International audience

Synchronization errors, including insertions, deletions, and substitutions, may occur in bursts in communication systems such as DNA data storage, file synchronization, and magnetic recording. In this paper, we study an error model con?sisting of one burst of t-deletions and one burst of t-substitutions. By reformulating the original sequence into a matrix form, we propose an explicit construction of error-correcting codes capable of correcting one burst of t-deletions and one burst of t-substitutions with O(log n) redundancy.

Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating the development of channel codes that can correct such errors. In this paper, we construct error-correcting codes (ECCs) capable of handling multiple bursts of t1-deletion-t2-insertion ((t1, t2)-DI) errors, where each burst consists of t1 deletions followed by t2 insertions in a binary sequence. We make three key contributions: First, we establish the fundamental equivalence among (i) ECCs correcting two bursts of (t1, t2)-DI errors, (ii) ECCs correcting two bursts of (t2, t1)-DI errors, and (iii) ECCs correcting one burst of (t1, t2)-DI together with one burst of (t2, t1)-DI errors. Then, we derive lower and upper bounds on the code size of two-burst (t1, t2)-DI ECCs, which can naturally be extended to the case of multiple bursts. Finally, we present constructions of ECCs correcting two bursts of (t1, t2)-DI errors. Compared with codes obtained via the direct application of the syndrome compression technique, the proposed constructions achieve substantially improved computational efficiency.

Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-burst deletion-correcting codes. Specifically, we first characterize several structural properties of the associated deletion balls. Then, leveraging these properties, we derive several upper bounds and a combinatorial lower bound on the maximum size of such codes. As a consequence, our bounds improve upon the previously known results for general parameter regimes and are shown to be asymptotically optimal for certain cases.

Synchronization errors, such as insertions and deletions, pose significant challenges in communication and storage systems, including DNA data storage. Among different alternatives, serially concatenated coding schemes, where a powerful outer code is concatenated with an inner marker code, have proven effective in mitigating such errors. A common method of decoding the inner marker code is to employ the forward-backward algorithm implementing bitwise or symbolwise maximum a posteriori (MAP) detection. Recently, bit-level deep-learning based solutions have also been proposed for decoding marker codes. In this paper, we consider symbol-level deep-learning based decoders, which exploit correlations among adjacent bits to improve the decoding performance, and develop new channel detection algorithms. Unlike existing symbol-level MAP decoding approaches that can combine only two or three consecutive bits, the proposed deep-learning methods extend well beyond this limit, and achieve improved error correction performance. We also develop deep-learning based decoders for insertion/deletion channels further exacerbated by intersymbol interference, motivated by bit-patterned media recording channels and nanopore sequencing. Extensive numerical results show that the proposed symbol-level deep-learning architectures are highly effective for communication over insertion/deletion channels.

We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse bound, which, though available for any channel, is inefficient and not easily computable without a good reference distribution over the output alphabet. We obtain a reference output distribution for a general finite-input finite-output channel and provide a simple formula for the converse bound on the capacity employing this distribution. We then evaluate the bound for the deletion channel with a finite block length, and show that the resulting upper bound on the code size is tighter than that for a binary erasure channel, which is the only alternative converse bound for this finite-length setting. We also provide similar results for the insertion channel. Furthermore, we present a simple algorithm for computing an achievability bound for a general discrete-input discrete-output channel. Although the algorithm has exponential complexity, it is useful for comparison purposes.

Particularly motivated by DNA data storage systems, we consider channels with synchronization errors modeled as insertions and deletions, along with substitutions. We focus on the case where the synchronization error process has memory and investigate the information stability of these channels, hence the existence of their Shannon capacity. We assume that the synchronization errors are governed by a stationary and ergodic finite-state Markov chain and prove that such a channel is information-stable, which implies the existence of a coding scheme that achieves the limit of mutual information. This result implies the existence of the Shannon capacity for a wide range of channels with synchronization errors, with implications for various applications.We also provide specific examples of deletion channels with Markov memory and numerically evaluate their capacity bounds, thereby allowing us to quantify the capacity difference between memoryless deletion channels and those with memory, with the same deletion probability, and to reveal that having memory increases the channel capacity.

Channels with synchronization errors, exhibiting deletion and insertion errors, find practical applications in DNA storage, data reconstruction, and various other domains. The presence of insertions and deletions renders the channel with memory, complicating capacity analysis. For instance, despite the formulation of an independent and identically distributed (i.i.d.) deletion channel more than fifty years ago, and proof that the channel is information stable, hence its Shannon capacity exists, calculation of the capacity remained elusive. However, a relatively recent result establishes the capacity of the deletion channel in the asymptotic regime of small deletion probabilities by computing the dominant terms of its capacity expansion. This paper extends that result to binary insertion channels, determining the dominant terms of the channel capacity for small insertion probabilities and establishing capacity in this asymptotic regime. Specifically, we consider two i.i.d. insertion channel models: the simple insertion channel, where a random bit may be inserted after each transmitted bit, and the Gallager insertion model, for which a bit is replaced by two random bits with a certain probability. To prove our results, we build on methods used for the deletion channel, employing Bernoulli(1/2) inputs for achievability and coupling this with a converse using stationary and ergodic input processes, and show that the channel capacity differs only in the higher order terms from the achievable rates with i.i.d. inputs. The results, for instance, show that the capacity of the simple insertion channel is higher than that of the Gallager insertion channel, and quantify the difference in the asymptotic regime.

DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence, we propose constrained codes with polynomial-time encoding and decoding algorithms. Compared to the existing works, our codes simultaneously satisfy both$\ell$-runlength limited and$\epsilon$balanced constraints. By enumerating all valid sequences, our codes achieve the maximum rate, matching the capacity. Additionally, we design constrained error-correcting codes capable of correcting one insertion or deletion in the obtained DNA sequence while still adhering to the constraints.

We develop the first non-asymptotic upper bound on code size for the deletion channel for a given code length and target error probability. The bound is obtained as a variation of a general converse bound, which, though available for any channel, is inefficient and not easily computable without a good reference distribution over the output alphabet. We obtain a reference output distribution for a general finite-input finite-output channel and provide a simple formula for the converse bound on the capacity employing this distribution. We then evaluate the bound for the binary deletion channel with a finite block length and show that the resulting upper bound on the code side is tighter than that for a binary erasure channel, which is the only alternative converse bound for this finite-length setting.

Channels with synchronization errors, such as deletions and insertions, are encountered in DNA storage, data reconstruction, and other applications. These errors introduce memory to the channel, complicating its capacity analysis. As an example of synchronization error channels, this paper analyzes binary insertion channels for small insertion probabilities, identifying dominant terms of the capacity expansion, and hence establishing its capacity in this regime. This is accomplished by using independent and identically distributed (i.i.d.) Bernoulli$(1/2)$inputs for achievability and a converse based on the use of stationary and ergodic processes that match closely with each other, differing only in higher-order terms.

We consider binary input deletion/substitution channels, which model certain types of synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an approach developed for the deletion-only channel, we obtain an asymptotic characterization of the channel capacity for independent and identically distributed (i.i.d.) deletion/substitution channels. To do so, given a target probability of successful decoding, we first develop an upper bound on the codebook size for arbitrary but fixed numbers of deletions and substitutions, and then extend the result to the case of random deletions and substitutions to obtain a bound on the channel capacity. Our final result is: The i.i.d. deletion/substitution channel capacity is approximately 1 − H(pd) − H(ps), for pd, ps≈ 0, where pdand psare the deletion and substitution probabilities, respectively.

We present an alternative take on the recently popularized concept of ‘joint sensing and communications’, which focuses on using communication resources also for sensing. Here, we propose the opposite, where we utilize the receiver’s sensing capabilities for communication. Our goal is to characterize the fundamental limits of communication over such a channel, which we call ‘communication via sensing’. We assume that changes in the sensed attributes, such as location and speed, are limited due to practical constraints, which are captured by assuming a finite-state channel (FSC) with an input cost constraint. We first formulate an upper bound on the N-letter capacity as a cost-constrained optimization problem over the input sequence distribution, and then convert it to an equivalent problem over the state sequence distribution. Moreover, by breaking a walk on the underlying Markov chain into a weighted sum of traversed graph cycles in the long walk limit, we obtain a compact single-letter formulation of the capacity upper bound. Finally, for a specific case of a two-state FSC with noisy sensing characterized by a binary symmetric channel (BSC), we obtain a closed-form expression for the capacity upper bound. Comparison with an existing numerical lower bound shows that our proposed upper bound is very tight for all crossover probabilities.

We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into non-overlapping segments, each of which may experience at most one burst of deletions. In this paper, we develop error correction codes for segmented burst-deletion channels over arbitrary alphabets under the assumption that each segment may contain only one burst of t-deletions. The main idea is to encode the input subsequence corresponding to each segment using existing one-burst deletion codes, with additional constraints that enable the decoder to identify segment boundaries during the decoding process from the received sequence. The resulting codes achieve redundancy that scales as O(log b), where b is the length of each segment.

Goal-oriented semantic communications and signal processing are foreseen to play a key role in advancing future communication networks. Leveraging recent advances in machine learning (ML) techniques and artificial intelligence (AI), research is shifting towards intelligent end-to-end systems that can extract relevant semantic information and transmit only when necessary. It was recently proposed that graph languages representing semantic information can be modeled using a hidden semi-Markov model (HSMM) for smoothing, learning, and fusion algorithms. This paper aims to build upon this HSMM framework for multi-sensor goal-oriented semantic communications and proposes an expectation-maximization (EM) algorithm to learn the underlying semantic model by incorporating multi-sensor observations and handling missing data. The results show that the proposed algorithm learns the semantic model by utilizing the set of observations and effectively mitigates the effects of missing observations.

We propose novel fusion algorithms based on hidden semi-Markov models (HSMMs) for robust goal-oriented signal processing in wireless sensor networks with noisy and missing data. We extend the prior work that models the temporal evolution of semantic information as an HSMM to handle practical challenges encountered in massive machine-type communication (mMTC) scenarios. Our first contribution is to introduce a method to statistically model missing observations by adjusting the emission probabilities of the HSMM, enabling the system to continue functioning even in the event of sensor failure. Secondly, by integrating signals from multiple sensors whose observations are conditionally independent given the semantic state and using their joint likelihoods, we develop HSMM-based fusion solutions using the Viterbi and forward-backward algorithms. The effectiveness of the proposed approach is validated by extensive simulation results, demonstrating notable improvements in hidden semantic state estimation even with high sensor error and missing data rates. These findings highlight the potential of HSMM-based fusion for enhancing robustness in semantic communication systems for 6G and beyond.

Considering the demanding requirements of 6G integrated sensing and communication (ISAC) applications [1], we propose a radar-centric ISAC system design methodology. This approach is enabled by semantic downlink communication within the goal-oriented semantic signal processing framework [2] and incorporates an improved monopulse direction-finding (MDF) technique for accurate direction-finding. In addition, the computational complexity analysis of the proposed MDF method is also provided. The proposed scheme employs frequency-modulated continuous wave radar signals and differential phase-shift keying. In a case study, we demonstrate an example ISAC system design and show that the proposed MDF technique outperforms the state-of-the-art. Furthermore, we demonstrate the communication performance of the proposed scheme under 3GPP tapped delay line and clustered delay line channel models [3] and show that the communication performance is robust to the choice of radar waveform.

International audience

International audience

To accommodate new applications such as extended reality, fully autonomous vehicular networks and the metaverse, next generation wireless networks are going to be subject to much more stringent performance requirements than the fifth-generation (5G) in terms of data rates, reliability, latency, and connectivity. It is thus necessary to develop next generation advanced transceiver (NGAT) technologies for efficient signal transmission and reception. In this tutorial, we explore the evolution of NGAT from three different perspectives. Specifically, we first provide an overview of new-field NGAT technology, which shifts from conventional far-field channel models to new near-field channel models. Then, three new-form NGAT technologies and their design challenges are presented, including reconfigurable intelligent surfaces, flexible antennas, and holographic multi-input multi-output (MIMO) systems. Subsequently, we discuss recent advances in semantic-aware NGAT technologies, which can utilize new metrics for advanced transceiver designs. Finally, we point out other promising transceiver technologies for future research.

The noisy shuffling channel models the conditions encountered in DNA storage systems, where transmitted data segments experience random permutation and substitution errors. Reliable communication over this channel requires effective indexing and channel coding strategies for segment order restoration and error correction. This paper introduces a concatenated coding approach for communication over the noisy shuffling channel using Reed-Solomon (RS) codes as outer codes and polar codes as inner codes. A coset-based indexing method, derived from polar codes, is proposed. A joint decoder is designed to detect the permutation pattern and perform polar decoding simultaneously. An upper bound on the frame error rate (FER) is derived when minimum distance decoding is employed for decoding. Also, an approximate analysis of the FER using random coding is conducted. A mapping between the cosets of the polar code and subsets of its frozen bits is established to design cosets achieving lower FERs compared to a commonly used explicit indexing method. Furthermore, a low-complexity decoding approach is devised, providing a trade-off between the computational complexity of the joint decoder and its performance.

This paper considers an unsourced random access (URA) set-up equipped with a passive reconfigurable intelligent surface (RIS), where a massive number of unidentified users (only a small fraction of them being active at any given time) are connected to the base station (BS). We introduce a slotted coding scheme for which each active user chooses a slot at random for transmitting its signal, consisting of a pilot part and a randomly spread polar codeword. The proposed decoder operates in two phases. In the first phase, called the RIS configuration phase, the BS detects the transmitted pilots. The detected pilots are then utilized to estimate the corresponding users’ channel state information, using which the BS suitably selects RIS phase shift employing the proposed RIS design algorithms. The proposed channel estimator offers the capability to obtain the channel coefficients of the users whose pilots interfere with each other without prior access to the list of transmitted pilots or the number of active users. In the second phase, called the data phase, transmitted messages of active users are decoded. Moreover, we establish an approximate achievability bound for the RIS-based URA scheme, providing a valuable benchmark. Computer simulations show that the proposed scheme outperforms the state-of-the-art RIS-aided URA.

