment, is proposed in which both vector and real interference alignment techniques are exploited together with joint processing at receiver sides. Data streams, having fractional multiplexing gains, in the desired directions are sent by transmitters to align the interfering signals at receivers efficiently. To decode the intended messages at receivers, a new number theoretic joint processing technique which exploits the availability of several received antennas, is proposed. This processing is backed up by a recent result in the field of Simultaneous Diophantine Approximation, which is introduced in this paper for the firs time. It is shown that incorporating the layered interference alignment is essential to characterize the total DOF of 2 km/ k+1, in the k × 2 m-antenna X-channel.

We address a two-user decentralized interference channel with static non-frequency selective channel gains. Both users are unaware of each other's code-books and there is no central controller to manage the allocation of resources between the two users. As multiuser detection is not possible, the conventional scheme of transmitting a continuous stream of i.i.d. symbols from Gaussian codebooks by each transmitter (referred to as continuous transmission) results in excessive interference. To provide both users with a partially interference-free channel, we propose that each user randomly quits transmitting from transmission slot to transmission slot independently with a probability of 1 - ε; ε ∈ (0, 1). This is called the Randomized Masking (RM) protocol. Due to the on-off nature of transmissions, the noise plus interference process has a mixed distribution. As a result, the mutual information between the input and the output of the channels does not accept any closed form expression. Assuming each user transmits i.i.d. signals upon activation, the highest achievable rate by each user is denoted by CRM-I. We derive upper and lower bounds on CRM-Iwhere Entropy Power Inequality (EPI) and the extremal inequality of Liu and Viswanath are two important tools in this analysis. Using the proposed lower bound, we devise a distributed strategy to select the activity factor e. Note that this strategy includes the conventional continuous transmission by setting ε = 1. The main result of the paper states that there exist values of 0 ≤ αRM-Ias far as the Signal-to-Noise Ratio (SNR) is sufficiently large. Therefore, it is proved that transmitting i.i.d. signals in consecutive transmission slots is not optimum under the RM protocol.

In this paper, we first investigate the Degrees Of Freedom (DOF) for the M-user Interference Channel (IC) in static environments with the help of a MIMO relay. The relay stores the received signal during the first time-slot and sends a linearly-transformed version over the next time-slot. Using this scheme, it is shown that Interference Alignment can be done with much less complexity. Having very loose constraints on the channel structure, the proposed method calculates a proper choice for the relay gains such that the M-user IC is able to achieve a DOF of M/2. It is also proved that if the relay's output power scales as P/(log P)twhere P is the power of the transmitters, there is no loss in the achieved DOF. This result is true for all positive and negative ranges of t. In other words, in an M-user IC with quasi-static channel gains, it is possible to achieve M/2 DOF through the use of a MIMO relay whose power grows at a rate slower than that of the transmitters. Similarly, a network of low-power users can benefit from our proposed method if the relay power scales faster than the power of the main transmitters. The results of this paper are valuable when being applied to a practical system. While it is very difficult to use Interference Alignment in M-user IC setup, adding a relay can make alignment more affordable by simplifying the transmitter/receiver structure.

A key element for many fading-compensation techniques is a (long-range) prediction tool for the fading channel. A linear approach, usually used to model the time evolution of the fading process, does not perform well for long-range prediction applications. An adaptive fading channel prediction algorithm using a sum-sinusoidal-based state-space approach is proposed. This algorithm utilises an improved adaptive Kalman estimator, comprising an acquisition mode and a tracking algorithm. Furthermore, for the sake of a lower computational complexity, an enhanced linear predictor for channel fading is proposed, including a multi-step AR predictor and the respective tracking algorithm. Comparing the two methods in our simulations show that the proposed Kalman-based algorithm can significantly outperform the linear method, for both stationary and non-stationary fading processes, and especially for long-range predictions. The performance and the self-recovering structure, as well as the reasonable computational complexity, makes the algorithm appealing for practical applications.

In this paper, a communication system includingninterfering additive white Gaussian noise (AWGN) links is considered. Each transmitter uses a Gaussian codebook and each receiver only decodes the data of the corresponding transmitter. For the case that the transmit powers are subject to arbitrary linear constraints, a mathematical expression for the boundary points of the signal-to-interference-plus-noise-ratio (SINR) region is obtained. Moreover, when the channels are time-varying and the average powers are constrained, the zero-outage SINR region of the system is derived. In addition, a scenario where the demanded SINR of the users is out of the SINR region is considered. A common approach is to remove a subset of the users such that the demanded SINR can be provided for the remaining users; the removed users are serviced in a later time slot. With the aim of maximizing the number of serviced users in each time slot, a suboptimal algorithm is developed, which outperforms the other known alternatives.

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e.,simultaneousandsuccessiverelaying, associated with two possible relay schedulings are proposed. The simultaneous relaying protocol is based on theBroadcast-Multiaccess with Common Message (BCM)scheme considered in. For the successive relaying protocol: (i) anon-cooperativescheme based on theDirty Paper Coding (DPC)and (ii) acooperativescheme based on theBlock Markov Encoding (BME)are considered. The composite scheme of employing BME inat mostone relay and DPC inat leastanother one is also proposed. It is proved that this scheme achieves at least the same rate when compared to thecooperativeandnon-cooperativeschemes for the Gaussian case. ASimultaneous-Successive Relaying based on Dirty Paper Coding scheme (SSRD)is also proposed. The optimum scheduling of the relays, and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios, is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.

In this paper, the inherent drawbacks of the naive lattice decoding (NLD) for MIMO fading systems is investigated. We show that using the NLD for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the nonvanishing determinant property cannot achieve the optimal diversity-multiplexing tradeoff. Indeed, we show that in the case of NLD, when we fix the underlying lattice, all the codes based on full-rate lattices have the same diversity-multiplexing tradeoff as V-BLAST. Also, we derive a lower bound on the symbol error probability of the NLD for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the NLD has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

Path diversity works by setting up multiple parallel connections between the endpoints using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. We prove that the probability of irrecoverable loss (PE) decays exponentially with the number of paths. Furthermore, the rate allocation (RA) problem across independent paths is studied. Our objective is to find the optimal RA, i.e., the allocation that minimizesPE. The RA problem is solved for a large number of paths. Moreover, it is shown that in such asymptotically optimal RA, each path is assigned a positive rate iff its quality is above a certain threshold. Finally, using memoization technique, a heuristic suboptimal algorithm with polynomial runtime is proposed for RA over a finite number of paths. This algorithm converges to the asymptotically optimal RA when the number of paths is large. For a practical number of paths, the simulation results demonstrate the close-to-optimal performance of the proposed algorithm .

In this paper, a single-hop single-relay system with a direct link between the source and the destination is considered when the relay operates in the half-duplex mode. Motivated by the concept of signal space diversity, this paper introduces signal space cooperation, in which cooperation between the source and the relay is achieved using a novel constellation design. In this approach, the original constellation is expanded so that the expanded constellation consists of all possible combinations of different components of signal points in the original constellation. The expanded constellation enables the relay to extract the required information in order to effectively cooperate in the relay phase, and it helps the destination to efficiently combine received signals during the broadcast phase and the relay phase. The analytical study of the proposed scheme leads to the development of two design criteria for the constellation expansion. Numerical results depict superior performance in comparison with other cooperative schemes, such as the distributed turbo coded cooperative schemes and the trans-modulation scheme.

In the closed-loop transmit diversity systems, feedback delay and feedback error, as well as the sub-optimum reconstruction of the quantized feedback data, are the usual sources of deficiency. We address the efficient reconstruction of the beamforming weights in the presence of the feedback imperfections, by exploiting the residual redundancies in the feedback stream. We propose two approaches to improve the performance. One is based on using a channel predictor at the receiver to compensate for the delay. Another approach deals with the feedback imperfections in a unified reconstruction algorithm using JSCC techniques. Furthermore, we introduce the concept of Blind Antenna Verification (BAV). The closed-loop Mode 1 of the 3GPP standard is used as a benchmark, and the performance is examined within a Wideband-CDMA simulation framework. It is demonstrated that the proposed algorithms outperform the standard at all mobile speeds, and are suitable for the implementation in practice.

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. It is assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. It is shown that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.