We investigate the unsourced random access scheme assuming that the base station is equipped with multiple antennas, and propose a high-performing solution utilizing on-off-division multiple access. We assume that each user spreads its pilot sequence and polar codeword to the pilot and data parts of the transmission frame, respectively, based on a transmission pattern. The iterative receiver operation consists of pilot and pattern detection followed by channel vector and symbol estimation, polar decoding, and successive interference cancellation. Numerical findings demonstrate that the proposed scheme has superior performance compared to the state-of-the-art in various antenna settings.

In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional or a low-density parity-check (LDPC) code, and the inner code is a marker code. We utilize Bidirectional Gated Recurrent Units (BI-GRUs) as log-likelihood ratio (LLR) estimators and outer code decoders for estimating the message bits. Our results indicate that decoders powered by BI-GRUs perform comparably in terms of error rates with the MAP detection of the marker code. We also find that a single network can work well for a wide range of channel parameters. In addition, it is possible to use a single BI-GRU based network to estimate the message bits via one-shot decoding when the outer code is a convolutional code.11Code is available at https://github.com/Bilkent-CTAR-Lab/DNN-for-Deletion-Channel

We consider channels with synchronization errors. A classical result for such channels is their information stability, when the synchronization errors are memoryless. In this paper, we extend this result to the case where the synchronization errors have memory. Specifically, we assume that the synchronization errors are governed by a stationary and ergodic finite state Markov chain, and prove that such channel is information-stable, which implies the existence and achievability of the limit of normalized mutual information. This result applies to a wide range of channels with synchronization errors, with different applications including DNA storage. The developed methodology may also be useful to prove other coding theorems for non-trivial channel sequences.

We study the problem of unsourced random access (URA) over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We propose a slotted structure with multiple stages of orthogonal pilots, each of which is randomly picked from a codebook. In the proposed signaling structure, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. Accordingly, the transmitted signal is composed of multiple orthogonal pilot parts and a polar-coded part, which is sent through a randomly selected slot. The performance of the proposed scheme is further improved by randomly dividing users into different groups each having a unique interleaver-power pair. We also apply the idea of multiple stages of orthogonal pilots to the case of a single receive antenna. In all the set-ups, we use an iterative approach for decoding the transmitted messages along with a suitable successive interference cancellation technique. The use of orthogonal pilots and the slotted structure lead to improved accuracy and reduced computational complexity in the proposed set-ups, and make the implementation with short blocklengths more viable. Performance of the proposed set-ups is illustrated via extensive simulation results which show that the proposed set-ups with multiple antennas perform better than the existing MIMO URA solutions for both short and large blocklengths, and that the proposed single-antenna set-ups are superior to the existing single-antenna URA schemes.

We examine federated learning (FL) with over-the-air (OTA) aggregation, where mobile users (MUs) aim to reach a consensus on a global model with the help of a parameter server (PS) that aggregates the local gradients. In OTA FL, MUs train their models using local data at every training round and transmit their gradients simultaneously using the same frequency band in an uncoded fashion. Based on the received signal of the superposed gradients, the PS performs a global model update. While the OTA FL has a significantly decreased communication cost, it is susceptible to adverse channel effects and noise. Employing multiple antennas at the receiver side can reduce these effects, yet the path-loss is still a limiting factor for users located far away from the PS. To ameliorate this issue, in this paper, we propose a wireless-based hierarchical FL scheme that uses intermediate servers (ISs) to form clusters in the areas where the MUs are more densely located. Our scheme utilizes OTA cluster aggregations for the communication of the MUs with their corresponding IS, and OTA global aggregations from the ISs to the PS. We present a convergence analysis for the proposed algorithm, and show through numerical evaluations of the derived analytical expressions and experimental results that utilizing ISs results in a faster convergence and a better performance than the OTA FL alone while using less transmit power. We also validate the results on the performance using different numbers of cluster iterations with different datasets and data distributions. We conclude that the best choice of cluster aggregations depends on the data distribution among the MUs and the clusters.

We consider unsourced random access over fading channels with a massive number of antennas at the base station, and propose a simple, yet energy-efficient solution by dividing the transmission frame into slots. We utilize non-orthogonal pilot sequences followed by a polar codeword for transmission in each slot. At the receiver side, we first detect the transmitted pilot sequences by employing a generalized orthogonal matching pursuit algorithm and utilize a linear minimum mean square error solution to estimate the channel vectors. We then perform an iterative decoding based on maximal ratio combining, single-user polar decoding, and successive interference cancellation with re-estimation of the channel vectors to recover the data bits. We also analyze the performance of the proposed scheme using normal approximations and provide a detailed complexity analysis. Numerical examples demonstrate that the proposed scheme either outperforms the existing schemes in the literature or has a competitive performance with a lower complexity. Furthermore, it is suitable for fast-fading scenarios due to its excellent performance in the short blocklength regime.

This paper considers an unsourced random access (URA) setup equipped with a passive reconfigurable intelligent surface (RIS), where a massive number of unidentified users (of which only a small fraction are active at a given time) share the same communication resources. We propose a slotted transmission scheme that operates in two phases. In the first phase, called the RIS configuration phase, the base station (BS) detects the active pilots and estimates their respective channel state information (CSI). Then, using the estimated CSI, the BS suitably selects the phase shifts of the RIS elements. In the second phase, called the data phase, transmitted messages of active users are decoded. The proposed channel estimator offers the capability to estimate the channel coefficients of the users whose pilots interfere with each other without prior access to the list of selected pilots or the number of active users. In this paper, we consider the direct link between the users and the BS to be completely blocked, and show that employing RIS improves the performance of the URA system by creating additional links between the BS and the users. The effectiveness of the proposed algorithms is confirmed through computer simulations.

We consider orthogonal frequency division multi-plexing (OFDM) over frequency-selective channels without cyclic prefix (CP) insertion. We design a specific recurrent neural network utilizing gated recurrent units to mitigate the effects of inter-symbol interference and inter-carrier interference for improved symbol detection. Numerical examples demonstrate that the proposed deep neural network outperforms conventional equalizers for CP-free OFDM in terms of bit error rate. Moreover, through block error rate simulations, we show that the proposed solution yields higher performance compared to OFDM systems with sufficiently long CP when the multipath spread is high, hence the new approach offers significant potential for enhancing the spectral efficiencies for certain wireless communication scenarios.

Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments, practical indexing and channel coding strategies are required to restore the order and combat the channel noise. In this paper, we develop a finite-length concatenated coding scheme that employs Reed-Solomon (RS) codes as outer codes and polar codes as inner codes, and utilizes an implicit indexing method based on cosets of the polar code. We propose a matched decoding method along with a metric for detecting the index that successfully restores the order, and correct channel errors at the receiver. Residual errors that are not corrected by the matched decoder are then corrected by the outer RS code. We derive analytical approximations for the frame error rate of the proposed scheme, and also evaluate its performance through simulations to demonstrate that the proposed implicit indexing method outperforms explicit indexing.

We consider unsourced random access for which the base station is equipped with a massive number of antennas and there are residual hardware impairments at both the base station and the user equipment. We divide the transmission frame into slots where each user sends a non-orthogonal pilot selected based on part of its message bits followed by its data bits encoded by a polar code. At the receiver side, we first identify the selected pilot sequences by a generalized orthogonal matching pursuit algorithm and estimate the user channels employing a newly developed hardware-impairment aware linear minimum mean-squared error solution. We then perform symbol estimation by maximal ratio combining and data decoding by a single-user polar decoder followed by successive interference cancellation in an iterative fashion. Numerical examples illustrate that hardware impairments degrade the system performance; however, the proposed solution alleviates this loss in terms of both energy efficiency and the number of supported active users.

Deep neural networks offer reliable solutions for many classification and regression tasks; however, their applicability in real-time wireless applications with simple sensor networks is limited due to the significant amount of bandwidth required for data transmission. In this study, we propose a multisensor wireless inference system where an edge device combines features sensed by different sensors. Due to the limited computational capabilities of sensors, the features obtained through the front part of the network are transmitted to the edge device, which uses Lp-norm inspired and LogSumExp (LSE) approximations for the maximum operation to obtain transformation-invariant features. These features can be transmitted in an over-the-air manner, ensuring bandwidth-efficient transmission. We also consider multi-modal network branches for sensors based on their computational capabilities, improving the overall performance by using data obtained from both computationally limited and powerful devices enhancing the usefulness of the overall sensed data.

We develop bounds on the capacity of Poisson-repeat channels (PRCs) for which each input bit is independently repeated according to a Poisson distribution. The upper bounds are obtained by considering an auxiliary channel where the output lengths corresponding to input blocks of a given length are provided as side information at the receiver. Numerical results show that the resulting upper bounds are significantly tighter than the best known one for a large range of the PRC parameter λ (specifically, for λ ≥0.35). We also describe a way of obtaining capacity lower bounds using information rates of the auxiliary channel and the entropy rate of the provided side information.

Semantic signal processing and communications are poised to play a central part in developing the next generation of sensor devices and networks. A crucial component of a semantic system is the extraction of semantic signals from the raw input signals, which has become increasingly tractable with the recent advances in machine learning (ML) and artificial intelligence (AI) techniques. The accurate extraction of semantic signals using the aforementioned ML and AI methods, and the detection of semantic innovation for scheduling transmission and/or storage events are critical tasks for reliable semantic signal processing and communications. In this work, we propose a reliable semantic information extraction framework based on our previous work on semantic signal representations in a hierarchical graph-based structure. The proposed framework includes a time integration method to increase fidelity of ML outputs in a class-aware manner, a graph-edit-distance based metric to detect innovation events at the graph-level and filter out sporadic errors, and a Hidden Markov Model (HMM) to produce smooth and reliable graph signals. The proposed methods within the framework are demonstrated individually and collectively through simulations and case studies based on real-world computer vision examples.

We consider orthogonal frequency division multiplexing over rapidly time-varying multipath channels, for which performance of standard channel estimation and equalization techniques degrades dramatically due to inter-carrier interference (ICI). We focus on improving the overall system performance by designing deep neural network (DNN) architectures for both channel estimation and data demodulation. To accomplish this, we employ the basis expansion model to track the channel tap variations, and exploit convolutional neural networks’ learning abilities of local correlations together with a coarse least square solution for a robust and accurate channel estimation procedure. For data demodulation, we use a recurrent neural network for improved performance and robustness as single tap frequency-domain equalizers perform poorly, and more sophisticated equalization techniques such as band-limited linear minimum mean squared error equalizers are vulnerable to model mismatch and channel estimation errors. Numerical examples illustrate that the proposed DNN architectures outperform the traditional algorithms. Specifically, the bit error rate results for a wide range of Doppler values reveal that the proposed DNN-based equalizer is robust, and it mitigates the ICI effectively, offering an excellent demodulation performance. We further note that the DNN-based channel estimator offers an improved performance with a reduced computational complexity.

We analyze the performance of Coded Slotted ALOHA (CSA) protocols in scenarios where users are equipped with limited batteries that are recharged through Energy Harvesting (EH). First, we assume a Perfect Packet Recovery Scenario (PPRS) for which the received packets are decoded with no errors when there is no interference. We introduce Battery Outage Probability (BOP) as an extra performance metric; and, we derive the optimal EH-CSA transmission policies, which offer the maximum attainable traffic load while maintaining an asymptotically negligible Packet Loss Ratio (PLR), under specific rate and BOP constraints. We extend our study to Imperfect Packet Recovery Scenario (IPRS) where impairments at the physical layer, including channel estimation and channel decoding errors, will distort messages being passed through the iterative Successive Interference Cancellation (SIC) process. The distorted messages being passed through the SIC process potentially lead to error propagation. In order to track the error propagation process, we define the concept ofAccumulated Noise plus Interference Power(ANIP), and analytically track the evolution of its probability distribution. We employ our results to evaluate the bit error rates for different transmission policies for the case of IPRS. We also demonstrate the advantages of the optimal transmission policies through numerical examples for both PPRS and IPRS. Our results show that the optimal EH-CSA policies outperform the policies optimized for standard CSA without EH considerations, and the schemes that are optimal for PPRS are not necessarily optimal for the IPRS case. Furthermore, the EH-CSA optimal policies strictly outperform standard CRDSA when the system is required to support higher traffic loads.

We present a decentralized feedback-aided Irregular Repetition Slotted ALOHA (IRSA) scheme that improves energy efficiency. The scheme divides the IRSA MAC frame into several sub-frames, performs tentative decoding after each sub-frame, and uses limited feedback for users to detect whether their packet has been decoded at the receiver. Once a user detects that its packet is decoded, it stops transmitting its remaining replicas, resulting in a decrease in the expected number of transmitted packet replicas and an increase in energy efficiency. For analysis, we employ a graph-based representation of the successive interference cancellation decoding of IRSA. We prove several results for a fixed graph, and extend our analysis to a randomly selected graph to derive the efficiency of the proposed scheme. Numerical results show that the proposed feedback-aided IRSA solution outperforms standard IRSA and performs similarly to the best known Coded Slotted ALOHA (CSA) schemes. Also, the proposed scheme achieves efficiencies significantly larger than the threshold of 0.5 which is an upper bound for standard IRSA.

We consider the downlink of a multiuser system operating in the time-division duplexing mode, for which base station (BS) and users are equipped with multiple antennas, and provide a robust precoding/combining design against imperfect channel state information (CSI) and calibration errors due to hardware mismatch. Towards this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean squared error optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and the user sides. We also provide asymptotic closed-form expressions for the mean squared error (MSE) and the achievable sum-rate in the massive MIMO regime. The results indicate that while the MSE linearly increases with the calibration errors at the user side, the sum-rate is asymptotically independent of them. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions while having the same order of complexity. Moreover, when the BS sends a quantized version of the combining coefficients to the users, it is observed that the proposed solution is more robust to the quantization errors than the existing algorithms.

We study federated learning (FL) with over-the-air aggregation over time-varying wireless channels. Independent workers compute local gradients based on their local datasets and send them to a parameter server (PS) through a time-varying multipath fading multiple access channel via orthogonal frequency-division multiplexing (OFDM). We assume that the workers do not have channel state information, hence the PS employs multiple antennas to alleviate the fading effects. Wireless channel variations result in inter-carrier interference, which has a detrimental effect on the performance of OFDM systems, especially when the channel is rapidly varying. We examine the effects of the channel time variations on the convergence of the FL with over-the-air aggregation, and show that the resulting undesired interference terms have only limited destructive effects, which do not prevent the convergence of the learning algorithm. We also validate our results via extensive simulations, which corroborate the theoretical expectations.

We consider federated edge learning among mobile devices that harvest the required energy from their surroundings, and share their updates with the parameter server (PS) through a shared wireless channel. In particular, we consider energy harvesting FL with over-the-air (OTA) aggregation, where the participating devices perform local computations and wireless transmission only when they have the required energy available, and transmit the local updates simultaneously over the same channel bandwidth. In order to prevent bias among the heterogeneous devices, we utilize a weighted averaging with respect to their latest energy arrivals and data cardinalities. We provide a convergence analysis and carry out numerical experiments with different energy arrival profiles, which show that the proposed scheme is robust against heterogeneous energy arrivals in error-free scenarios while having less than 10% performance loss for fading channels.

We consider unsourced random access over fading channels with a massive number of antennas at the base station and propose a simple yet energy-efficient solution by dividing the transmission frame into slots where each slot is also divided into pilot and data parts. We utilize non-orthogonal pilot sequences selected based on part of the information bits, and encode the remaining message bits with a polar code for transmission. At the receiver side, we first detect the transmitted pilot sequences by employing the generalized orthogonal matching pursuit algorithm, and utilize a linear minimum mean square error solution to estimate the channel vectors. We perform symbol estimation by maximal ratio combining, and pass the symbol estimates to a single-user polar decoder to recover the data bits with succes-sive cancellation list decoding, along with successive interference cancellation at the end of each iteration. Numerical examples demonstrate that the proposed scheme either outperforms the existing schemes in the literature, or has a lower complexity while achieving a comparable performance.

We consider the downlink of a multiuser multiple-input multiple-output (MIMO) system operating in the time-division duplexing (TDD) mode. In this mode, assuming reciprocity, the channel coefficients estimated during the uplink channel training are utilized by the base station (BS) in the downlink data transmission. However, due to hardware mismatches, the uplink and downlink channels are not exactly the same, and therefore, there are calibration errors, which degrade the system performance. In this paper, our goal is to provide a transceiver design which has a robust performance under imperfect channel reciprocity. To this end, we first formulate a robust joint precoder and combiner design as a stochastic minimum mean square error (MMSE) optimization problem. Then, employing an alternating optimization approach, we propose an algorithm to obtain the precoding and combining matrices assuming imperfect CSI and calibration errors at both the BS and user sides. Extensive simulation results show that the proposed robust joint precoder/combiner outperforms the existing solutions in the literature.

Federated learning (FL) over wireless communication channels, specifically, over-the-air (OTA) model aggregation framework is considered. In OTA wireless setups, the adverse channel effects can be alleviated by increasing the number of receive antennas at the parameter server (PS), which performs model aggregation. However, the performance of OTA FL is severely limited by the presence of mobile users (MUs) located far away from the PS. In this paper, to mitigate this limitation, we propose hierarchical over-the-air federated learning (HOTAFL), which utilizes intermediary servers (IS) to form clusters near MUs. We provide a convergence analysis for the proposed setup, and demonstrate through experimental results that local aggregation in each cluster before global aggregation leads to a better performance and faster convergence than OTA FL.

We study the problem of unsourced random access (URA) over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We employ multiple stages of orthogonal pilots, each of which is randomly picked from a codebook. In the proposed scheme, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. Accordingly, the received signal consists of superposition of the users’ signals each composed of multiple orthogonal pilot parts and a polar coded part. We use an iterative approach for decoding the transmitted messages along with a suitable successive interference cancellation scheme. Performance of the proposed scheme is illustrated via extensive set of simulation results which show that it significantly outperforms the existing approaches for URA over multiple-input multiple-output fading channels.

Irregular Repetition Slotted ALOHA (IRSA) achieves load thresholds very close to 1 at the expense of reduced energy efficiency compared to its competitor, Coded Slotted ALOHA (CSA). The efficiency is related to the expected number of transmitted replicas, and is upper-bounded by 0.5 in the case of IRSA. In this paper, we present a feedback-aided IRSA scheme, analyze its efficiency, and show that utilizing a very limited feedback will offer considerable improvements. Remarkably, the feedback-aided scheme enables IRSA to achieve efficiencies greater than 0.5, and in some cases, perform very close to the more complex CSA schemes.

Polarization-adjusted convolutional (PAC) codes combine polar and convolutional transformations to enhance the distance properties of polar codes. They offer a performance very close to the finite-length information-theoretic bounds for short blocklengths. In this paper, we develop a method of computing the weight distribution of PAC codes in an approximate form by employing a probabilistic technique. We demonstrate that the results well match the exact weight distributions for small codes that can be computed using a brute-force algorithm. We also present a way of employing the results (along with a union bound on the code performance) to design specific PAC codes or, more precisely, to determine suitable rate profiles via simulated annealing. Numerical examples illustrate that the PAC codes with the designed rate profiles offer superior performance.

Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for the computations at the agents is affected by the availability of local resources and/or poor channel conditions, thus giving rise to the “straggler problem.” In this paper, we address this problem for distributed approximate matrix multiplication. In particular, we employ Unequal Error Protection (UEP) codes to obtain an approximation of the matrix product to provide higher protection for the blocks with a higher effect on the multiplication outcome. We characterize the performance of the proposed approach from a theoretical perspective by bounding the expected reconstruction error for matrices with uncorrelated entries. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN) for an image classification task in the evaluation of the gradients. Our numerical experiments show that it is indeed possible to obtain significant improvements in the overall time required to achieve DNN training convergence by producing approximation of matrix products using UEP codes in the presence of stragglers.

As a building block toward a simple and scalable solution for massive random access, we introduce collision-resolution algorithms using successive interference cancellation (SIC) based on the received signals, with no need for any coordination or codebook differentiation. We first consider two-user multiple access with the ZigZag algorithm. We prove that the original ZigZag and a modified version of it, calleddouble-zipper ZigZag, attain the same performance as the optimal coordinated time-sharing in the high signal to noise ratio (SNR) regime, even in the presence of channel state information (CSI) errors. We then extend the results to the case of arbitrary number of users employing delay-domain processing. Specifically, we introduce delay-domain zero forcing and its regularized version, which are able to cancel and suppress the interference among users, respectively. By obtaining a post-processing system model and characterizing the accumulated noise during the decoupling process, we also derive bounds on the achievable sum-rates of the proposed algorithm for both cases of perfect and imperfect CSI. Simulation results show that the newly proposed approach have comparable performance with coordinated time-sharing at high SNRs.

We study federated learning over wireless channels where a massive dataset is distributed across independent workers which compute their local gradients based on their own datasets. Workers send their gradients through a multipath fading multiple access channel with orthogonal frequency division multiplexing to mitigate the frequency selectivity of the channel. We assume that there is no channel state information (CSI) at the workers, and the parameter server (PS) employs multiple antennas to align the received signals. To reduce the power consumption and hardware costs, we employ complex-valued low-resolution analog-to-digital converters (ADCs) at the receiver side, and study the effects of practical low-cost ADCs on the learning performance. Our results show that the impairments caused by low-resolution ADCs, including those of one-bit ADCs, do not prevent the convergence of the federated learning algorithm, and the multipath channel effects vanish when a sufficient number of antennas are used at the PS.

We study distributed machine learning (ML) sys-tems where independent workers compute local gradients based on their local datasets and send them to a parameter server (PS) through a time-varying multipath fading multiple access channel (MAC) via orthogonal frequency-division multiplexing (OFDM). We assume that the workers do not have channel state information (CSI), and hence the PS employs multiple antennas to remove the fading effects. Time variations in the wireless channel result in inter-carrier interference (ICI), which has a detrimental effect on the performance of OFDM systems, especially when the channel variations are rapid. To examine the effects of channel variations on federated learning systems, we perform an analysis of the interference in the aggregate gradient term at the PS due to Doppler, and show that the undesired effects caused by them are limited. Specifically, the ICI term becomes insignificant for slow to moderate time variations. We also validate our theoretical expectations via simulations and demonstrate that the destructive effect of ICI can be alleviated for moderate level of channel variations.

In this paper, we consider an asynchronous random access scheme called irregular repetition ALOHA (IRA) as a generalization of contention resolution ALOHA (CRA) with varying repetitions. We present an asymptotic performance analysis of CRA and IRA on the collision channel for regular and irregular repetition rates. We also propose an improvement by merging the clean parts of packet replicas in partial collisions, and extend our analysis to this scenario as well. Specific designs of repetition distributions based on the new analysis show that the optimized solutions of irregular repetition slotted ALOHA (IRSA) perform well in both IRA and the enhanced scheme, and they considerably outperform the regular repetition distributions. We also introduce energy harvesting (EH) to both schemes as a practical and sustainable adaptation, where users are able to harvest energy and store it in their finite-capacity batteries. We model the battery state by a discrete-time Markov chain and derive an optimal transmission policy to maximize the asymptotic performance of the system. We provide comprehensive numerical results for both practical and asymptotic scenarios to verify the validity of the proposed analyses, and illustrate the benefits of the proposed systems.

We study federated edge learning (FEEL), where wireless edge devices, each with its own dataset, learn a global model collaboratively with the help of a wireless access point acting as the parameter server (PS). At each iteration, wireless devices perform local updates using their local data and the most recent global model received from the PS, and send their local updates to the PS over a wireless fading multiple access channel (MAC). The PS then updates the global model according to the signal received over the wireless MAC, and shares it with the devices. Motivated by the additive nature of the wireless MAC, we propose an analog `over-the-air' aggregation scheme, in which the devices transmit their local updates in an uncoded fashion. However, unlike recent literature on over-the-air FEEL, here we assume that the devices do not have channel state information (CSI), while the PS has imperfect CSI. On the other hand, the PS is equipped with multiple antennas to alleviate the destructive effect of the channel, exacerbated due to the lack of perfect CSI. We design a receive beamforming scheme at the PS, and show that it can compensate for the lack of perfect CSI when the PS has a sufficient number of antennas. We also derive the convergence rate of the proposed algorithm highlighting the impact of the lack of perfect CSI, as well as the number of PS antennas. Both the experimental results and the convergence analysis illustrate the performance improvement of the proposed algorithm with the number of PS antennas, where the wireless fading MAC becomes deterministic despite the lack of perfect CSI when the PS has a sufficiently large number of antennas.

We study collaborative machine learning systems where a massive dataset is distributed across independent workers which compute their local gradient estimates based on their own datasets. Workers send their estimates through a multipath fading multiple access channel with orthogonal frequency division multiplexing to mitigate the frequency selectivity of the channel. We assume that there is no channel state information (CSI) at the workers, and the parameter server (PS) employs multiple antennas to align the received signals. To reduce the power consumption and the hardware costs, we employ complex-valued low-resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), at the transmitter and the receiver sides, respectively, and study the effects of practical low-cost DACs and ADCs on the learning performance. Our theoretical analysis shows that the impairments caused by low-resolution DACs and ADCs, including those of one-bit DACs and ADCs, do not prevent the convergence of the federated learning algorithms, and the multipath channel effects vanish when a sufficient number of antennas are used at the PS. We also validate our theoretical results via simulations, and demonstrate that using low-resolution, even one-bit, DACs and ADCs causes only a slight decrease in the learning accuracy.

As a building block toward a simple and scalable solution to massive random access, we consider two-user multiple access with ZigZag decoding, with no need for any coordination or codebook differentiation. We derive closed-form bounds on the achievable sum-rates of the original ZigZag and a modified version of it, called double-zipper ZigZag, for both cases of perfect and imperfect channel state information (CSI). We also show that performances of both versions of ZigZag approach that of optimal coordinated time-sharing in the high signal to noise ratio regime, even in the presence of CSI errors.

We study uncoordinated random access over fading channels where each user independently decides whether to send a packet or not to a common receiver at any given time slot. Specifically, we develop an information theoretic formulation to characterize the overall system throughput. We consider two scenarios: classical slotted ALOHA, where no multiuser detection (MUD) capability is available and slotted ALOHA with MUD. In each case, in order to maximize the system throughput, we provide methods to obtain the optimal rates and channel activity probabilities using the user distances to the receiver (or, equivalently, their average signal to noise ratios) assuming a Rayleigh block fading channel. The results demonstrate that the newly proposed optimal rate selection solutions offer significant increase in the expected system throughputs compared to the “same rate to all users” approach commonly used in the literature. In addition to the overall throughput optimization, we also address the issue of fairness among users and propose approaches guaranteeing a minimum amount of individual throughput to each user, and design systems with limited individual outage probabilities for increased energy efficiency and reduced delay.

We propose a generalized version of the slot- asynchronous random access scheme called Irregular Repetition ALOHA (IRA). In the proposed scheme, users are allowed to transmit their packets with varying durations independently from each other in such a way that the overall system throughput is increased. We present an asymptotic throughput analysis of the newly proposed scheme when it is used together with time diversity, i.e., by repetition of the users' packets. We also optimize the probability distributions governing the repetition rates and packet durations with the aid of the developed analysis. We demonstrate that the optimized distributions achieve considerably higher throughputs than those achievable by IRA only, and we verify the asymptotic results via finite length simulations.

In this paper, we present an asymptotic performance analysis of contention resolution ALOHA (CRA) on the collision channel for both regular and irregular repetition rates. In addition, we consider an improvement to CRA by merging the clean parts of replicas in partial collisions and extend our analysis to this scenario. Specific designs of repetition distributions based on the new analysis show that the optimized solutions for irregular repetition slotted ALOHA (IRSA) perform well in both CRA and the enhanced scheme.