In this paper, the tradeoff between diversity and multiplexing gains in the two-user quasi-static Raleigh fading interference channel (IC) is derived. Under the short-term average power constraint and for the delay limited communication, we show that only a partial channel state information at the transmitter (CSIT) is enough to achieve the optimum diversity-multiplexing tradeoff (DMT) at the IC. We develop a coding scheme for the two-user quasi-static Raleigh fading IC. At the low rate region, this results in a one-level Gaussian code independent of the channel condition. At the high rate region, the result can be one-level or two-level Gaussian codes depending on the partial CSIT. The partial state information for each channel gain can be represented by only one bit corresponding to its absolute value. At the high rate region, we assume that the partial state information of all channel gains is available at the two transmit sides. The optimality of the proposed scheme is established by deriving an outer bound, which coincides with the achieved DMT.

In this paper, a new Selective Mapping (SLM) technique is introduced for a Multiple-Input Multiple-Output (MIMO) broadcast (or MIMO point-to-point) system with channel inversion. We present a unified framework which links the problem of minimizing the average transmit energy from the constellation point of view, to the sum-rate maximization problem from the capacity viewpoint. First, we consider the point-to-point setup and derive the average transmit energy that can asymptotically be achieved by the proposed SLM technique. It is established that SLM achieves the minimum theoretical average transmit energy achievable by constellation shaping. Then, using the same idea, the average transmit energy in a broadcast system is derived and the relation between this value and the transmission rate is established. Finally, it is shown that the proposed SLM method can achieve the sum-capacity of the MIMO broadcast (or capacity of a MIMO point-to-point) channel at high SNR values.

This paper addresses a distributed signaling scheme to improve the multiplexing gain (MG) in a wireless decentralized network with a fixed number u > 1 of frequency sub-bands to be shared among K transmitter-reciever pairs. In a decentralized network, users are not aware of the code-books of each other. Hence, in the high SNR regime, interference highly degrades the achievable rates of users as canceling the interference is impossible. On the other hand, decentralized networks have no fixed underlying infrastructure, i.e., there is no central management to assign certain non-overlaping portions of the spectrum to different users. As such, choosing the same sub-band by different users may result in losing the data transmitted on this sub-band. These shortcomings motivate us to propose a decentralized scheme that enables all users to coexist fairly, while utilizing the spectrum efficiently. We introduce a distributed signaling scheme (using i.i.d. Gaussian code-books) called repetition-frequency hopping (RFH) where all users keep transmitting the same set of independent signals over different portion of the spectrum along a certain repetition frame. Due to the dynamic nature of interference, sensing the spectrum to locate the interference is practically not possible. This makes the interference plus noise probability density function (PDF) be mixed Gaussian. We obtain upper and lower bounds on the rates of users that coincide as SNR tends to infinity. This enables us to derive a general formula for the sum-rate multiplexing gain in the network. We show that it is possible to achieve higher multiplexing gains in such systems if the length of the repetition frame along the time-axis is large enough. In fact, in many cases, there is a certain amount of repetition that leads to the highest multiplexing gain per user.

We consider a two-user interference channel where the users are not synchronous meaning there exists a delay between their transmitted codes. Assuming no user is aware of the location of the interference burst on its code, no interference cancellation is performed, i.e., users treat each other as noise. By the same token, the interference is no longer Gaussian as a result of the ambiguity on the start of the interference burst. We propose a stationary channel model for this setup for which we are able to derive the achievable rates based on upper and lower bounds on the mutual information between the input and output of the channel. These bounds meet each other as the code length grows to infinity. We define the outage capacity for each user as the largest transmission rate such that the outage probability is ensured to be below a certain threshold. In case the users are sharing a certain number of frequency sub-bands, we propose to divide the spectrum among the users to maximize the outage capacity for each user. We demonstrate that depending on the probabilistic parameters of the delay model and the value of the outage threshold, there are cases where the best strategy is to assign both private and common frequency sub-bands to the users.

This paper provides a unified measure to design binary pseudo-random (PN) codes in a wireless decentralized network in which several transmitter-reciever pairs share the spectrum. In a decentralized network, users are not aware of the code-books of each other. Hence, in the high SNR regime, interference highly degrades the achievable rates of users as interference cancellation is impossible. On the other hand, decentralized networks have no fixed underlying infrastructure, i.e., there is no central management to assign ldquogoodrdquo PN codes with appropriate cross-correlation properties to different users. As such, choosing the same PN code by different users may result in losing the packets transmitted by these users. These shortcomings motivate us to propose a decentralized scheme that enables all users to coexist fairly, while utilizing the spectrum efficiently. We introduce a distributed signaling scheme (using i:i:d: Gaussian code-books) called Bernoulli-Direct-Sequence (BDS) where all users spread their signals by locally generated binary PN codes. Due to the dynamic nature of interference, sensing the spectrum to measure the interference is practically not possible. This makes the interference plus noise probability density function (PDF) be mixed Gaussian. We obtain upper and lower bounds on the rates of users that coincide as SNR tends to infinity. This enables us to derive a general formula for the sum-rate multiplexing gain in the network. Subsequently, we propose a general rule to design the PN codes in the sense of increasing the sum-rate multiplexing gain in the network. It is shown that depending on the number of active users in the system, there is a certain amount of spreading length that leads to the highest multiplexing gain per user. Several design examples are provided at the end.

In this paper, the degrees of freedom (DOF) of the symmetric 3-user Gaussian interference channel is considered. It is shown that by using un-coded signaling, the achievable DOF is a discontinuous function of the channel parameter. More importantly, for the set of irrational channel gains, which has measure 1 in real numbers, it is proved that the total system's DOF, i.e., 3/2, is achievable. This result is obtained using Hurwitz's theorem in number theory.

In this paper, we first introduce a simple procedure for aligning interference directions in an M×N user MIMO X channel. The scheme is then modified for an M×2 user X channel in which each user is equipped with M + 1 antennas. Next we investigate the degrees of freedom (DOF) for a single antenna X channel in slow fading environments with the help of a simple relay. The relay stores all the received signals and sends their linear combination in subsequent transmissions. Using this scheme, it is shown that adding a relay can help the system to achieve all the available DOF. It is also proved that if the relay's output power scales with P/(log P)s, there is no loss in the achieved DOF as long as s > 0. In other words, in a network with quasi-static channels, it is possible to achieve a higher DOF through the use of randomizing relays whose powers grow at a much slower rate than the main transmitters. Similarly, when there are stricter constraints on the output power scaling of the transmitters, all the DOF can still be utilized, if the relay power can grow with P/(log P)tfor any t > 0. These results suggest that adding relays to a network can be beneficial in terms of simultaneously acquiring higher DOF.

Given a slowly fading channel, the performance of multi-layer coding is studied for single-user scenarios. Both the source and destination are equipped with multiple antennas. The channel state information is perfectly known at the destination but not at the source. The objective is to maximize the average data rate received at the destination when the destination is able to perform successive decoding. This paper, first, proposes a design rule for constructing an infinite-layer code for Multiple Input Multiple Output (MIMO) channels. Furthermore, we present a procedure describing how the introduced design rule is applied to optimally determine the multi-layer code parameters. The achievable rate of the multi-layer coding and successive decoding for the Rayleigh fading 2×2 MIMO channel is also evaluated.

Schein and Gallager introduced the Gaussian parallel relay channel in 2000. They proposed the amplify-and-forward (AF) and the decode-and-forward (DF) strategies for this channel. For a long time, the best known achievable rate for this channel was based on the AF and DF with time sharing (AF-DF). A rematch-and-forward (RF) scheme for the scenario in which different amounts of bandwidth can be assigned to the first and second hops were proposed. In this paper, we propose acombinedamplify-and-decodeforward(CADF) scheme for the Gaussian parallel relay channel. We prove that the CADF scheme always gives a better achievable rate compared to the RF scheme, when there is a bandwidth mismatch between the first hop and the second hop. Furthermore, for the equal bandwidth case (Schein's setup), we show that the time sharing between the CADF and the DF schemes (CADF-DF) leads to a better achievable rate compared to the time sharing between the RF and the DF schemes (RF-DF) as well as the AF-DF.

Channel inversion, and its minimum mean square error (MMSE) variation, are low complexity methods for space division multiple access (SDMA) in multiple input multiple output broadcast channel (MIMO-BC). As the channel matrix deviates from orthogonal, these methods result in a waste of transmit power. This paper proposes a trellis precoding method (across time and space) to improve the power efficiency. Adopting a 4-state trellis shaping method, the complexity of the proposed method, which is entirely at the transmitter side, is equivalent to the search in a trellis with 4Nstates where N is the number of transmit antennas. Numerical results are presented showing that the achievable gains, which depend on the channel realization, can be significantly higher than the traditional shaping gain which is limited to 1.53 dB.