We propose an irregular repetition slotted ALOHA (IRSA) based uncoordinated random access scheme for energy harvesting (EH) nodes. Specifically, we consider the case in which each user has a battery that is recharged with harvested energy from the environment in a probabilistic manner. We analyze this scheme starting with a unit-sized battery at the nodes and extend the analysis to the case of a finite-sized battery. For both scenarios, we derive the asymptotic throughput expressions and obtain the optimized probability distributions for the number of packet replicas of the users. We demonstrate that for the case of IRSA with EH nodes, these optimized distributions perform considerably better than the alternatives, including slotted ALOHA (SA), contention resolution diversity slotted ALOHA (CRDSA), and IRSA, which do not take into account the EH process for both asymptotic and finite frame length scenarios.

We propose a serially concatenated coding scheme to communicate over binary energy harvesting communication channels with additive white Gaussian noise (AWGN), and design explicit and implementable codes for both long and short block lengths. Run length limited (RLL) codes are used to induce the required nonuniform input distributions for both cases. We employ low density parity check (LDPC) codes for long block lengths, while for short block lengths, we utilize convolutional codes as outer error correction codes. We consider different decoding approaches for the two cases, i.e., an iterative decoder is used for the former while Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm over the product trellis of the convolutional and run length limited codes is used for the latter. We also extend our work to joint energy and information transfer for both cases since similar coding solutions can be employed. Numerical examples demonstrate that the newly optimized codes with an inner RLL code are superior to the optimal codes over standard AWGN channels for long block lengths. Our results also show that, for the short block length case, concatenated convolutional and RLL codes with higher minimum distances offer excellent performance.

We focus on transmit signal design for multiple- input single-output (MISO) wiretap channels with simultaneous wireless information and power transfer (SWIPT). Assuming that the channel inputs are drawn from standard constellation sets, we formulate secrecy rate maximization problems subject to power and harvested energy constraints. We tackle these problems under two different assumptions on the channel state information (CSI) at the transmitter. First, we consider a scenario in which the transmitter knows the CSI for both the information receiver and the energy receiver (potential eavesdropper), and we propose a precoder optimization approach. Then, we investigate the case where only perfect CSI of the information receiver is available along with the statistical CSI of the energy receiver. Our numerical results demonstrate the efficacy of the proposed solutions.

We propose an irregular repetition slotted ALOHA (IRSA) based uncoordinated random access scheme for energy harvesting (EH) nodes. Specifically, we consider the case in which each user has a unit- sized battery that is recharged with energy harvested from the environment in a probabilistic manner. We analyze this scheme by deriving asymptotic throughput expressions, and obtain optimized probability distributions for the number of packet replicas for each user. We demonstrate that for the case of IRSA with EH nodes, these optimized distributions perform considerably better than those of slotted ALOHA (SA), contention resolution diversity slotted ALOHA (CRDSA) and IRSA, which do not take into account the EH process, for both asymptotic and finite frame length scenarios.

We focus on two-user Gaussian interference channels (ICs) with fast fading and study implementation of explicit all public and Han-Kobayashi (HK) coding schemes with low-density parity-check (LDPC) codes. Stability conditions for the coding schemes are derived, and a modified form of the EXIT chart analysis is proposed to estimate the decoding threshold of LDPC code ensembles. The proposed code design is employed in several examples and the obtained rate pairs are compared with the achievable rate region (ARR) boundaries demonstrating that rate pairs very close to the ARR boundaries are attained. Performance of finite block length codes are also studied through simulations of specific codes picked from the optimized LDPC code ensembles in order to verify the analysis.

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis‐based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error‐rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi‐static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point‐to‐point (P2P) trellis‐based codes and off‐the‐shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

We study the design of explicit and implementable codes for the two-user discrete memoryless interference channels (DMICs). We consider Han-Kobayashi (HK) type encoding where both public and private messages are used and propose coding techniques utilizing a serial concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. Since exact analytical treatment of the BCJR decoder for the inner trellis-based code appears infeasible, we analytically investigate the iterative decoding process in the asymptotic regime where the probability of decoding error tends to zero. Based on this approximate analysis, we derive a stability condition for this type of a concatenated coding scheme for the first time in the literature. Furthermore, we use an extrinsic information transfer analysis to design the outer LDPC code while fixing the inner NLTC, and utilize the derived stability condition to accelerate the design process and to avoid code ensembles that potentially produce high error floors. Via numerical examples, we demonstrate that our designed codes achieve rate pairs close the optimal boundary of the HK subregion, which cannot be obtained without the use of nonlinear codes. Also, we verify that the estimated thresholds of the designed codes via finite block length simulations and show that our designs significantly outperform the point-to-point optimal codes, hence demonstrating the need for designs specifically tailored for DMICs.

We address the problem of finding the capacity of two classes of channels with amplitude-limited inputs. The first class is frequency flat fading channels with an arbitrary (but finite support) channel gain with the channel state information available only at the receiver side; while the second one we consider is the class of additive noise channels with signal-dependent Gaussian noise. We show that for both channel models and under some regularity conditions, the capacity-achieving distribution is discrete with a finite number of mass points. Furthermore, finding the capacity-achieving distribution turns out to be a finite-dimensional optimization problem, and efficient numerical algorithms can be developed using standard optimization techniques to compute the channel capacity. We demonstrate our findings via several examples. In particular, we present an example for a block fading channel where the channel gain follows a truncated Rayleigh distribution, and two instances of signal-dependent noise that are used in the literature of magnetic recording and optical communication channels.

We propose a secure transmission scheme based on space shift keying (SSK) in which the indices associated with the transmit antennas are assigned dynamically according to the channel towards the legitimate receiver. We first derive an asymptotic secrecy rate under the perfect channel reciprocity assumption. Then, we study the impacts of imperfect reciprocity and presence of a nearby eavesdropper on the reliability and eavesdropping resilience of the proposed scheme. Finally, we introduce an enhanced antenna index assignment algorithm which is more robust to imperfect reciprocity, and is capable of preventing a nearby eavesdropper from acquiring the transmitted bits.

In this paper, we consider a random access scheme over wireless fading channels based on slotted ALOHA where each user independently decides whether to send a packet or not to a common receiver at any given time slot. To characterize the system throughput, i.e., the expected sum- rate, an information theoretic formulation is developed. We consider two scenarios: classical slotted ALOHA where no multi-user detection (MUD) capability is available and slotted ALOHA with MUD. Our main contribution is that the optimal rates and channel activity probabilities can be characterized as a function of the user distances to the receiver to maximize the system throughput. In addition, we address the issue of fairness among the users and provide solutions, which guarantee a minimum amount of individual throughput.

We study application of parallel and serially concatenated convolutional codes known as turbo codes to the randomized encoding scheme introduced by Wyner for physical layer security. For this purpose, we first study how randomized convolutional codes can be constructed. Then, we use them as building blocks for developing randomized turbo codes. We also develop iterative low-complexity decoders corresponding to the randomized schemes introduced and evaluate the code performance. We demonstrate via several examples that the newly designed schemes can outperform other existing coding methods in the literature (e.g., punctured low density parity check (LDPC) and scrambled BCH codes) in terms of the resulting security gap.

We consider a binary energy harvesting communication system with a finite battery transmitter over a noisy channel, and design explicit and implementable codes based on concatenation of a nonlinear trellis code (NLTC) with an outer low density parity check (LDPC) code. We propose two different decoding methods where the simplified one ignores the memory in the battery state while the more sophisticated one utilizes the memory. Numerical results demonstrate that the designed codes outperform other reference schemes. The results also show the superiority of the improved decoding approach over the naive solution.

We propose transmit optimization techniques for multi-input multi-output (MIMO) wiretap channels with statistical channel state information (CSI) at the transmitter. We consider doubly correlated channels towards the legitimate receiver and the eavesdropper. The aim is to maximize the secrecy rates using the knowledge of the channel correlation matrices. We develop gradient-descent based optimization algorithms for obtaining the optimal transmit signals for both Gaussian and finite-alphabet inputs. Furthermore, we introduce a joint precoder and artificial noise (AN) design scheme. We demonstrate the efficacy of the proposed schemes via numerical examples.

We consider downlink of a multiuser massive multiple-input multiple-output (MIMO) system and focus on reducing the hardware costs by using a single common power amplifier and separate phase shifters (PSs) for antenna front-ends. In the previous literature, the use of analog PSs in this setup has been considered. Here, we study the use of practical digital PSs, which only support a limited set of discrete phases. Considering the sum of interference powers as a metric, we formulate the corresponding nonlinear discrete optimization problem and solve for the phases to be used during transmission. We devise a low-complexity algorithm, which employs a trellis structure providing suboptimal, but efficient and effective solutions. We demonstrate via examples that the proposed solutions have comparable performance to conventional analog PS-based algorithms. Furthermore, we prove that by utilizing discrete-phase constant envelope precoding, the interference can be made arbitrarily small by increasing the number of antennas. Therefore, the asymptotic gains promised by massive MIMO systems are preserved. We also obtain closed-form expressions for the rate loss due to errors in the phase and amplitude of the PSs, for both low and high SNR regimes.

We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper's channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap.

We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finite-alphabet input assumption. We assume that the transmitter has access to the channel coefficients of the legitimate receiver and knows the statistics of the eavesdropper's channel. Accordingly, we propose a secrecy rate maximization algorithm using a gradient descent-based optimization of the precoder matrix and an exhaustive search over the power levels allocated to the AN. We also propose algorithms to reduce the complexities of direct ergodic secrecy rate maximization by: 1) maximizing a cut-off rate-based approximation for the ergodic secrecy rate, simplifying the mutual information expression, which lacks a closed-form and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a per-group precoding-based technique. Our numerical results reveal that jointly optimizing the precoder and the AN outperforms the existing solutions in the literature, which rely on the precoder optimization only. We also demonstrate that the proposed low complexity alternatives result in a small loss in performance while offering a significant reduction in computational complexity.

Multifunctional and reconfigurable multiple-input multiple-output (MR-MIMO) antennas are capable of dynamically changing the operation frequencies, polarizations, and radiation patterns, and can remarkably enhance system capabilities. However, in coherent communication systems, using MR-MIMO antennas with a large number of operational modes may incur prohibitive complexity due to the need for channel state estimation for each mode. To address this issue, we derive an explicit relation among the radiation patterns for the antenna modes and the resulting channel gains. We propose a joint channel estimation/prediction scheme where only a subset of all the antenna modes is trained for estimation, and then, the channels associated with the modes that are not trained are predicted using the correlations among the different antenna modes. We propose various training mechanisms with reduced overhead and improved estimation performance, and study the impact of channel estimation error and training overhead on the MR-MIMO system performance. We demonstrate that one can achieve significantly improved data rates and lower error probabilities utilizing the proposed approaches. For instance, under practical settings, we observe about 25% throughput increase or about 3-dB signal-to-noise ratio improvement under the same training overhead with respect to non-reconfigurable antenna systems.

We propose a low complexity transmit signal design scheme for achieving information-theoretic secrecy over a MIMO wiretap channel driven by finite-alphabet inputs. We assume that the transmitter has perfect channel state information (CSI) of the main channel and also knows the statistics of the eavesdropper's channel. The proposed transmission scheme relies on jointly optimizing the precoder matrix and the artificial noise so as to maximize the achievable secrecy rates. In order to lower the computational complexity associated with the transmit signal design, we employ a design metric using the cut-off rate instead of the mutual information. We formulate a gradient-descent based optimization algorithm and demonstrate via extensive numerical examples that the proposed signal design scheme can yield an enhanced secrecy performance compared with the existing solutions in spite of its relatively lower computational complexity. The impacts of the modulation order as well as the number of antennas at the transmitter and receiver ends on the achievable secrecy rates are also investigated.

We address the problem of finding the capacity of fading channels under the assumption of amplitude-limited inputs. Specifically, we show that if the fading coefficients have a finite support and the channel state information is only available at the receiver side, there is a unique input distribution that achieves the channel capacity and this input distribution is discrete with a finite number of mass points.

We focus on short block length code design for Gaussian interference channels (GICs) using trellis-based codes. We employ two different decoding techniques at the receiver side, namely, joint maximum likelihood (JML) decoding and single user (SU) minimum distance decoding. For different interference levels (strong and weak) and decoding strategies, we derive error-rate bounds to evaluate the code performance. We utilize the derived bounds in code design and provide several numerical examples for both strong and weak interference cases. We show that under the JML decoding, the newly designed codes offer significant improvements over the alternatives of optimal point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check (LDPC) codes with the same block lengths.

Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios, such as radio frequency identification (RFID) systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for the use in such systems taking into account both energy transmission and error rate requirements. In particular, we propose using concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. We design the NLTC based on maximization of its free distance. We give necessary and sufficient conditions for its catastrophicity; in order to avoid catastrophic codes, we connect each designed NLTC to a corresponding linear convolutional code allowing for the use of simpler conditions for verification. Furthermore, we use EXIT charts to design the outer LDPC code while fixing the inner NLTC. Via examples, we demonstrate that our designed codes operate at ~0.8 dB away from the information theoretic limits, and they outperform both regular LDPC codes and optimized irregular LDPC codes for additive white Gaussian noise (AWGN) channels. In addition, we show that the proposed scheme outperforms the reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode.

We propose upper and lower bounds on the capacity of multiple-input multiple-output (MIMO) systems with amplitude-limited inputs. The results are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived bounds for high and low noise levels, and study the gap between them. We also consider parallel Gaussian channels with peak and average power-constrained inputs. For such channels, the capacity-achieving distribution has been reported in the literature to be discrete, which can be computed using numerical optimization techniques. However, there is no closed-form expression and finding the capacity-achieving distribution is computationally tedious. With this motivation, we derive approximate expressions for the capacity at low and high noise variance levels. We illustrate our findings on both MIMO channels and parallel Gaussian channels via several numerical examples.

We study code design for two-user Gaussian multiple access channels (GMACs) under fixed channel gains and under quasi-static fading. We employ low-density parity-check (LDPC) codes with BPSK modulation and utilize an iterative joint decoder. Adopting a belief propagation (BP) algorithm, we derive the PDF of the log-likelihood-ratios (LLRs) fed to the component LDPC decoders. Via examples, it is illustrated that the characterized PDF resembles a Gaussian mixture (GM) distribution, which is exploited in predicting the decoding performance of LDPC codes over GMACs. Based on the GM assumption, we propose variants of existing analysis methods, named modified density evolution (DE) and modified extrinsic information transfer (EXIT). We derive a stability condition on the degree distributions of the LDPC code ensembles and utilize it in the code optimization. Under fixed channel gains, the newly optimized codes are shown to perform close to the capacity region boundary outperforming the existing designs and the off-the-shelf point-to-point (P2P) codes. Under quasi-static fading, optimized codes exhibit consistent improvements upon the P2P codes as well. Finite block length simulations of specific codes picked from the designed ensembles are also carried out and it is shown that optimized codes perform close to the outage limits.

Abstract Underwater acoustic (UWA) communications have attracted a lot of interest in recent years motivated by a wide range of applications including offshore oil field exploration and monitoring, oceanographic data collection, environmental monitoring, disaster prevention, and port security. Different signaling solutions have been developed to date including non‐coherent communications, phase coherent systems, multi‐input and multi‐output solutions, time‐reversal‐based communication systems, and multi‐carrier transmission approaches. This paper deviates from the traditional approaches to UWA communications and develops a scheme that exploits biomimetic signals. In the proposed scheme, a transmitter maps the information bits to the parameters of a biomimetic signal, which is transmitted over the channel. The receiver estimates the parameters of the received signal and demaps them back to bits to estimate the message. As exemplary biomimetic signals, analytical signal models with nonlinear instantaneous frequency are developed that match mammal sound signatures in the time‐frequency plane are developed. Suitable receiver structures as well as performance analysis are provided for the proposed transmission scheme, and some results using data recorded during the Kauai Acomms MURI 2011 UWA communications experiment are presented. Copyright © 2016 John Wiley & Sons, Ltd.

Abstract We propose two schemes for asynchronous multi‐relay two‐way relay (MR‐TWR) systems in which neither the users nor the relays know the channel state information. In an MR‐TWR system, two users exchange their messages with the help of NR relays. Most of the existing works on MR‐TWR systems based on differential modulation assume perfect symbol‐level synchronization between all communicating nodes. However, this assumption is not valid in many practical systems, which makes the design of differentially modulated schemes more challenging. Therefore, we design differential modulation schemes that can tolerate timing misalignment under frequency‐selective fading. We investigate the performance of the proposed schemes in terms of either probability of bit error or pairwise error probability. Through numerical examples, we show that the proposed schemes outperform existing competing solutions in the literature, especially for high signal‐to‐noise ratio values. Copyright © 2016 John Wiley & Sons, Ltd.

Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios such as RFID systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for use in such systems taking into account both energy transmission and error rate requirements. Specifically, we propose using concatenation of a nonlinear trellis code with an outer low density parity check code. Via examples, we observe that our designed codes operate at SNRs 2.4dB away from information theoretic limits, and they outperform reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode. We note that it is possible to close the gap to the information theoretic limits further by more sophisticated receiver designs and more complex encoders.

In this paper, we explore code optimization for two-user discrete memoryless interference channels (DMICs) wherein the inputs and outputs of the channel are from a finite alphabet. For encoding, we employ irregular low-density parity-check (LDPC) codes combined with non-linear trellis codes (NLTCs) to satisfy the desired distribution of zeros and ones in the transmitted codewords. At the receiver sides, we adopt BCJR algorithm based decoders to compute the symbol-by-symbol log-likelihood ratios (LLRs) of LDPC coded bits to be fed to message passing decoders. As a specific example, we consider the binary-input binary-output Z interference channel (BIBO ZIC) for which the transmitted and received signals are binary and one of the receivers is interference free. For a specific example of a BIBO ZIC, we examine the Han-Kobayashi inner bound on the achievable rate pairs and show that with a simple scheme of sending the messages as private one can achieve the sum-capacity of the channel. We also perform code optimization and demonstrate that the jointly optimized codes outperform the optimal single user codes with time sharing.

We focus on linear precoding strategies as a physical layer technique for providing security in Gaussian interference channels. We consider an artificial noise aided scheme where transmitters may broadcast noise in addition to data in order to confuse eavesdroppers. We formulate the problem of minimizing the total mean-square error at the legitimate receivers while keeping the error values at the eavesdroppers above target levels. This set-up leads to a non-convex problem formulation. Hence, we propose a coordinate block descent technique based on a tight semi-definite relaxation and design linear precoders as well as spatial distribution of the artificial noise. Our results illustrate that artificial noise can provide significant performance gains especially when the secrecy levels required at the eavesdroppers are demanding.

We focus on Gaussian interference channels (GICs) and study the Han-Kobayashi coding strategy for the two-user case with the objective of designing implementable (explicit) channel codes. Specifically, low-density parity-check codes are adopted for use over the channel, their benefits are studied, and suitable codes are designed. Iterative joint decoding is used at the receivers, where independent and identically distributed channel adapters are used to prove that log-likelihood-ratios exchanged among the nodes of the Tanner graph enjoy symmetry when BPSK or QPSK with Gray coding is employed. This property is exploited in the proposed code optimization algorithm adopting a random perturbation technique. Code optimization and convergence threshold computations are carried out for different GICs employing finite constellations by tracking the average mutual information. Furthermore, stability conditions for the admissible degree distributions under strong and weak interference levels are determined. Via examples, it is observed that the optimized codes using BPSK or QPSK with Gray coding operate close to the capacity boundary for strong interference. For the case of weak interference, it is shown that nontrivial rate pairs are achievable via the newly designed codes, which are not possible by single user codes with time sharing. Performance of the designed codes is also studied for finite block lengths through simulations of specific codes picked with the optimized degree distributions with random constructions, where, for one instance, the results are compared with those of some structured designs.

We study memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol drop-outs or symbol insertions with particular emphasis on the binary and non-binary deletion channels. We offer a different look at these channels by considering equivalent models by fragmenting the input sequence where different subsequences travel through different channels. The resulting output symbols are combined appropriately to come up with an equivalent input–output representation of the original channel which allows for derivation of new upper bounds on the channel capacity. We consider both random and deterministic types of fragmentation processes applied to binary and nonbinary deletion channels. With two specific applications of this idea, a random fragmentation applied to a binary deletion channel and a deterministic fragmentation process applied to a nonbinary deletion channel, we prove certain inequality relations among the capacities of the original channels and those of the introduced subchannels. The resulting inequalities prove useful in deriving tighter capacity upper bounds for: 1) independent identically distributed (i.i.d.) deletion channels when the deletion probability exceeds 0.65 and 2) nonbinary deletion channels. Some extensions of these results, for instance, to the case of deletion/substitution channels are also explored.

Communication strategies that utilize wireless media for simultaneous information and power transfer offer a promising perspective for efficient usage of energy resources. With this motivation, we focus on the design of optimal linear precoders for interference channels utilizing such strategies. We formulate the problem of minimizing the total minimum mean-square error while keeping the energy harvested at the energy receivers above given levels. Our framework leads to a non-convex problem formulation. For point-to-point multiple-input multiple-output channels, we provide a characterization of the optimal solutions under a constraint on the number of transmit antennas. For the general interference scenario, we propose two numerical approaches, one for the single antenna information receivers case, and the other for the general case. We also investigate a hybrid signalling scheme, where the transmitter sends a superposition of two signals: a deterministic signal optimized for energy transfer and an information carrying signal optimized for information and energy transfer. It is illustrated that if hybrid signalling is not incorporated into the transmission scheme, interference can be detrimental to the system performance when the number of antennas at the receivers is low.

We consider design of asynchronous orthogonal frequency division multiplexing (OFDM) based diamond two-way-relay (DTWR) systems in a time-varying frequency-selective (doubly-selective) fading channel. In a DTWR system, two users exchange their messages with the help of two relays. Most of the existing works on asynchronous DTWR systems assume only small relative propagation delays between the received signals at each node that do not exceed the length of the cyclic-prefix (CP). However, in certain practical communication systems, significant differences in delays may take place, and hence existing solutions requiring excessively long CPs may be highly inefficient. In this paper, we propose a delay-independent CP insertion mechanism in which the CP length depends only on the number of subcarriers and the maximum delay spread of the corresponding channels. We also propose a symbol detection algorithm that is able to tolerate very long relative delays, that even exceed the length of the OFDM block itself, without a large increase in complexity. The proposed system is shown to significantly outperform other alternatives in the literature through a number of specific examples.

We present lower bounds on the error probability of turbo codes under maximum likelihood (ML) decoding. We focus on additive white Gaussian noise (AWGN) channels, and consider both ensembles of codes with uniform interleaving and specific turbo codes with fixed interleavers. To calculate the lower bounds, instead of using the traditional approach that only makes use of the distance spectrum, we propose to utilize the exact second order distance spectrum. This approach together with a proper restriction of the error events results in promising lower bounds.

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.

We focus on trellis-based joint code design for two-user Gaussian multiple-access channel (MAC) in the short block length regime. We propose a design methodology, provide specific code designs and report numerical performance results. We compare the performance of the jointly designed codes with the performance of the codes designed for point-to-point (P2P) channels including optimum (in terms of minimum distance) convolutional codes. Our results show that the proposed codes achieve superior performance compared to these alternatives especially in the high signal-to-noise (SNR) regime in equal power scenarios.

A relay communication system with two amplify and forward (AF) relays under flat fading channel conditions is considered where the signals received from the relays are not necessarily time aligned. We propose a new time-reversal (TR)-based scheme providing an Alamouti code structure which needs a smaller overhead in transmitting every pair of data blocks in comparison with the existing schemes and, as a result, increases the transmission rate significantly (as much as 20%) in exchange for a small performance loss. The scheme is particularly useful when the delay between the two relay signals is large, e.g., in typical underwater acoustic (UWA) channels.

We develop several lower bounds on the capacity of binary input symmetric output channels with synchronization errors, which also suffer from other types of impairments such as substitutions, erasures, additive white Gaussian noise (AWGN), etc. More precisely, we show that if a channel suffering from synchronization errors as well as other type of impairments can be decomposed into a cascade of two component channels where the first one is another channel with synchronization errors and the second one is a memoryless channel (with no synchronization errors), a lower bound on the capacity of the original channel in terms of the capacity of the component synchronization error channel can be derived. A primary application of our results is that we can employ any lower bound derived on the capacity of the component synchronization error channel to find lower bounds on the capacity of the (original) noisy channel with synchronization errors. We apply the general ideas to several specific classes of channels such as synchronization error channels with erasures and substitutions, with symmetric q-ary outputs and with AWGN explicitly, and obtain easy-to-compute bounds. We illustrate that, with our approach, it is possible to derive tighter capacity lower bounds compared to the currently available bounds in the literature for certain classes of channels, e.g., deletion/substitution channels and deletion/AWGN channels (for certain signal-to-noise ratio (SNR) ranges).

In cooperative UWA systems, due to the low speed of sound, a node can experience significant time delays among the signals received from geographically separated nodes. One way to combat the asynchronism issues is to employ orthogonal frequency division multiplexing (OFDM)-based transmissions at the source node by preceding every OFDM block with an extremely long cyclic prefix (CP) which reduces the transmission rates dramatically. One may increase the OFDM block length accordingly to compensate for the rate loss which also degrades the performance due to the significantly time-varying nature of UWA channels. In this paper, we develop a new OFDM-based scheme to combat the asynchronism problem in cooperative UWA systems without adding a long CP (in the order of the long relative delays) at the transmitter. By adding a much more manageable (short) CP at the source, we obtain a delay diversity structure at the destination for effective processing and exploitation of spatial diversity by utilizing a low complexity Viterbi decoder at the destination, e.g., for a binary phase shift keying (BPSK) modulated system, we need a two-state Viterbi decoder. We provide pairwise error probability (PEP) analysis of the system for both time-invariant and block fading channels showing that the system achieves full spatial diversity. We find through extensive simulations that the proposed scheme offers a significantly improved error rate performance for time-varying channels (typical in UWA communications) compared to the existing approaches.

We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser in [1] are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability d, denoted by C2K(d), and the capacity of the binary deletion channel with the same deletion probability, C2(d), that is, C2K(d) ≤ C2(d)+(1-d) log(K). Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as d → 0.

We develop an information theoretic characterization and a practical coding approach for segmented deletion channels. Compared to channels with independent and identically distributed (i.i.d.) deletions, where each bit is independently deleted with an equal probability, the segmentation assumption imposes certain constraints, i.e., in a block of bits of a certain length, only a limited number of deletions are allowed to occur. This channel model has recently been proposed and motivated by the fact that for practical systems, when a deletion error occurs, it is more likely that the next one will not appear very soon. We first argue that such channels are information stable, hence their channel capacity exists. Then, we introduce several upper and lower bounds with two different methods in an attempt to understand the channel capacity behavior. The first scheme utilizes certain information provided to the transmitter and/or receiver while the second one explores the asymptotic behavior of the bounds when the average bit deletion rate is small. In the second part of the paper, we consider a practical channel coding approach over a segmented deletion channel. Specifically, we utilize outer LDPC codes concatenated with inner marker codes, and develop suitable channel detection algorithms for this scenario. Different maximum-a-posteriori (MAP) based channel synchronization algorithms operating at the bit and symbol levels are introduced, and specific LDPC code designs are explored. Simulation results clearly indicate the advantages of the proposed approach. In particular, for the entire range of deletion probabilities less than unity, our scheme offers a significantly larger transmission rate compared to the other existing solutions in the literature.