For a state-dependent discrete memoryless channel with input alphabet${\cal X}$, state alphabet${\cal S}$, and output alphabet${\cal Y}$where the independent and identically distributed (i.i.d.) state sequence is known causally at the transmitter, it is shown that by using at most$\min \{\vert{\cal X}\vert \vert{\cal S}\vert -\vert{\cal S}\vert +1,\vert{\cal Y}\vert \}$out of$\vert{\cal X}\vert^{\vert{\cal S}\vert}$inputs of the Shannon's derived channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter,$M$-ary signal transmission for the additive white Gaussian noise (AWGN) channel with additive$Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. The optimal precoding scheme is derived under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet. It is shown that at low signal-to-noise ratio (SNR) not doing precoding is optimal. For the special case where the Gaussian noise power is zero, it is shown that the rate$\log_2 M$is achievable by a one-shot coding scheme if${\cal X}$is an arithmetic progression.

This paper studies the setup of a multiple-relay network in which$K$half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we callrandom sequential(RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay$(K > 1)$networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.

For a wide class of multiuser systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiple-access channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among the active users. This problem is addressed in two cases: (i) where the complexity of achieving interior points is not feasible, and (ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized is desired. A simple greedy algorithm is introduced to find such an optimum corner point. In addition, it is shown for single-antenna Gaussian multiple-access channels, the resulting corner point is leximin maximal with respect to the set of the corner points. For the second case, the properties of the unique leximin maximal rate vector with respect to the polymatroid are reviewed. It is shown that the problems of deriving the time-sharing coefficients or rate-splitting scheme to attain the leximin maximal vector can be solved by decomposing the problem into some lower dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is presented.

The capacity region of the two-user Gaussian interference channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise are optimal. It is shown that when Gaussian codebooks are used, the full Han–Kobayashi achievable rate region can be obtained by using the naive Han–Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, an alternative proof for the Sato's outer bound is presented. We derive the full Han–Kobayashi achievable rate region when Gaussian codebooks are utilized. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full Han–Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

In this paper, a downlink system in which a single-antenna base station communicates with k single antenna users over a time-correlated fading channel is considered. It is assumed that each receiver knows its own channel state, while the rate of the channel variation for all users and the corresponding initial fading gains are known to the base station. The average (per channel use) throughput of the system is studied by applying various adaptive signaling schemes. Assuming a large number of users in the system, it is shown that using a scheduling scheme in which the base station transmits to the user with the maximum initial fading gain, while using a fixed codeword length for all users, achieves the order of the maximum throughput. Moreover, an alternative scheduling scheme is proposed (by accounting for users' delays) and shown to achieve the optimum long-term fairness, while preserving the order of the maximum throughput.

A non-regenerative dual-hop wireless system based on distributed Alamouti space-time coding is considered. It is assumed that each relay retransmits an appropriately scaled space-time coded version of its received signal. The main goal of this paper is to find a scaling function for each relay to minimize the outage probability. In the high signal-to-noise ratio (SNR) regime for the relay-destination link, it is shown that a threshold-based scaling function (i.e., the relay remains silent if its channel gain with the source is less than its predetermined threshold) is optimum from the outage probability point of view. Numerical results demonstrate a dramatic performance improvement as compared to the case that the relay stations forward their received signals with full power even for finite SNR scenarios.

In this paper, a downlink communication system, in which a base station (BS) equipped with M antennas communicates with N (N Gt 1) single-antenna users, in a Rician fading environment is considered. The asymptotic (in terms of the number of users) sum-rate capacity of the system, as well as the capacity-achieving strategies, are derived. The main results of the paper are as follows: i) in the region of K = o(log N), where K denotes the Rician factor, the sum-rate capacity scales as M log(1 + P/Meta), where P denotes the SNR and eta =Deltalog N/1+K, which is achieved by zero-forcing beam-forming (ZFBF) along with a low-complexity user selection algorithm that considers only the scattered component of the userspsila channels, ii) in the region K = omega(log N), in the case of co-located transmit antennas, the capacity scales as log(1+MP), which is achieved by time division multiple access (TDMA), iii) in the region K = omega(log N), in the case of isotropically-distributed specular components, the sum-rate capacity behaves as M log(1 + P), which is achieved by ZFBF, along with a user selection algorithm that considers only the specular component of the userspsila channels.

In this paper, a MIMO Broadcast Channel (MIMO-BC) with large (K) number of users is considered. It is assumed that all users have a hard delay constraint D. We propose a scheduling algorithm for maximizing the throughput of the system, while satisfying the delay constraint for all users. It is proved that by using the proposed algorithm, it is possible to achieve the maximum throughput and maximum fairness in the network, simultaneously, in the asymptotic case of K rarr infin. We introduce a new performance metric in the network, called "minimum average throughput", and prove that the proposed algorithm is capable of maximizing the minimum average throughput in a MIMO-BC, in the asymptotic case of K rarr infin. Finally, it is established that the proposed algorithm reaches the boundaries of the capacity region and stability region of the network, simultaneously, in the asymptotic case of K rarr infin.

An erasure channel with a fixed alphabet size q, where q Gt 1, is studied. It is proved that over any erasure channel (with or without memory),maximumdistanceseparable(MDS) codes achieve the minimum probability of error (assuming maximum likelihood decoding). Assuming a memoryless erasure channel, the error exponent of MDS codes are compared with that of random codes. It is shown that the envelopes of these two exponents are identical for rates above the critical rate. Noting the optimality of MDS codes, it is concluded that random coding is exponentially optimal as long as the block size N satisfies N < q + 1.

We consider a wireless communication network with a fixed number of frequency sub-bands to be shared among several transmitter-receiver pairs. In traditional frequency division (FD) systems, the available sub-bands are partitioned into disjoint clusters (frequency bands) and assigned to different users (each user transmits only in its own band). If the number of users sharing the spectrum is random, this technique may lead to inefficient spectrum utilization (a considerable fraction of the bands may remain empty most of the time). In addition, this approach inherently requires either a central network controller for frequency allocation, or cognitive radios which sense and occupy the empty bands in a dynamic fashion. These shortcomings motivate us to look for a decentralized scheme (without using cognitive radios) which allows the users to coexist, while utilizing the spectrum efficiently. We consider a frequency hopping (FH) scheme (with iid Gaussian code-books) where each user transmits over a selection of sub-bands and hops to another selection (with the same cardinality) from transmission to transmission. We derive lower and upper bounds on the achievable rate of each user and demonstrate that for large signal-to-noise ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum-rate multiplexing gain (SMG) of the system. Subsequently, we show how each user can regulate its rate to guarantee fairness while maximizing SMG. We compare the FH and FD systems in terms of the following performance measures: average sum-rate multiplexing gain (eta1), average multiplexing gain per user (eta2), the minimum multiplexing gain per user (eta3) and service capability. We show that (depending on the probability mass function of the number of active users), the FH system can offer a significant improvement in terms of eta1and eta2(implying a more efficient usage of the spectrum). It is also shown that 1/epsi les eta3(FH)/eta3(FD)les 1, i.e., the loss incurred in eta3is not more than 1/epsi . Finally, computation of the so-called service capability shows that in FH systems any number of users can coexist fairly, while the maximum number of users in FD system is limited by the number of available bands.

The capacity region of the two-user Gaussian interference channel (IC) is studied. Two classes of channels are considered: weak and mixed Gaussian IC. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise is optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi (HK) achievable rate region can be obtained by using the naive HK achievable scheme over three frequency bands. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full HK achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

It is known that the achievable data rate per user can be increased when relays are deployed in wireless networks. However, the drawback with this solution is that some of the network resources should be allocated to the relays. In this paper, we consider a two-tier network where all users should send/receive data in two hops (via a relay). Applying vector quantization, we approximately find the location of the relays. These approximate relays' locations are also computed analytically when the number of relays is less than six. Having the relays' locations, the network average transmission rate is evaluated in terms of a set of network parameters. Then, in the multi-dimensional space of these network parameters, we introduce the concept of neutrality-surface. The neutrality-surface is defined such that the performance of any relay network operating below this surface is inferior to that of a simple no-relay network with the same parameters. Finally, we study the relative and differential relaying gain for different network configurations.

Density evolution (DE) is a technique for tracking the distribution of the log likelihood ratio (LLR) messages exchanged between the variable nodes and the check nodes in a bipartite graph. It is widely assumed that these distributions are close to Gaussian. However, in many scenarios, this assumption is not valid, for example, the case that the signal to noise ratio is low, or the degree of variable nodes exceeds a certain threshold. A new (suboptimal) method for DE algorithm in low-density parity-check codes is introduced. We provide a more accurate model for the distribution of message bits (as compared to Gaussian) through matching the first n statistical moments. An iterative message passing algorithm is proposed to compute these moments from the graphical representation of the underlying code. It shown that the proposed algorithm results in an improved estimate of the underlying EXIT chart as compared to using a Gaussian assumption. In this respect, the proposed method achieves a performance very close to that of the best earlier methods, while it offers a much lower complexity.