We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and output sequences. For the deletion channel, we consider two different models: i.i.d. deletion–substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). These two models are considered to incorporate effects of the channel noise along with the synchronization errors. For the insertion channel case, we consider Gallager's model in which the transmitted bits are replaced with two random bits and uniform over the four possibilities independently of any other insertion events. The general approach taken is similar in all cases, however the specific computations differ. Furthermore, the approach yields a useful lower bound on the capacity for a wide range of deletion probabilities of the deletion channels, while it provides a beneficial bound only for small insertion probabilities (less than 0.25) of the insertion model adopted. We emphasize the importance of these results by noting that: 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion–substitution case, 3) for the Gallager insertion channel model, the new lower bound improves the existing results for small insertion probabilities.

We consider coding schemes over an independent and identically distributed (i.i.d.) insertion/deletion channel with inter-symbol interference (ISI). The idea is based on a serial concatenation of a low-density parity check (LDPC) code with a marker code. First, we design a maximum-a-posteriori (MAP) detector operating at the bit level which jointly achieves synchronization for the insertion/deletion channel (with the help of the marker code) and equalization for the ISI channel. Utilizing this MAP detector together with an LDPC code with powerful error-correction capabilities, we demonstrate that reliable transmission over this channel is feasible. Then, we consider low-complexity channel detection algorithms needed for proper synchronization/equalization. Specifically, we use separate synchronization and equalization algorithms instead of joint detection and also explore the performance of M- and T-algorithms implemented as low complexity soft output channel detectors. Such schemes greatly reduce the amount of computations needed at the cost of some performance loss as illustrated via a set of simulation results.

In this paper, we develop several lower bounds on the capacity of binary input symmetric q-ary output channels with synchronization errors, e.g., substitution/erasure channels with synchronization errors. More precisely, we show that if a channel with synchronization errors can be decomposed into a cascade of two independent channels where only the first one suffers from synchronization errors, a lower bound on its capacity related to the capacity of the one with only synchronization errors can be given. We present several examples with the new approach and demonstrate that for certain channels, e.g., deletion/substitution channel, it is possible to derive tighter capacity lower bounds than the existing ones.

We investigate different decoding strategies at the relay over a frequency selective two-way relay channel with physical-layer network coding (PNC). The incorporation of the PNC scheme enables two users exchange information via a relay in two transmission phases. We study two approaches at the relay to decode the XOR of the transmitted codewords namely; a) an approximately optimal decoding scheme which is implemented using a list decoding algorithm, and b) a minimum mean square error (MMSE) based detector followed by a PNC decoder. The list decoding scheme selects L most likely pairs of sequences corresponding to the transmitted codewords and sorts them in the order of decreasing a-posteriori probabilities. From this list, estimates of the highly likely network coded sequences are obtained. Numerical examples show that a joint detector/physical-layer network coded sequence decoder (JD/PNCD) has a performance similar to the list decoding scheme and can be implemented with a lower complexity. The detection scheme based on the MMSE criterion is a suboptimal approach that generates soft information corresponding to the linear sum of the received symbols and is particularly useful in scenarios where the number of channel taps is large.

A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.

A gap between theory and practice in signals and systems courses is often reported at many universities as a key problem in recruiting signals and systems students. On the other hand, instructors often cite a lack of fundamental understanding in mathematics as an issue in this course. Students seem to be discontent with some of the abstraction of the signals and systems courses. In this work-in-progress paper, we describe a new pathways concept we introduced to address these problems by introducing in-depth discussions, several applications and hands-on exercises.

We develop several analytical lower bounds on the capacity of deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information rate between the input and output sequences. We consider the usual independent identically distributed (i.i.d.) binary deletion channel, i.i.d. deletion/substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). We emphasize the importance of these results by noting that 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion/substitution case, 3) for the deletion only channel, our results compete well with the best available lower bounds for small deletion probabilities and they explicitly obtain the first order terms in the recently derived capacity expansions.

We consider achievable rates over binary input insertion channels for small values of insertion probabilities by computing bounds on the mutual information rate of insertion channels for independent uniformly distributed (i.u.d.) input sequences. We consider two scenarios: random insertions, where transmitted bits are replaced with a certain probability by two random bits independent of any other insertions, and sticky channels where bits are duplicated with a certain probability again independent of the other insertion errors. Derived lower bounds improve the existing results available in the literature as demonstrated by specific examples.

We present novel bounds on the capacity of binary channels with independent and identically distributed insertions, deletions, and substitutions. The proposed bounds are obtained by exploiting an auxiliary system where the channel is the same as the one in the system of interest, but the receiver is provided with (partial) genie-aided information on the insertion/deletion process. In particular, we show that, when this information is revealed, we obtain a memoryless channel whose capacity, evaluated by means of the Blahut-Arimoto algorithm, gives an upper bound on the capacity of interest. We also show that capacity lower bounds can be derived as well, by exploiting the same auxiliary system and resorting to suitable information-theoretical inequalities. In most scenarios, the proposed bounds improve the existing ones, and significantly narrow the region to which the actual capacity can belong.

In this paper we propose new bounds on the achievable information rate for discrete-time Gaussian channels with intersymbol interference (ISI) and independent and uniformly distributed (i.u.d.) channel input symbols drawn from finite-order modulation alphabets. Specifically, we are interested in developing new bounds on the achievable rates for sparse channels with long memory. We obtain a lower bound which can be achieved by practical receivers, based on MMSE channel shortening and suboptimal symbol detection for a reduced-state channel. An upper bound is given in the form of a semi-analytical solution derived using basic information theoretic inequalities, by a grouping of the channel taps into several clusters resulting in a newly defined single-input multiple-output (SIMO) channel. We show that the so obtained time-dispersive SIMO channel can be represented by an equivalent single-input single-output (SISO) channel with a significantly shorter channel memory. The reduced computational complexity allows the use of the BCJR algorithm for the newly defined channel. The proposed bounds are illustrated through several sparse channel examples and i.u.d. input symbols, showing that the upper bound significantly outperforms existing bounds. Performance of our lower bound strongly depends on the channel structure, showing best results for minimum-phase and maximum-phase systems.

We investigate a promising coding scheme over channels impaired by insertion, deletion, and substitution errors, i.e., interleaved concatenation of an outer low-density parity-check (LDPC) code with error-correction capabilities and an inner marker code for synchronization purposes. To limit the decoding latency, we start with a single-pass decoding algorithm, that is, marker code-based synchronization is performed only once per received packet and iterative decoding with information exchange between the inner decoder and outer decoder is not allowed. Through numerical evaluations, we first find the marker code structures which offer the ultimate achievable rate when standard bit-level synchronization is performed. Then, to exploit the correlations in the likelihoods corresponding to different transmitted bits, we introduce a novel symbol-level synchronization algorithm that works on groups of consecutive bits, and show how it improves the achievable rate along with the error rate performance by capturing part of the rate loss due to interleaving. When decoding latency is not an issue and multiple-pass decoding is performed, we utilize extrinsic information transfer (EXIT) charts to analyze the convergence behavior of the receiver, which leads to design of outer LDPC codes with good degree distributions. Finally, design examples are provided along with simulation results which confirm the advantage of the newly designed codes over the ones optimized for the standard additive white Gaussian noise (AWGN) channels, especially for channels with severe synchronization problems.

We study two-receiver degraded binary broadcast channels (DBBCs), focusing on the capacity region and the encoding schemes that achieve its boundary. First, we derive the conditions for a general binary broadcast channel to be degraded, and show that only a very limited subset of the possible degraded configurations have been investigated in the previous literature. Then, we show how to design a capacity-achieving encoding scheme for a general DBBC, and give a detailed specific example. The designed scheme turns out to be very general and to include, as special cases, the encoding schemes that achieve the capacity boundary of the DBBCs previously studied in the literature.

We investigate two methods for estimating the matched signal transformations caused by time-varying underwater acoustic channels in orthogonal frequency division multiplexing (OFDM) communication systems. The underwater acoustic channel for this 12-20 kHz medium frequency range OFDM system is best modeled using multipath and wideband Doppler scale changes on the transmitted signal. As a result, our first channel estimation method is based on discretizing the wideband spreading function time-scale representation of the channel output using the Mellin transform. The second method is based on extracting the time-scale features of distinct ray paths in the received signal using a modified matching pursuit decomposition algorithm. We validate and discuss both methods using data from the recent Kauai Acomms MURI 2008 (KAM08) underwater acoustic communication experiment.

We consider serially-concatenated coding schemes over channels impaired by insertion, deletion, and substitution errors. Specifically, we focus on the interleaved concatenation of an outer channel code with error-correction capabilities and an inner marker code with synchronization capabilities. To limit the decoding latency, marker code-based synchronization is performed only once per received packet, i.e., iterations with the outer decoder are not allowed. We first numerically evaluate, through mutual information analyses, the ultimate rate achievable by this concatenated scheme when standard bit-level synchronization is performed. Then, we introduce a novel symbol-level synchronization algorithm that works on groups of consecutive bits, and show that it improves the achievable rate. Besides the achievable rate analyses, which allow us to optimize the marker code, we also report error-rate simulation results that confirm the superiority of symbol-level synchronization.

Unequal error-protection schemes obtained by means of two-level superposition coding are considered. Their performance over Gaussian broadcast channels (GBCs) is investigated with optimal maximum-likelihood decoding as well as with a suboptimal decoding strategy based on interference cancellation. We focus on GBCs without fading and, assuming that linear codes are used, we evaluate, for both decoding strategies, analytical approximations of the word-error rate based on a suitable application of the union bound. As in the case of turbo codes and turbo-coded modulations in schemes without superposition, the derivation of the approximations exploits the concept of uniform interleaving. The analytical expressions obtained are in excellent agreement with the simulation results, and thus provide a useful tool for analysis and design of practical superposition-coding schemes. Unlike the existing design tools, which rely on the assumption of infinite-length superposition codes, the proposed approach allows us to study the effectiveness of finite-length coding schemes with known distance spectrum.

We propose to use various trellis structures to characterize different types of insertion and deletion channels. We start with binary independent and identically distributed (i.i.d.) insertion or deletion channels, propose a trellis representation and develop a simulation based algorithm to estimate the corresponding information rates with independent and uniformly distributed inputs. This approach is then generalized to other cases, including channels with additive white Gaussian noise, channels with both insertions and deletions, and channels with intersymbol interference (ISI) where the latter model is motivated by the recent developments on bit-patterned media recording. We demonstrate that the proposed algorithm is an efficient and flexible technique to closely estimate the achievable information rates for channels with insertions and/or deletions with or without intersymbol interference when i.i.d. inputs are employed while we also provide some notes on the achievable information rates when Markov inputs are used. We emphasize that our method is useful for evaluating information rates for channels with insertion/deletions with additional impairments where there does not seem to be a hope of obtaining fully analytical results.

We give a branch-and-cut algorithm for finding the minimum distance of a binary linear block code. We give two integer programming (IP) models and study the convex hull of the single constraint relaxation of these IP models. We use the new inequalities as cuts in a branch-and-cut scheme. Finally, we report computational results based on turbo and low density parity check (LDPC) codes that demonstrate the effectiveness of our cuts. We demonstrate that our IP formulation and specific cuts are efficient tools for determining the minimum distance of moderate size linear block codes, specifically, they are very efficient for LDPC codes, and provide us with an additional tool for solving this important problem.

We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined random processes. Since some of the proposed bounds involve infinite series, we also introduce provable inequalities that lead to more manageable results. For most values of the deletion probability, these bounds improve the existing ones and significantly narrow the gap with the available lower bounds. Exploiting the same auxiliary processes, we also derive, as a by-product, two simple lower bounds on the channel capacity, which, for low values of the deletion probability, are almost as good as the best existing lower bounds.

We consider unequal error-protection schemes obtained by means of two-level superposition coding. The performance over additive white Gaussian noise channels is investigated for optimal maximum-likelihood decoding as well as for a suboptimal decoding strategy based on interference cancellation. Assuming that linear codes are used, we evaluate, for both strategies, analytical approximations of the word-error rate, based on the union bound. As in the case of turbo codes and turbo-coded modulations, the derivation exploits the concept of uniform interleaving, and the bounds are in excellent agreement with the simulation results obtained using iterative decoding. The analytical expressions are useful for code design and for the selection of decoding strategies providing a suitable performance/complexity tradeoff.

We consider unequal error-protection schemes obtained by two-level superposition coding. While the existing schemes implement superposition by means of linear modulations, we propose superposition implemented through continuous phase modulations (CPMs). In the considered scheme, unlike in the linearly-modulated ones, the transmitted signal has constant envelope and thus the system does not rely on the presence of expensive amplifiers. We investigate the potential of CPMs for multi-rate transmissions over channels impaired by additive white Gaussian noise. Particularly, we derive the relevant algorithm for maximum-a-posteriori symbol detection, evaluate the ultimate information rate, and design practical coding schemes that perform fairly close to the theoretical limits.

We present two upper bounds on the capacity of the binary deletion channel. Both bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined random processes. Since the closed-form expressions of the proposed bounds involve infinite series, we also introduce provable inequalities that lead to more manageable results. For most values of the deletion probability, these bounds improve the existing ones and significantly narrow the gap with the available lower bounds.

We present novel bounds on the capacity of binary channels with independent and identically distributed deletions and substitutions. The proposed bounds are obtained by exploiting an auxiliary system where the channel is the same as in the system of interest, but the receiver is provided with (partial) genie-aided information on the deletion/substitution process. In the case of the deletion channel, that is, when no substitutions occur, the proposed upper bound improves the existing ones for most values of the deletion probability, while the proposed lower bound does not. On the other hand, when the channel model also includes substitution errors, both proposed bounds improve the existing ones, significantly narrowing the region to which the actual capacity can belong.

In this work, we propose to use trellis structures to characterize channels with insertions, deletions and substitutions. We start with binary-input binary-output channels with either insertions or deletions, and develop a simulation based approach to estimate the corresponding information rates. This approach is then generalized to the case where there exist both insertions and deletions. We show that, the proposed algorithm is an efficient and flexible technique to closely estimate the information rates for channels with insertions, deletions and substitutions.