In this paper, a downlink communication system, in which a base station (BS) equipped with antennas communicates with users each equipped with receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum-rate throughput of the system, in a Rayleigh-fading environment. For the asymptotic case when tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sum-rate throughput, such that the difference between the achievable sum-rate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the BS, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity.

In a multiple-antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter's data (noncooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters' points of view) and two multiple-access channels (from the receivers' points of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two noninterfering multiple-antenna broadcast subchannels or two noninterfering multiple-antenna multiple-access subchannels. The main objective in the design of the filters is to exploit the structure of the channel matrices to achieve the highest multiplexing gain (MG). It is shown that the proposed noncooperative signaling schemes outperform other known noncooperative schemes in terms of the achievable MG. In particular, it is shown that in some specific cases, the achieved MG is the same as the MG of the system if full cooperation is provided either between the transmitters or between the receivers.

A simple signaling method for broadcast channels with multiple-transmit multiple-receive antennas is proposed. In this method, for each user, the direction in which the user has the maximum gain is determined. The best user in terms of the largest gain is selected. The corresponding direction is used as the modulation vector (MV) for the data stream transmitted to the selected user. The algorithm proceeds in a recursive manner where in each step, the search for the best direction is performed in the null space of the previously selected MVs. It is demonstrated that with the proposed method, each selected MV has no interference on the previously selected MVs. Dirty-paper coding is used to cancel the remaining interference. For the case that each receiver has one antenna, the presented scheme coincides with the known scheme based on Gram-Schmidt orthogonalization (QR decomposition). To analyze the performance of the scheme, an upper bound on the cumulative distribution function (CDF) of each subchannel is derived which is used to establish the diversity order and the asymptotic sum-rate of the scheme. It is shown that using fixed rate codebooks, the diversity order of the jth data stream, 1 les j les M, is equal to N(M - j + 1)(K - j + 1), where M, N, and K indicate the number of transmit antennas, the number of receive antennas, and the number of users, respectively. Furthermore, it is proven that the throughput of this scheme scales as M log log(K) and asymptotically (K rarr infin) tends to the sum-capacity of the multiple-input multiple-output (MIMO) broadcast channel. The simulation results indicate that the achieved sum-rate is close to the sum-capacity of the underlying broadcast channel.

Path diversity works by setting up multiple parallel connections between the end points using the topological path redundancy of the network. In this paper, forward error correction (FEC) is applied across multiple independent paths to enhance the end-to-end reliability. Internet paths are modeled as erasure Gilbert-Elliot channels. First, it is shown that over any erasure channel, maximum distance separable (MDS) codes achieve the minimum probability of irrecoverable loss among all block codes of the same size. Then, we prove the probability of irrecoverable loss decays exponentially for the asymptotically large number of paths. Moreover, it is shown that in the optimal rate allocation, each path is assigned a positive rate iff its quality is above a certain threshold. The quality of a path is defined as the percentage of the time it spends in the bad state. Finally, using dynamic programming, a heuristic suboptimal algorithm with polynomial runtime is proposed for rate allocation over the available paths. This algorithm converges to the asymptotically optimal rate allocation when the number of paths is large. The simulation results show that the proposed algorithm approximates the optimal rate allocation very closely, and provides significant performance improvement compared to the alternative schemes of rate allocation.

In this article, a new method for performance evaluation of turbo-like codes is presented. This is based on estimating the probability density function (pdf) of the bit log-likelihood-ratio (LLR) using higher order statistics. We do not restrict ourselves to any specific model for thepdfand try to estimate it directly using a cumulant matching method. Numerical results show a close agreement between the proposed method and simulations. The complexity of this method is similar to the Monte-Carlo simulation with the advantage of providing similar accuracy using significantly fewer samples.

A single-hop wireless network with K links is considered, where the links are partitioned into M clusters, each operating in a subchannel with bandwidth W/M. We assume that the links in each cluster perform the on-off power allocation strategy proposed in [1]. The problem is to analyze the average sum-rate of the network in terms of M and under the shadow- fading effect with probability a. It is demonstrated that for M ~ o(K) and 0 < alpha les 1, where alpha is a fixed parameter, the average sum-rate of the network scales as W/alpha log K. For M ~ Theta(K), we present an upper bound for the average sum-rate. It is proved that the maximum average sum-rate of the network for every value of 0 < alpha les 1 is achieved at M = 1. In fact, in the proposed model, partitioning the bandwidth W into M subchannels has no gain in terms of enhancing the throughput.

In this paper, an asymptotic analysis for the delay-throughput of a single-hop wireless network with n pairs of nodes is presented. The analysis relies on the decentralized on-off power allocation strategy, in which the on-off transmission policy for each link is based on comparing its direct channel gain with optimum threshold τn. We first provide a new definition of the transmission delay in a homogenous network. It is proved that the delay threshold level that results the dropping probability for each link tends to zero, while achieving the maximum average sum-rate scales as ω(n / log n). Also, the minimum delay in order to make the dropping probability for the whole network approach zero scales as ω(n / log n) + n. Furthermore, we drive lower and upper bounds for the link activation probability, q, such that the order of the average sum-rate is preserved. Based on the upper bound on q, an asymptotic analysis shows that the delay in each link and in the network improves without any significant impact on the the average sum-rate. Finally, we present a new definition of the throughput for the link in the cases of one and infinite buffer size. It is demonstrated that the maximum average throughput of the network with the decentralized on-off power allocation strategy is independent of the buffer size.

For a state-dependent DMC with input alphabet X and state alphabet S where the i.i.d. state sequence is known causally at the transmitter, it is shown that by using at most |X||S|-|S|+1 out of |X||S|input symbols of the Shannon's associated channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, M-ary signal transmission over AWGN channel with additive Q-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. For the special case where the Gaussian noise power is zero, a sufficient condition, which is independent of interference, is given for the capacity to be log2M bits per channel use. The problem of maximization of the transmission rate under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet is investigated. For this setting, the general structure of a communication system with optimal precoding is proposed.

AK-user memoryless interference channel is considered where each receiver sequentially decodes the data of a subset of transmitters before it decodes the data of the designated transmitter. Therefore, the data rate of each transmitter depends on (i) the subset of receivers which decode the data of that transmitter, (ii) the decoding order, employed at each of these receivers. In this paper, a greedy algorithm is developed to find the users which are decoded at each receiver and the corresponding decoding order such that the minimum rate of the users is maximized. It is proven that the proposed algorithm is optimal.

In this paper, an n-user Gaussian interference channel under arbitrary linear power constraints is considered. Using Perron-Frobenius theorem, a closed-form expression for the boundary points of the rate region of such a channel is derived. This is a generalization of the well-known result on the maximum rate that some interfering links can simultaneously achieve when the power is unbounded. Moreover, this result is extended to the time-varying channels with constraints on the average power.

A wireless multicast network with a stringent decoding delay constraint and a minimum required multicast data rate is characterized. Assuming the channel state information is available only at the receiver sides, and a single antenna system, the optimal expected rate achievable by a random user in the network is derived in terms of the minimum multicast requirement in two scenarios: hard coverage constraint and soft coverage constraint. In the first case, the minimum multicast requirement is expressed by multicast outage capacity while in the second case, the expected multicast rate should satisfy the minimum requirements. Also, the optimum power allocation in an infinite layer superposition code, achieving the highest expected typical rate, is derived subject to the coverage constraints. For the MISO case, a suboptimal coding scheme is proposed, which is shown to be asymptotically optimal, when the number of transmit antennas grows at least logarithmically with the number of users in the network.

We address data transmission over the M-user Gaussian interference channel, where users send data using single Gaussian codebooks. We first present a polynomial-time algorithm for finding the maximum decodable subset among interfering users, provided the users' rates and powers are given. Given any ordering of users, we characterize an achievable rate vector in which users' rates are successively maximized based on the ordering. It is also shown that in a noncooperative scenario where users refuse to send below their conservative rates, there are achievable vectors that are feasible with respect to the conservative rates vector which can be obtained by using a simple iterative algorithm.

In this paper, the diversity-multiplexing trade-off is derived for a one-dimensional equally-spaced Rayleigh fading ad-hoc network. It is assumed that the interference from each link to the other links in the network declines exponentially with the distance, such that the attenuation between two neighbor links is rhoalpha0. For any given multiplexing gain r, the maximum diversity gain is achieved by utilizing a general time-sharing scheme. We obtain an explicit formula for the maximum diversity gain, and show that depending on the value of r and alpha0, there is an optimum time-sharing factor which yields the maximum diversity gain.

In this paper, the inherent drawbacks of the naive lattice decoding for MIMO fading systems is investigated. We show that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the rate-diversity tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal rate-diversity trade-off. Indeed, we show that in the case of naive lattice decoding, all the codes based on full-rate lattices have the same rate-diversity trade-off as V-BLAST. Also, we drive a lower bound on the symbol error probability of the naive lattice decoding for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the naive lattice decoding has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

In this paper, we consider the problem of robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme which achieves the optimal slope for the signal-to-distortion (SDR) curve (unlike the previous known coding schemes). We also drive some theoretical bounds on the asymptotic performance of delay-limited hybrid digital-analog (HDA) coding schemes. We show that, unlike the delay-unlimited case, for any family of HDA codes, the asymptotic performance loss is unbounded (in terms of dB).

Abstract—Exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth efficient way to combat the noisy channel degradations. In this paper, we consider soft reconstruction of speech spectrum, in GSM adaptive multirate and IS-641 vocoders, transmitted over a channel disturbed with noise and/or packet loss. Several schemes are presented which exploit different levels of intraframe and interframe residual redundancy for improved source decoding at the receiver. A packetization strategy is proposed which is matched to the presented error concealment units. For decoders that exploit the residual redundancy, extensive complexity has been a serious concern, especially as the quantizer bitrate increases. In this paper, a novel method is presented to construct reduced complexity algorithms. The proposed methodology is based on the classification of the signal domain and efficient approximation of the residual redundancy or the a priori transition probabilities. The presented schemes provide high quality error concealment solutions for code excited linear prediction (CELP) coders. Index Terms—Erasure channel, forward–backward recursion, global system for mobile communications–adaptive multirate (GSM–AMR), IS-641, joint source channel coding (JSC), linear predictive coding (LPC), line spectral frequency (LSF), Markov models, minimum mean squared error (MMSE) estimation, multiple description coding (MDS), packet loss concealment (PLC), residual redundancies, source decoding, speech coding, speech error concealment. I.

In this paper, a new method for performance evaluation of turbo-like codes is presented. This is based on estimating the probability density function of the bit log-likelihood-ratio using higher order statistics. We do not restrict ourselves to any specific model for the pdf and try to estimate it directly using a cumulant matching method. Numerical results show a close agreement between the proposed method and the simulations. The complexity of this method is similar to the Monte-Carlo simulation with the advantage of providing similar accuracy using significantly fewer samples.

This work studies certain properties of the probability density function (pdf) of the bit log-likelihood ratio (LLR) for binary linear block codes over a memoryless channel with discrete input and discrete or continuous output. We prove that under a set of mild conditions, the pdf of the bit LLR of a specific bit position is independent of the transmitted codeword. It is also shown that the pdf of a given bit LLR when the corresponding bit takes the values of zero and one are symmetric with respect to each other (reflection of one another with respect to the vertical axis). For the case of channels with binary input, a sufficient condition for two bit positions to have the same pdf is presented.

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like log n; (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.

In multiple-input multiple-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an$N$-dimensional complex space. In general, this problem is known to be NP-hard. In this paper, a quasi-ML algorithm based on semi-definite programming (SDP) is proposed. We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems.

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.

A new viewpoint for adopting the lattice reduction in communication over multiple-input multiple-output (MIMO) broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided (LRA) preceding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior (signal-to-noise ratio (SNR) rarr infin) of the symbol error rate for the LRA precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum rate is analyzed. It is shown that the LRA method, using the Lenstra-Lenstra-Lovasz (LLL) algorithm, achieves the optimum asymptotic slope of symbol error rate (called the precoding diversity).

Diversity order is an important measure for the performance of communication systems over multiple-input-multiple-output (MIMO) fading channels. In this correspondence, we prove that in MIMO multiple- access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.

In this paper, a downlink communication system, in which a base station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas is considered. We study the minimum required amount of feedback at the BS, in order to achieve the maximum sum-rate capacity. First, we define the amount of feedback as the average number of users who send information to the BS. In the asymptotic case of N rarr infin, we show that with finite amount of feedback, it is not possible to achieve the maximum sum-rate. Indeed, in order to reduce the gap between the achieve sum-rate and the optimum value to zero, a minimum feedback of ln ln ln N is asymptotically necessary. Then, we consider a practical scenario, in which the amount of feedback is defined as the average number of bits which is sent to the BS. We show that to achieve the maximum sum-rate, infinite amount of feedback is required. Moreover, the minimum amount of feedback, in order to reduce the gap to the optimum sum-rate to zero, scales as otimes(ln ln ln N), which is achievable by the random beam-forming scheme proposed in M. Sharif and B. Hassibi, (2005)

For a wide class of multiuser systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. In one case, the corner point for which the minimum rate of the active users is maximized (max-min corner point) is computed for signaling. In another case, the polymatroid properties are exploited to locate a rate-vector on the sum-capacity facet which is optimally fair in the sense that the minimum rate among all users is maximized (max-min rate). It is shown that the problems of deriving the time-sharing coefficients or rate-splitting scheme can be solved by decomposing the problem to some lower-dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is proposed

A new structure for multi-base systems is studied in which each user receives data from two nearby base stations, rather than only from the strongest one. This system can be considered as a combination of broadcast and multi-access channels. By taking advantages of both perspectives, an achievable rate region for a discrete memoryless channel modeled by Pr(y1,y2|x1,x2) is derived. In this model, x1and x2represent the transmitted signals by the transmitter one and two, respectively, and y1and y2denote the received signals by the receiver one and two, respectively. In this derivation, it is assumed that each transmitter is unaware of the data of the other transmitter, and therefore x1and x2are independent. To investigate the advantage of this scheme, an efficient signaling method which works at a corner point of the achievable region for multiple-antenna scenarios is developed. In the proposed scheme, each base station only requires the state information of the channels between the other base station and each user. In this paper, the signaling scheme is elaborated for the case that each transmitter/receiver is equipped with three antennas. It is proven that in such a scenario, the multiplexing gain of four is achievable, which outperforms any other conventional schemes

In this paper, a downlink scenario in which a single-antenna base station communicates with K single antenna users, over a time-correlated fading channel, is considered. It is assumed that channel state information is perfectly known at each receiver, while the statistical characteristics of the fading process and the fading gain at the beginning of each frame are known to the transmitter. By evaluating the random coding error exponent of the time-correlated fading channel, we show that there is an optimal codeword length which maximizes the throughput. We examine the throughput of the conventional scheduling that transmits to the user with the maximum signal to noise ratio using both fixed length codewords and variable length codewords. Although optimizing the codeword length improves the performance, it is shown that using the conventional scheduling, a gap of Omega(radiclog log log K) exists between the achievable throughput and the maximum possible throughput of the system. We propose a simple scheduling that considers both the signal to noise ratio and the channel time variation. We show that by using this scheduling, the gap between the achievable throughput and the maximum throughput of the system approaches zero

A sub-optimum a-posteriori probability (APP) detector is proposed for iterative joint detection/decoding in a multiple-input multiple-output (MIMO) wireless communication system employing an outer code. The proposed detector searches inside a given sphere in a parallel manner to simultaneously find a list of m-best points based on an additive metric. The metric is formed by combining the channel output and the a-priori information. The parallel structure of the proposed method is suitable for hardware parallelization. The radius of the sphere and the value of m are selected according to the channel condition to reduce the complexity. Numerical results are provided showing a significant reduction in the average complexity (for a similar performance and peak complexity) as compared to the best earlier known method. The proposed scheme is applied for the decoding of the rate 2, 4 times 2 MIMO code employed in the 802.16e standard

A lattice-based scheme for the single-frame and the double-frame quantization of the speech line spectral frequency parameters is proposed. The lattice structure provides a low-complexity vector quantization framework, which is implemented using a trellis structure. In the single-frame scheme, the intraframe dependencies are exploited using a linear predictor. In the double-frame scheme, the parameters of two consecutive frames are jointly quantized and hence the interframe dependencies are also exploited. A switched scheme is also considered in which, lattice-based double-frame and single-frame quantization is performed for each two frame and the one which results in a lower distortion is chosen. Comparisons to the Split-VQ, the Multi-Stage VQ, the Trellis Coded Quantization, the interframe Block-Based Trellis Quantizer, and the interframe scheme used in IS-641 EFRC and the GSM AMR codec are provided. These results demonstrate the effectiveness of the proposed lattice-based quantization schemes, while maintaining a very low complexity. Finally, the issue of the robustness to channel errors is investigated

A technique is presented to reduce the multiple-access interference in the forward link of a direct-sequence code-division multiple-access system. For each symbol period, an energy-constrained nonlinear transformation is applied at the transmitter output to minimize the mean-squared error at the receiver, subject to a constraint on the peak transmitted energy. The proposed algorithm can be implemented with existing optimization techniques that solve the quadratic trust-region problem. It is shown that in the presence of forward error-correction codes, the proposed method results in a significant gain over earlier known techniques at the cost of a modest increase in computational complexity at the base station. Another advantage of the proposed precoder is that it caps the peak energy (while earlier methods cap the average energy), requiring less sophisticated power amplifiers.