We propose a simple cooperative diversity scheme for a communication system consisting of two cooperating nodes that receive a single channel state information (CSI) bit from the destination node. Essentially, the feedback bit tells which cooperating node has the strongest channel, and this information is used appropriately to obtain cooperative diversity. A simple linear receiver is proposed and its performance is shown to be very close to the maximum-likelihood performance. An upper bound on the average error probability is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels under the assumption of ideal inter-user channel. In addition, through computer simulations, it is verified that the proposed scheme presents a good error performance when the inter-user channel signal-to-noise ratio is high or when the inter-user channel has a well-defined line-of-sight component. In other words, the new scheme becomes interesting when the cooperating nodes are close to each other. Comparisons with a cooperative scheme based on the Alamouti code are provided.

In this work, we use various trellis structures to characterize insertion/deletion channels with intersymbol interference (ISI). We propose to use a two-element state vector to represent the channel memory and possible insertions/deletions, and develop a suitable trellis to describe the communication process. Using a simulation based approach, we compute the corresponding information rates. We show that, the proposed algorithm is an efficient and flexible technique to closely estimate the information rates for insertion/deletion channels with ISI.

We give a branch-and-cut algorithm for finding the minimum distance of a binary linear error correcting code. We give two integer programming (IP) models and study the convex hull of the single constraint relaxation of these IP models. We use the new inequalities as cuts in a branch-and-cut scheme. Finally, we report computational results based on low density parity check (LDPC) codes that demonstrate the effectiveness of our cuts.

In this paper, we propose linear dispersion codes (LDCs) for multiple-input multiple-output (MIMO) channels with a prescribed amount of feedback. The proposed scheme selects the LDC from a set of LDCs that minimizes the error probability based on the instantaneous channel conditions. The determination of the best set of LDCs, i.e., the one that minimizes the average error probability, is described as a constrained optimization problem. While this problem appears to be intractable in general, for certain parameters we present good sets of LDCs, obtained from an iterative optimization algorithm. Results are given for rate-one LDCs only, but this restriction can be removed. Computer simulations show that the proposed schemes outperform previously reported comparable schemes for the same number of feedback bits.

A non-coherent multiple input multiple output (MIMO) coded communication system over frequency selective block fading channel is considered. A theoretical limit for the channel estimation error is established via a closed form derivation of the modified Cramer-Rao bound (MCRB), for the underlying channel model and equi-power signal constellations. Furthermore, a specific coded MIMO system with an appropriate iterative receiver is studied, and the mean square error (MSE) in the channel estimation with the proposed structure is demonstrated to asymptotically approach the derived theoretical limit.

We consider a unified framework to develop various graph-based detection algorithms for layered space-time architectures. We start with a factor graph representation for the communication channel, apply a belief propagation (BP) based algorithm for channel detection, and show that the detector achieves a near optimal performance even when number of receive antennas is smaller than number of transmit antennas. Based on this baseline algorithm, we further develop three different extensions of the BP detector that provide a good complexity/performance trade-off, which are especially useful for systems with a large number of antennas or when we encounter a frequency-selective fading channel with a long ISI span. Moreover, all the proposed detectors are soft-input soft-output in nature and they can be directly applied for use in turbo processing without any additional modifications. We study the performance of the new detectors via both simulations and convergence analysis using the measure of average mutual information.

In the above-named work (ibid., vol. 49, no. 10, pp. 2669-2681, Oct. 2003) the authors developed performance bounds for multiple antenna systems that use receive antenna selection and proved results regarding the diversity and coding gains in such systems. In reference to above correspondence, the probability density function given by eq. (30) should not include the scaling factor of 1/L. This is shown via a short derivation. As a result, the factor 1/L should be omitted from the pairwise error probability expressions, and (32), (34), (35), and (38)-(41) are corrected herein. The main results regarding the diversity gain of the system are not effected by the absence of this scaling factor, while the ones on the coding gain should be modified accordingly.

The paper considers two different antenna selection schemes for space-time coded systems over flat fading channels. First we explore antenna selection at the transmitter side based on the received signal to noise ratios. We then study the joint selection of receive and transmit antennas. Both schemes assume a slowly fading channel (i.e., quasi-static fading) and require some limited feedback from the receiver to the transmitter. By computing upper bounds on the pairwise error probabilities and conducting extensive simulations, we show that the space-time coded systems achieve full diversity even with antenna selection provided that the code is full rank. These results are extensions of earlier work on antenna selection for MIMO systems (Bahceci et al., 2003) which only considers receive antenna selection.

We study information-rate calculations and coded cooperation strategies for relay channels with frequency-selective (FS) fading. We develop suitable channel trellises for the multiaccess and broadcast parts of the relay channel, and employ simulation-based techniques to calculate (approximate) ergodic information-rate bounds with FS Rayleigh fading. Our results show that frequency selectivity provides higher information rates than flat fading when the fading coefficients are known at the receiver, however, the improvement becomes marginal with increasing number of channel taps (when the overall signal to noise ratio is kept constant). Furthermore, we develop a distributed turbo-coding strategy and several decode-and-forward type detection/decoding schemes to ensure successful cooperative communication where the source and the relay may transmit simultaneously. We show that with suitable coding and iterative decoding, one can approach the approximate information-rate limits closely, and that detection schemes based on MMSE criterion provide a good performance/complexity trade-off.

A non-coherent multiple input multiple output (MIMO) coded communication system over a frequency selective (FS) block fading channel is considered. A theoretical limit for the channel estimation error is established via a closed form derivation of the modified Cramer-Rao bound (MCRB) (more precisely, a tight lower bound to it) for the underlying channel model and equi-power signal constellations. Furthermore, it is shown that, for a practical coded MIMO system that employs turbo coding and an appropriate iterative decoding, the resulting mean squared error (MSE) in channel estimation approaches very closely to the derived theoretical limit.

We study coding techniques and information rate calculations for relay channels with frequency-selective (FS) fading. Our main objective is to extend the available results on flat fading channels to FS fading. We develop suitable channel trellises, and employ simulation-based techniques to calculate constrained capacity bounds. Furthermore, we propose a distributed turbo coding strategy and several detection/decoding schemes to ensure successful cooperative communication. Our results show that, with suitable turbo coding and iterative decoding, one can approach the constrained capacity limits closely.

This paper studies performance of space-time coded (STC) systems with joint transmit and receive antenna selection over multiple input multiple output (MIMO) flat and frequency-selective (FS) fading channels. Specifically, we first perform a pairwise error probability analysis over flat fading channels explicitly. Then, we comment on our expectations for the case of FS fading channels. We show that the joint transmit and receive antenna selection based on received power levels does not degrade the achievable diversity order when full rank STCs are employed. Simulation results are provided to verify our theoretical results for both full rank and rank-deficient codes.

We propose belief propagation (BP) based detection algorithms for the Bell labs layered space-time (BLAST) architectures. We first develop a full complexity BP algorithm, and show that the detector achieves a near optimal performance even when the number of receive antennas is smaller than the number of transmit antennas. We also consider three different extensions that provide a good complexity/performance trade-off. Being soft-input-soft-output in nature, we also argue that the proposed detectors are suitable for use in turbo processing which can further enhance the system performance when there is an outer code. In addition to the simulation results, we also study the convergence behavior of the proposed detectors by exploiting the measure of average mutual information.

This paper studies bit-patterned media recording channels when there exist written-in errors. Using a signal processing point of view, we consider an abstract model for the overall recording channel, incorporating errors occurred during the write process. Based on the resulting channel model, we develop various trellis structures, and propose several detection algorithms for data recovery. Furthermore, we investigate the achievable information rates for patterned media recording systems with different levels of write error probability, which provide an information theoretical performance assessment for such systems.

In this paper, we develop capacity approaching turbo coding schemes for half-duplex relay systems as an extension of our previous work on coding for full-duplex relays. We consider the use of specific signal constellations (e.g., binary phase-shift keying) in transmission, develop practical coding schemes to be used at the source and the relay nodes, and describe a suitable information combining technique at the destination node. Unlike the full-duplex relay systems, the destination node does not perform joint decoding of multiple consecutive blocks; instead, it works with one frame at a time. Furthermore, for the half-duplex relaying scheme, the optimization of the length of the listening period for the relay node is an issue. By utilizing the information theoretical tools, we perform this optimization, and use it in our development of capacity approaching coding/decoding schemes. Specifically, when the fraction of time turns out to be less than the transmission rate, the relay node is unable to decode all the information bits transmitted, and a partial decoding approach has to be used. Through a comprehensive set of examples, we observe that the proposed scheme is promising to approach the corresponding information theoretical limits (bounds). In particular, for all the cases studied, we have obtained bit error rates of$10^{-5}$or lower within 1–1.5 dB (in most cases, around within 1.2 dB) of the constrained capacity under a variety of channel conditions. Extensions of the proposed scheme to coded modulation and to multiple-input multiple-output systems are also described.

We exploit the capacity approaching capability of low density parity check (LDPC) codes to design coding schemes for relay channels. We consider the classical relay channel model, and the use of both full-duplex relays and half-duplex ones. In addition to the design of practical coding schemes and the development of the appropriate receiver structures, we also exploit the use of average mutual information to characterize the convergence behavior of the proposed systems. Using the convergence predictions and the simulation results, we demonstrate that the proposed LDPC coded relay systems, in particular, with irregular LDPC codes, have the capability to approach the ergodic/outage information rates very closely. This is true for both ergodic fading channels where the Shannon type (constrained, i.e., modulation specific) capacity is considered, and non-ergodic fading channels where the outage capacity provides the appropriate limits of reliable communication. For the (time-division) half-duplex relay schemes, we also discuss the optimization of the time-division parameters, and the bit allocation strategies to improve the system performance further.

In this letter, we propose an iterative belief propagation (BP) channel detector (equalizer) over single-input single- output (SISO) and multiple-input multiple-output (MIMO) frequency selective fading channels as an alternative to the typically used maximuma-posteriori(MAP) or maximum likelihood (ML) detectors. The proposed detector has a parallel structure, resulting in fast hardware implementations. Moreover, BP detector is less complex than the MAP detector and it has a short decoding delay. We analyze the bit error rate and the mutual information and show that, over frequency selective fading channels, the proposed BP detector achieves a near-optimal performance, even in the presence of the length 4 cycles in the corresponding channel factor graph.

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas

We develop performance bounds for half duplex relay systems operating in decode-forward mode over additive white Gaussian noise (AWGN) channels. We consider the distributed turbo coding scheme [1] where the relay decodes the information obtained from the source, interleaves, re-encodes and forwards it to the destination. Unlike most other half duplex schemes proposed in the literature where the source remains silent during the relay transmission, the source and the relay in our scheme are allowed to transmit simultaneously in the same frequency band, in order to improve the overall spectral efficiency of the system. We employ the union bound on the average error probability for the general case of imperfect source to relay link assuming uniform interleaving at the source and the relay. We compare the bound with the simulation results obtained by the iterative decoding algorithm of [1] and show that for relatively large signal to noise ratios and large interleaver sizes the performance of the iterative algorithm is close to that predicted by the bound. The bounds are not restricted to turbo codes alone, i.e, they can be applied to other linear block codes including LDPC codes as well.

We describe coded cooperation strategies for half-duplex relay channels based on low density parity check (LDPC) codes. In addition to designing practical coding schemes and developing appropriate receiver structures, we also exploit the use of average mutual information to characterize and analyze the convergence behavior of the LDPC coded relay systems. Both the convergence analysis and simulation results show that the LDPC coded relay system can approach the theoretical information rates very closely (0.8 ~ 1.1 dB) over half-duplex relay channels, and their performance is superior to other alternatives, including, the use of turbo codes. Furthermore, we consider the optimization of the time-division parameters and the bit allocation strategies

We propose a joint source-channel coding scheme for wireless communication systems with multiple transmit and receive antennas. The source coder is realized by a multiple description encoder that generates multiple bit streams. Each description is then separately turbo coded and transmitted using multiple antennas. For the receiver, we describe a suitable iterative joint source-channel decoding technique that exploits the correlations between the descriptions. We present several examples that illustrate the performance of the proposed system, and compare it with other approaches.

In a previous paper by Bahceci et al., antenna selection ' for multiple-antenna transmission systems under the assumption that the subchannels between antenna pairs fade independently was studied. In this paper, the performance of such systems when the subchannels experience correlated fading is considered. It is assumed that the channel-state information (CSI) is available only at the receiver, the antenna selection is performed only at the receiver, and the selection is based on the instantaneous received signal power. The effects of channel correlations on the diversity and coding gain when the receiver system is a subset of the antennas are quantified. Theoretical results indicate that the correlations in the channel do not degrade the diversity order, provided that the channel is full rank. However, it does result in some performance loss in the coding gain.

In this paper, we study the performance of space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. Specifically, we derive upper bounds on the pairwise-error probability (PEP) with antenna selection. In performing the selection, we adopt a criterion that is based on using L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L les M. We show that the diversity order resulting from antenna selection deteriorates significantly and is actually dictated by the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasi-static fading channels in which the diversity order is always preserved with antenna selection when the underlying STTC is full-rank. We present numerical examples that support our analysis

In this paper, we propose a soft-input soft-output stack equalizer for multiple input multiple output (MIMO) frequency selective fading channels. In the literature, the soft or hard input/output stack algorithms to equalize single or multiple antenna time-invariant intersymbol interference (ISI) channels exist. After some modifications of the original sequential decoding metric, we show that the soft-input soft-output stack algorithm can be used at the receiver of the coded systems over frequency selective fading channels. Our examples illustrate that the proposed metrics result in promising near-optimum equalizers while offering a complexity independent of the memory of the channel.

We introduce iterative noise whitening for belief propagation (BP) based channel detectors over intersymbol interference (ISI) channels with correlated noise. Called noise predictive belief propagation (NPBP), the new scheme iteratively whitens the noise samples by modifying the edge probability computation of the BP algorithm. NPBP detectors based on finite impulse response (FIR) and infinite impulse response (IIR) prediction filters are introduced. In addition, we propose a novel prediction filter optimization method leading to a better noise whitening performance. Simulation results for both coded and uncoded systems and comparisons with maximum a posteriori (MAP) and BP detectors show that, significant improvements can be obtained.