In this paper, the problem of reducing the peak-to-average-power ratio (PAPR) in an orthogonal frequency-division multiplexing system is considered. We design a cubic constellation, called the Hadamard constellation, whose boundary is along the bases defined by the Hadamard matrix in the transform domain. Then, we further reduce the PAPR by applying the selective-mapping technique. The encoding method, following the method introduced in the work of Kwok, is derived from a decomposition known as the Smith normal form. This new technique offers a PAPR that is significantly lower than those of the best-known techniques without any loss in terms of energy and/or spectral efficiency, and without any side information being transmitted. Moreover, it has a low computational complexity.

This paper describes a new approach to fixed-rate entropy-constrained vector quantization (FEVQ) for stationary memoryless sources where the structure of codewords are derived from a variable-length scalar quantizer. We formulate the quantization search operation as a zero–one integer optimization problem, and show that the resulting integer program can be closely approximated by solving a simple linear program. The result is a Lagrange formulation which adjoins the constraint on the entropy (codeword length) to the distortion. Unlike the previously known methods with a fixed Lagrange multiplier, we use an iterative algorithm to optimize the underlying objective function while updating the Lagrange multiplier until the constraint on the overall rate is satisfied. The key feature of the new method is the substantial reduction in the number of iterations, in comparison with previous related methods. In order to achieve some packing gain, we combine the process of trellis-coded quantization with that of FEVQ. This results in an iterative application of the Viterbi algorithm on the underlying trellis for selecting the Lagrange multiplier. Numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature.

This paper describes a new approach to fixed-rate entropy-constrained vector quantization (FEVQ) for stationary memoryless sources where the structure of codewords are derived from a variable-length scalar quantizer. We formulate the quantization search operation as a zero-one integer-optimization problem, and show that the resulting integer program can be closely approximated by solving a simple linear program. The result is a Lagrange formulation which adjoins the constraint on the entropy (codeword length) to the distortion. Unlike the previously known methods with a fixed Lagrange multiplier, we use an iterative algorithm to optimize the underlying objective function, while updating the Lagrange multiplier until the constraint on the overall rate is satisfied. The key feature of the new method is the substantial reduction in the number of iterations in comparison with previous related methods. In order to achieve some packing gain, we combine the process of trellis-coded quantization with that of FEVQ. This results in an iterative application of the Viterbi algorithm on the underlying trellis for selecting the Lagrange multiplier. Numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature

In this paper, a method is proposed to construct spectral-efficient unitary space–time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods, which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood decoding algorithm. Also, we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas. As an example, we present a construction for a 4$times$4 unitary constellations which has a good performance, as compared with the other known codes.

In this paper, a method is proposed to construct spectrally efficient unitary space-time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood (ML) decoding algorithm. Also, we demonstrate that similar ideas can be applied to designing codes for more than two transmit antennas. As an example, we present a construction for 4-by-4 unitary constellations which has a good performance, compared with the other known codes

A full diversity block space-time code over two transmit antennas and two symbol periods is introduced. In this method, each code is equal to the addition of two matrices; A/sup m/ and DA/sup n/, where A and D are the two constant matrices and m and n are the two data symbols. A is selected such that the set A/sup m/, 0 /spl les/ m /spl les/ 2/sup b/ - 1 is closed under the matrix multiplication. This structure allows a simple maximum likelihood (ML) decoding method, and at the same time, simplifies the optimization of the coding advantage. Simulations show that the performance of the new code is very close to that of the Damen code (M. O. Damen et al., 2002) which is the best known block space-time code in terms of the coding advantage. Moreover, the decoding complexity of the proposed method is significantly lower than that of the Damen code.

We study a multiple-input multiple-output (MIMO) wireless system where the channel state information is partially available at the transmitter through a feedback link. Based on singular value decomposition, the MIMO channel is split into independent sub-channels. Effective feedback of the required spatial channel information entails efficient quantization/encoding of a unitary matrix. We propose two schemes for quantizing unitary matrices via Givens rotations and examine the performance for a scenario where the rates allocated to the sub-channels are selected according to their corresponding gains. Numerical results show that the proposed schemes offer a significant performance improvement as compared to that of MIMO systems without feedback, with a negligible increase in the complexity.

In this paper, we consider a downlink communication system, in which a base station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas. We propose an efficient suboptimum algorithm for selecting a set of users in order to maximize the sum-rate throughput of the system. For the asymptotic case of N rarr infin, it is shown that by using a very simple preceding scheme of zero-forcing beam-forming, the optimum sum-rate which behaves like M log log N can be achieved. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the base station, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sum-rate capacity, with a very low complexity

In multi-input multi-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on semi-definite programming (SDP). We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models

Diversity order is an important measure for the performance of different communication systems over MIMO fading channels. In this paper, we define the preceding diversity for the fixed-rate MIMO broadcast systems and we prove that in these systems, lattice-reduction-aided preceding achieves the preceding diversity. Also, we prove that lattice-reduction-aided decoding achieves the receive diversity in MIMO point-to-point and multiple-access systems

In this work, we study a multiple-input multiple-output wireless system, where the channel state information is partially available at the transmitter through a feedback link. Based on singular value decomposition, the MIMO channel is split into independent subchannels, which allows separate, and therefore, efficient decoding of the transmitted data signal. Effective feedback of the required spatial channel information entails efficient quantization/encoding of a Haar unitary matrix. The parameter reduction of an n /spl times/ n unitary matrix to its n/sup 2/ - n basic parameters is performed through Givens decomposition. We prove that Givens matrices of a Haar unitary matrix are statistically independent. Subsequently, we derive the probability distribution function (PDF) of the corresponding matrix elements. Based on these analyses, an efficient quantization scheme is proposed. The performance evaluation is provided for a scenario where the rates allocated to each independent channel are selected according to its corresponding gain. The results indicate a significant performance improvement compared to the performance of MIMO systems without feedback at the cost of a very low-rate feedback link.

A method to construct spectrally-efficient unitary space-time codes is proposed for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (minimum determinant distance), we aim at increasing the spectral efficiency. Simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the known alternatives. In the special case of two transmit antennas, which is the main focus of the paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum likelihood decoding algorithm. We also show that similar ideas can be applied to more than two transmit antennas. As an example, we present a construction for 4 by 4 unitary constellations which has good performance as compared to the other known codes.

The design of source decoders that employ the residual redundancy at the source coder output is an interesting research direction in the joint source channel coding framework. Such decoders are expected to replace the traditionally heuristic error concealment units that are elements of most multimedia communication systems. In this work, we consider the reconstruction of signals encoded with a multi-stage vector quantizer (MSVQ) and transmitted over a noisy channel. The MSVQ maintains a moderate complexity and, due to its successive refinement feature, is a suitable choice for the design of layered (progressive) source codes. An approximate MMSE source decoder for MSVQ is presented and its application to reconstruction of LPC parameters in MELP is analyzed. Numerical results demonstrates the effectiveness of the proposed schemes.

An analytical method for approximate performance evaluation of binary linear block codes using an additive white Gaussian noise channel model with binary phase-shift keying modulation is presented. We focus on the probability density function of the bit log-likelihood ratio (LLR), which is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit LLR. We introduce an analytical method for calculating these moments. This is based on some recursive calculations involving certain weight enumerating functions of the code. It is proved that the approximation can be as accurate as desired, if we use enough terms in the Gram-Charlier series expansion. Numerical results are provided for some examples, which demonstrate close agreement with simulation results.

In this paper, we consider the problem of decoding predictively encoded signal over a noisy channel when there is residual redundancy (captured by a /spl gamma/-order Markov model) in the sequence of transmitted data. Our objective is to minimize the mean-squared error (MSE) in the reconstruction of the original signal (input to the predictive source coder). The problem is formulated and solved through minimum mean-squared error (MMSE) decoding of a sequence of samples over a memoryless noisy channel. The related previous works include several maximum a posteriori (MAP) and MMSE-based decoders. The MAP-based approaches are suboptimal when the performance criterion is the MSE. On the other hand, the previously known MMSE-based approaches are suboptimal, since they are designed to efficiently reconstruct the data samples received (the prediction residues) rather than the original signal. The proposed scheme is set up by modeling the source-coder-produced symbols and their redundancy with a trellis structure. Methods are presented to optimize the solutions in terms of complexity. Numerical results and comparisons are provided, which demonstrate the effectiveness of the proposed techniques.

Exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth-efficient way to combat noisy channel degradations. This redundancy can be employed to either assist the channel decoder for improved performance or design better source decoders. In this work, a family of solutions for the asymptotically optimum minimum mean-squared error (MMSE) reconstruction of a source over memoryless noisy channels is presented when the redundancy in the source encoder output stream is exploited in the form of a /spl gamma/-order Markov model (/spl gamma//spl ges/1) and a delay of /spl delta/,/spl delta/>0, is allowed in the decoding process. It is demonstrated that the proposed solutions provide a wealth of tradeoffs between computational complexity and the memory requirements. A simplified MMSE decoder which is optimized to minimize the computational complexity is also presented. Considering the same problem setup, several other maximum a posteriori probability (MAP) symbol and sequence decoders are presented as well. Numerical results are presented which demonstrate the efficiency of the proposed algorithms.

The error probability of maximum-likelihood (ML) soft-decision decoded binary block codes rarely accepts nice closed forms. In addition, for long codes, ML decoding becomes prohibitively complex. Nevertheless, bounds on the performance of ML decoded systems provide insight into the effect of system parameters on the overall system performance as well as a measure of goodness of the suboptimum decoding methods used in practice. Using the so-called Gallager's first bounding technique (involving a so-called Gallager region) and within the framework of tangential sphere bound (TSB) of Poltyrev, we develop a general bound referred to as the generalized TSB (GTSB). The Gallager region is chosen to be a general hyper-surface of revolution (HSR) which is optimized to tighten the bound. The search for the optimal Gallager region is a classical problem dating back to Gallager's thesis in the early 1960s. For the random coding case, Gallager provided the optimal solution in a closed form while for the nonrandom case the problem has been an active area of research in information theory for many years. We prove that for a sphere code, the optimal HSR within the proposed GTSB is a hyper-cone. This will climax to the TSB of Poltyrev, one of the tightest bounds ever developed for binary block codes, and therefore terminates the search for a better Gallager region in the groundwork of the GTSB.

Performance evaluation of maximum-likelihood (ML) soft-decision-decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). The tangential sphere bound (TSB) of Poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example. Within the framework of the TSB and GFBT, we apply a new method referred to as the "added-hyper-plane" (AHP) technique, to the decomposition of the error probability. This results in a bound developed upon the application of two stages of the GFBT with two different Gallager regions culminating in a tightened upper bound beyond the TSB. The proposed bound is simple and only requires the spectrum of the binary code.

An efficient block-based trellis quantization (BTQ) scheme is proposed for the quantization of the line spectral frequencies (LSF) in speech coding applications. The scheme is based on the modeling of the LSF intraframe dependencies with a trellis structure. The ordering property and the fact that LSF parameters are bounded within a range is explicitly incorporated in the trellis model. BTQ search and design algorithms are discussed and an efficient algorithm for the index generation (finding the index of a path in the trellis) is presented. Also the sequential vector decorrelation technique is presented to effectively exploit the intraframe correlation of LSF parameters within the trellis. Based on the proposed block-based trellis quantizer, two intraframe schemes and one interframe scheme are proposed. Comparisons to the split-VQ, the trellis coded quantization of LSF parameters, and the multi-stage VQ, as well as the interframe scheme used in IS-641 EFRC and the GSM AMR codec are provided. These results demonstrate that the proposed BTQ schemes outperform the above systems.

We present a method for maximum likelihood decoding of the (48,24,12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the (24,12,8) Golay code, the (48,24,12) code does not have a Pless-construction which has been an open question in the literature. It is determined that the highest minimum distance of a (48,24) binary code having a Pless (1986) construction is 10, and up to equivalence there are three such codes.

This article presents a technique to reduce multiple access interference in the forward-link of a conventional DS-CDMA system by applying an energy constrained transformation to the transmitter output. For each symbol period, a new transformation is selected which minimizes the mean-squared error at the output of a bank of matched-filter detectors. This selection is subject to a constraint on total transmitted energy. It is shown that the proposed method results in substantial advantages over earlier similar techniques. The proposed algorithm can be implemented efficiently at the transmitter with existing optimization techniques that solve the quadratic trust-region subproblem.

Exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth efficient way to combat the noisy channel degradations. We consider soft reconstruction of LSF parameters in the IS-641 CELP coder transmitted over a noisy channel. We propose two schemes. The first scheme attempts to exploit the interframe residual redundancies in the sequence of received parameters. The second approach exploits both interframe and intraframe residual redundancies. Simulation results are provided which demonstrates the efficiency of the algorithms. Another issue addressed here, is a methodology to efficiently approximate and store the residual redundancies or the a priori transition probabilities. For quantizers with high rates calculating these probabilities require a huge number of source samples, and storing them also require a large amount of memory. These issues can well make the decoder design process an impractical task. The proposed method is based on the classification of the signal domain. The presented schemes provide high quality error concealment solutions for CELP coders.

We present a scheme for single frame (20 msec) and double frame (40 msec) quantization of line spectral frequency (LSF) parameters in a code-excited linear prediction (CELP) speech coder using noise feedback coding. To improve the performance, an appropriate lattice structure is used as the quantizer in the noise feedback loop. We also consider a switched structure based on using either a double frame quantizer or two single frame quantizers for two subsequent frames where an extra bit is used to specify the choice offering a lower distortion. Numerical results are presented showing an excellent performance with very low complexity.

We prevent methods for the multi-user interference cancellation in a code division multiple access (CDMA) system where turbo codes are utilized for forward error correction (FEC). In the proposed methods, the individual users are decoded separately with the operation of iterative interference cancellation being mixed with the iterative decoding of turbo codes. This results in a modest increase in the overall complexity as compared to a conventional single user receiver utilizing turbo codes. Numerical results are presented showing that in the cases of practical interest for CDMA applications, the multiple access interference can be essentially removed at a reasonable level of complexity. These iterative decoders achieve a similar to better performance with a substantial reduction in the complexity as compared to similar previously known research works.

In this article, a low bit-rate low-complexity block-based trellis quantization (BTQ) scheme is proposed for quantization of line spectral frequencies for speech coding applications. The branches in the trellis diagram correspond to the LSF difference code-words and the states correspond to quantized LSF parameters. An efficient algorithm for the index generation (finding the index of a path in the trellis) is introduced. The proposed BTQ achieves the transparent coding quality at 23 bits/frame (1150 b/sec.) and offers a gain of 3 b/frame (150 b/s) and significant reduction in complexity, compared to the IS-641 split-VQ. An interframe BTQ scheme is also presented to exploit the redundancies between the adjacent frames. The interframe scheme is found to achieve an additional 50 b/sec reduction of the bit-rate and is based on adaptive block-based trellis quantization of the prediction residues.

Turbo codes have enjoyed a great attention. Among different soft-output decoding algorithms of turbo codes only maximum a posteriori (MAP) decoding as an iterative soft-output decoder (BCJR) allows for achieving an acceptable BER performance at Eb/No levels within only 1 dB of the value corresponding to the Shannon capacity. The drawback of the MAP algorithm is the excessive memory required. Here, we investigate the so-called symbol-based turbo codes. These codes allow for a reduced required memory by 30% for the BCJR method.

Traditional turbo-codes with binary phase-shift keying modulation assign equal noise margins to the turbo-encoder output bits. It is shown that by using unequal power allocation (UPA) among the encoder output streams, one can improve the code performance especially for large block lengths. On the other hand, there has been a growing interest in the application of turbo-codes for signaling over a code-division multiple-access (CDMA) channel. A usual practice in CDMA systems for matching of rate is based on repeating the encoder output bits. This feature can be used to provide UPA with a negligible increase in the complexity. Simulation results are presented showing a noticeable improvement in the bit error rate performance.

This article discusses the problem of optimizing a lattice-based signal constellation for signaling over a partial response channel. The objective is to minimize the probability of error which is determined by the combined effects of the additive Gaussian noise and channel memory.

Upper and lower bounds are derived for the decoding complexity of a general lattice L. The bounds are in terms of the dimension n and the coding gain /spl gamma/ of L, and are obtained based on a decoding algorithm which is an improved version of Kannan's (1983) method. The latter is currently the fastest known method for the decoding of a general lattice. For the decoding of a point x, the proposed algorithm recursively searches inside an, n-dimensional rectangular parallelepiped (cube), centered at x, with its edges along the Gram-Schmidt vectors of a proper basis of L. We call algorithms of this type recursive cube search (RCS) algorithms. It is shown that Kannan's algorithm also belongs to this category. The complexity of RCS algorithms is measured in terms of the number of lattice points that need to be examined before a decision is made. To tighten the upper bound on the complexity, we select a lattice basis which is reduced in the sense of Korkin-Zolotarev (1873). It is shown that for any selected basis, the decoding complexity (using RCS algorithms) of any sequence of lattices with possible application in communications (/spl gamma//spl ges/1) grows at least exponentially with n and /spl gamma/. It is observed that the densest lattices, and almost all of the lattices used in communications, e.g., Barnes-Wall lattices and the Leech lattice, have equal successive minima (ESM). For the decoding complexity of ESM lattices, a tighter upper bound and a stronger lower bound result are derived.

This work considers a combined source-channel coding scheme for image transmission over the uplink of a wireless IS-95 CDMA channel using discrete cosine transform. By adjusting the dimension of the orthogonal signaling scheme, we trade the system error-correction capability for a faster bit rate. The increase in channel error is relieved by employing a set of quantizers which are designed using a joint source-channel optimization algorithm. The bit allocation problem of the quantizer array is solved by using a new approach based on the integer programming technique. Without bandwidth expansion, our proposed scheme results in a substantial improvement in the reconstructed image quality, especially for good channel condition.

Traditional turbo-codes with BPSK modulation scheme, use equal error protection (EEP) for the turbo-encoder output bits. In this paper, it is shown that the role of the encoder output bits is not necessarily the same in determining the code performance. Imposing unequal error protection (UEP) on the output bits can result in improvement of the turbo-code performance.

In the quantization of a non-uniform source, the entropy coding of the quantizer output can result in a substantial decrease in bit rate. A straight-forward entropy coding scheme faces us with the problem of variable data rate. A solution in a space of dimensionality N is to select a subset of elements in the N-fold cartesian product of a scalar quantizer and represent them with code-words of the same length. For a memoryless source, a reasonable rule is to select the N-fold symbols with the lowest additive self-information. The search/addressing of this scheme can no longer be achieved independently along the one-D subspaces. Fortunately, the selected subset has a high degree of structure which can be used to substantially decrease the complexity. We discuss a method based on dynamic programming to facilitate the search/addressing operations. We build our recursive structure required for the dynamic programming in a hierarchy of steps. This results in several benefits over the conventional trellis-based approaches. Using this structure, we develop efficient rules (based on merging the states) to substantially reduce the search/addressing complexities while keeping the degradation negligible. We choose the quantizer points from a lattice resulting in a higher granular gain in comparison with simply using the cartesian product of a set of scalar quantizers. We introduce a special class of lattices which have a low decoding complexity, and at the same time result in a noticeable granular gain. Examples are given of image coding.

In quantization of any source with a nonuniform probability density function, the entropy coding of the quantizer output can result in a substantial decrease in bit rate. A straightforward entropy coding scheme faces us with the problem of variable data rate. A solution in a space of dimensionality N is to select an appropriate subset of elements in the N-fold Cartesian product of a scalar quantizer and represent its elements with codewords of the same length. The drawback is that the search/addressing of this scheme can no longer be achieved independently along the one-dimensional subspaces. A reasonable rule is to select the N-fold symbols of the highest probability. For a memoryless source, this is equivalent to selecting the N-fold symbols with the lowest additive self-information. In this case, due to the additivity property of the self-information, the selected subset has a high degree of structure which can be used to substantially decrease the search/addressing complexity. A dynamic programming approach is used to exploit this structure. We build our recursive structure required for the dynamic programming in a hierarchy of levels. This results in several benefits over the conventional trellis-based approaches. Using this structure, we develop efficient rules (based on aggregating the states) to substantially reduce the search/addressing complexities while keeping the degradation in performance negligible.

We introduce an efficient addressing scheme for the nearly optimum shaping of a multidimensional signal constellation. The 2-D (two-dimensional) subspaces are partitioned into K energy shells of equal cardinality. The average energy of a 2-D shell can be closely approximated by a linear function of its index. In an N=2n-D space, we obtain K/sup n/ shaping clusters of equal cardinality. Shaping is achieved by selecting T/spl les/K/sup n/ of the N-D clusters with the least sum of the 2-D indices. This results in a set of T integer n-tuples with the components in the range [0, K-1] and the sum of the components being at most a given number L. The problem of addressing is to find a one-to-one mapping between the set of such n-tuples and the set of integers [0, T-1] such that the mapping and its inverse can be easily implemented. In the proposed scheme, the N-D clusters are grouped into blocks of identical binary weight vectors. This results in a simple rule for the addressing of points within the blocks. The addressing of the blocks is based on some recursive relationship which allows us to decompose the problem into simpler parts. The overall scheme requires a modest amount of memory and has a small computational complexity.

A method is developed to compute the weight distribution of a set of points obtained from a lattice. The lattice is scaled (with possibly nonequal factors) along different dimensions, is shifted to an arbitrary point, and its lower dimensional subspaces are truncated within given shaping regions. Each branch in the lattice trellis diagram is labeled by the weight distribution of the corresponding coset incorporating the effects of scaling, shifting, and truncation. The weight distribution is obtained by multiplying the weight distribution of the serial branches and then adding the result over parallel paths.>

We find analytical expressions for the block-based input and output eigenvectors and eigenvalues of the systems with responses 1/spl plusmn/d and 1-D/sup 2/. The input eigenvectors form an orthonormal basis which is the optimum modulator for a channel with that transfer function. The output eigenvectors form an orthonormal basis with the same spectral nulls as the corresponding system. This basis can be used to produce line codes with spectral nulls. The eigenvectors are sinusoids. This reduces the computational complexity by allowing for fast transform algorithms to perform the modulation for a block of data.>

This paper describes a lookup table for the addressing of an optimally shaped constellation. The method is based on partitioning the subconstellations into shaping macro-shells of integer bit rate and increasing average energy. The macro-shells do not need to have an equal number of points. A lookup table is used to select a subset of the partitions in the cartesian product space. By devising appropriate partitioning/merging rules, we obtain suboptimum schemes of very low addressing complexity and small performance degradation. The performance is computed using the weight distribution of an optimally shaped constellation.>

The structure of the regions which provide the optimum tradeoff between gamma /sub s/ (shaping gain) and CER (constellation-expansion ratio) and between gamma /sub s/ and PAR (peak to average power ratio) in a finite dimensional space is introduced. Analytical expressions are derived for the corresponding tradeoff curves. In general, the initial parts of the curves have a steep slope. This means that an appreciable portion of the maximum shaping gain, corresponding to a spherical region, can be achieved with a small value of CER/sub s/, PAR. The technique of shell mapping is introduced. This is a change of variable which maps the optimum shaping region to a hypercube truncated within a simplex. This mapping is a useful tool in computing the performance, and also in facilitating the addressing of the optimum shaping region. Using the shell mapping, a practical addressing scheme is presented that achieves a point on the optimum tradeoff curves. For dimensionalities around 12, the point achieved is located near the knee of the corresponding tradeoff curve. For larger dimensionalities, a general shaping region with two degrees of freedom is used. This region provides more flexibility in selecting the tradeoff point.>

For Pt. I, see ibid., pp. 1799-1808, Nov. 1993. By appropriately selecting the boundary of a multidimensional signal constellation used for data transmission, the average energy of the constellation can be reduced. Reduction in the average energy (shaping gain) is obtained at the price of increasing the constellation-expansion ratio (CER/sub s/) and the peak-to-average-power ratio (PAR). The authors describe some practical means for selecting the boundary so as to achieve a point with low addressing complexity near the knee of the corresponding tradeoff curves (shaping gain versus CER/sub s/ or PAR). One class of addressing schemes is based on using a lookup table. A method to facilitate the realization of the addressing lookup table is introduced. This method is based on the decomposition of addressing into a hierarchy of addressing steps, each of a low complexity. This avoids exponential growth of the complexity. Using this addressing decomposition and a memory of a practical size, one can move along a tradeoff curve which has negligible suboptimality. Another class of addressing schemes is based on using a Voronoi constellation in a space of half the original dimensionality.>