In this paper, we develop capacity approaching turbo coding schemes for half-duplex relay systems as an extension of our previous work on the full-duplex relay systems. We design the codes to be used at the source and the relay nodes, and develop an information combining technique at the destination node. In addition, by utilizing information theoretical results, we compute the optimal fraction of time during which the relay node should listen, and use it in the design of capacity approaching coding/decoding schemes. We observe that the performance of the practical coding schemes proposed is about 1.2 dB away from the theoretical limits (for a variety of channel models)

In this paper, we design turbo-based coding schemes for relay systems together with iterative decoding algorithms. In the proposed schemes, the source node sends coded information bits to both the relay and the destination nodes, while the relay simultaneously forwards its estimate for the previous coded block to the destination after decoding and re-encoding. The destination observes a superposition of the codewords and uses an iterative decoding algorithm to estimate the transmitted messages. Different from the block-by-block decoding techniques used in the literature, this decoding scheme operates over all the transmitted blocks jointly. Various encoding and decoding approaches are proposed for both single-input single-output and multi-input multi-output systems over several different channel models. Capacity bounds and information-rate bounds with binary inputs are also provided, and it is shown that the performance of the proposed practical scheme is typically about 1.0-1.5 dB away from the theoretical limits, and a remarkable advantage can be achieved over the direct and multihop transmission alternatives.

We deal with antenna selection at the receiver side for space-time coded systems over frequency-selective fading channels. We reveal that introducing antenna selection based on the signal-to-noise-ratio (SNR) observed can still achieve the full diversity available, if the underlying space-time code (STC) is full-rank (i.e., if it achieves full diversity without antenna selection over the frequency-selective fading channel). We also argue that if the code is not full-rank, antenna selection results in a loss in the diversity of the system.

In I. Bahceci et al. (Oct 2003), antenna selection for multiple antenna transmission systems has been studied under the assumption that the subchannels between antenna pairs fade independently. In this paper, we consider the performance of such systems when the subchannels experience correlated fading. We assume that the channel state information is available only at the receiver, the antenna selection is performed only at the receiver, and the selection is based on the instantaneous received signal power. We quantify the effects of channel correlation on the diversity and coding gain when the receiver system uses all or a subset of the antennas. Theoretical results indicate that the correlations in the channel does not degrade the diversity order provided that the channel is full-rank. However, it does result in some performance loss in the coding gain. Furthermore, for non-full-rank channels, the diversity order of the system degrades significantly and is determined by the rank of the channel correlation matrix.

In this paper, turbo-based coding scheme for relay systems together with iterative decoding algorithms is designed. The performance of the proposed schemes is about 1.0-1.5 dB away from the information theoretical limits for various channel models.

We derive explicit upper bounds on the pairwise-error probability (PEP) for space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. In performing antenna selection, we adopt a selection criterion that is based on selecting L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L/spl les/M. We show that the resulting diversity order deteriorates significantly and becomes a function of the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasistatic fading channels in which the diversity order is always preserved with antenna selection when the underlying space-time code is full-rank. We also present simulation results that support our analysis.

This paper studies the antenna selection for space-time coded orthogonal frequency division multiplexing (OFDM) systems that employ multiple transmit and receive antennas. We assume that the channel state information (CSI) is exactly known at the receiver, and hence the selection is available only at the receiver. The selection criterion is based on the instantaneous signal-to-noise ratio at each receive antenna averaged over all carrier frequencies. We also assume that space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). Closed form expressions for the PEP hounds are derived for special cases. We also present numerical examples and simulation results that validate our analysis. It turns out that it is difficult to make remarks about the diversity order since the expressions are not simple, however, for some special cases with M = 2, N = 2 antennas, we show that using antenna selection, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity.

We propose a decentralized stochastic power control algorithm which exhibits superior performance over Rayleigh fading channels as compared to the existing methods. The algorithm is obtained by a modification of the original stochastic-power control (SPC) algorithm proposed in S. Ulukus et al. (1998), and it takes the time variations of the channel into account, while updating the transmit powers. We illustrate the performance enhancement provided by several practical examples. Furthermore, we combine the new algorithm and SPC with bit estimation developed in P. Akula et al. (2002) and study its performance.

We propose a simulation-based method to compute the achievable information rates for general multiple-input multiple-output (MIMO) intersymbol interference (ISI) channels with inputs chosen from a finite alphabet. This method is applicable to both deterministic and stochastic channels. As an example of the stochastic MIMO ISI channels, we consider the multiantenna systems over frequency-selective fading channels, and quantify the improvement in the achievable information rates provided by the additional frequency diversity (for both ergodic and nonergodic cases). In addition, we consider the multiaccess multiantenna system and present some results on the achievable information-rate region. As for the deterministic MIMO ISI channels, we use the binary-input multitrack magnetic recording system as an example, which employs multiple write and read heads for data storage. Our results show that the multitrack recording channels have significant advantages over the single-track channels, in terms of the achievable information rates when the intertrack interference is considered. We further consider practical coding schemes over both stochastic and deterministic MIMO ISI channels, and compare their performance with the information-theoretical limits. Specifically, we demonstrate that the performance of the turbo coding/decoding scheme is only about 1.0 dB away from the information-theoretical limits at a bit-error rate of 10/sup -5/ for large interleaver lengths.

Space-time coding is well established for high data rate communications over wireless channels with perfect channel state information. On the other hand, the case where the channel state information is unknown has received limited attention. Recently, a new signaling scheme called unitary space-time modulation that is suitable for the latter case has been proposed. We describe the use and design of trellis-coded space-time modulation schemes that use unitary space-time constellations. We construct these codes using a novel suboptimal code design criteria and study the performance of trellis-coded unitary space-time modulation for block fading channels under the assumption of no channel state information. Simulation results show that the proposed schemes improve the performance compared to uncoded transmission with the same spectral efficiency. The results are also compared with the turbo-coded modulation scheme Bahceci (2002) and the differential detection scheme described Jafarkhani (2001) under the same assumptions.

We propose a joint source-channel coding scheme for wireless communication systems with multiple transmit and receive antennas. The source coder is realized by a multiple description encoder that generates multiple bit streams for the same source. Each description is then separately turbo coded and transmitted using multiple antennas. For the receiver, we describe a suitable iterative joint source-channel decoding technique that exploits the correlations between the descriptions. Finally, we present several examples that illustrate the performance of the proposed system and compare it with other approaches.

Multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems employing space-time coding have been proposed for providing high-data rate services over wireless channels. These schemes combine the advantages of space-time coding and OFDM, resulting in a spectrally efficient wideband system. However, current MIMO-OFDM systems do not consider the problem of inherent high peak to average power ratio (PAPR). In this paper, we propose a general framework for PAPR reduction for space-time coded OFDM systems. We show that with the new scheme, significantly reduced PAPRs can be obtained at the cost of a slight decrease in the spectral efficiency of the system. In particular, using trellis shaping before space-time coding, examples show that a PAPR reduction of 4.5 dB is possible.

We derive performance bounds for turbo-coded systems with transmit and receive antenna diversity. The bounds are derived by limiting the conditional union bound before averaging over the fading process. It is demonstrated that this approach provides a tight upper bound on the error probability of the turbo-coded multiple antenna systems. We also describe a method for deriving the weight-enumerating function of turbo-coded multiple antenna systems in order to take into account the presence of transmit and receive antenna diversity. Examples of the bounds are presented to illustrate their usefulness.

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.

We derive the union bound for space-time trellis codes over quasi-static fading channels. We first observe that the standard approach for evaluating the union bound yields very loose, in fact divergent, bounds over the quasi-static fading channel. We then develop a method for obtaining a tight bound on the error probability. We derive the union bound by performing expurgation of the standard union bound. In addition, we limit the conditional union bound before averaging over the fading process. We demonstrate that this approach provides a tight bound on the error probability of space-time codes. The bounds can be used for the case when the fading coefficients among different transmit/receive antenna pairs are correlated as well. We present several examples of the bounds to illustrate their usefulness.

In this paper, we introduce a simulation-based method to compute the information rates of intersymbol interference (ISI) channels with signal-dependent Gaussian noise when the inputs are binary and independent identically distributed. The method extends the idea in Arnold et al. (2001), which focuses on the ISI channels with additive white Gaussian noise (AWGN). With the new method, we can compute the information rates of the Lorentzian channels with media noise that represents a suitable model for practical magnetic recording channels.

A distributed power control algorithm for a stochastic system when the estimates of the measured quantities are noisy has been proposed in Ululkus and Yates(1998). In this paper, we propose two different modifications of this algorithm that aim at lowering the noise variance of the measured quantities in order to achieve a faster rate of convergence. In the first approach, the received (possibly erroneous) bit of the desired user is used to obtain a more accurate estimate of its interference power. While in the second approach, the local information available at each base station is used to simulate an estimate of the interference power experienced by each one of its own users. Then a weighted average of this simulated interference power and the actual measured one is taken, effectively resulting in an average over a larger window, which lowers the noise variance. We demonstrate through simulations that both of these modifications achieve a faster rate of convergence compared to that of the existing algorithms for a distributed and stochastic system.

Space-time coding is well understood for high data rate communications over wireless channels with perfect channel state information. On the other hand, channel coding for multiple transmit antennas when channel state information is unknown has only received limited attention. A new signaling scheme, named unitary space-time modulation, has been proposed for the latter case. In this paper, we consider the use of turbo coding together with unitary space-time modulation. We demonstrate that turbo coded space-time modulation systems are well suited to wireless communication systems when there is no channel state information, in the sense that the turbo coding improves the bit error rate (BER) performance of the system considerably. In particular, we observe that the turbo-coded system provides 10-15 dB coding gain at a BER of 10/sup -5/ compared to the unitary space-time modulation for various transmit and receive antenna diversity cases.

Space-time coding is well established for high data rate communications in wireless channels with perfect channel state information. On the other hand, the case where channel state information is unknown has received limited attention. Recently, a new signaling scheme called unitary space-time modulation has been proposed for the latter case. In this paper, we describe the use and design of trellis coded space-time modulation schemes that use unitary space-time constellations. Simulation results show that the proposed schemes improve the performance compared to uncoded transmission with the same spectral efficiency.

In this paper, we study the problem of turbo coding for magnetic recording channels from a theoretical perspective. In particular we assume that the magnetic recording channel is modeled as a Lorentzian channel, and we develop performance bounds on the bit error probability of turbo codes (parallel or serial) with maximum likelihood decoding. The bound is also applicable to any (uniformly interleaved) binary linear code. This work is an extension of our recent work on performance bounds for partial response channels. The use of the bound is illustrated via some numerical examples, and comparisons based on the simulation results are provided.

We study the use of turbo-coded modulation for wireless communication systems with multiple transmit and receive antennas over block Rayleigh fading channels. We describe an effective way of applying turbo-coded modulation as an alternative to the current space-time codes with appropriate interleaving. We study the performance with the standard iterative turbo decoding algorithm, as well as the iterative demodulation-decoding algorithm. In addition to the introduction of the turbo-coded modulation scheme, we consider a variety of practical issues including the case of large number of antennas, the effects of estimated channel state information, and correlation among subchannels between different transmit-receive antenna pairs. We present examples to illustrate the performance of the turbo-coded modulation scheme and observe significant performance gains over the appropriately interleaved space-time trellis codes.

We develop union bounds for high-rate linear codes used for partial-response equalized channels with additive white Gaussian noise. The bounds assume uniform interleaving and are based on an approximation which is valid for high-rate linear codes. Furthermore, the derivation of the bounds assumes that maximum-likelihood decoding is employed. One particular application of the present setting is the computation of bounds for magnetic recording systems using turbo codes. The results can be considered as a generalization of the results of M. Oberg and P.H. Siegel (see Proc. Allerton Conf. Communications, Control and Computing, Sept. 1998) which develops the union bound for the dicode channel; however, our approach is completely different. We present several examples of the bounds developed together with the simulation results.

We apply the standard union bound to turbo-coded modulation systems with maximum-likelihood decoding. To illustrate the methodology, we explicitly derive the bounds for the 2-bits/s/Hz 16 QAM system. Generalization of this bound to other turbo-coded modulation systems is straightforward. As in the case of the standard union bound for turbo codes, we expect these bounds to be useful for rather large values of signal-to-noise ratios, i.e., signal-to-noise ratios for which the code rate is smaller than the corresponding cutoff rate. The bound is based on "uniform interleaving" just as its counterpart for standard turbo coding. The derived bound provides a tool for comparing coded modulation schemes having different component codes, interleaver lengths, mappings, etc., using maximum-likelihood decoding. It is also useful in studying the effectiveness of various suboptimal decoding algorithms. The bounding technique is also applicable to other coded-modulation schemes such as serially concatenated coded modulation.

We derive performance bounds for turbo-coded modulation systems over fading channels. We consider a Ricean fading channel model both with and without channel-state information (CSI). This model obviously includes Rayleigh fading channel as a special case. The bounds are extensions of similar bounds derived for additive white Gaussian noise channels. For the special case of a Rayleigh fading channel with CSI, we also derive a tighter version of the bound. We illustrate the use of the new bounds via some numerical examples.

We derive a new upper bound on the word- and bit-error probabilities of turbo codes with maximum-likelihood decoding by using the Gallager bound. Since the derivation of the bound for a given interleaver is intractable, we assume uniform interleaving as in the derivation of the standard union bound for turbo codes. The result is a generalization of the transfer function bound and remains useful for a wider range of signal-to-noise ratios, particularly for some range below the channel cutoff rate. The new bound is also applicable to other linear codes.

Optimal scalar quantizer design for transmission over a finite-state channel is considered. The objective Is to minimize the mean-squared error when the channel is in the normal mode of operation, while guaranteeing a minimum fidelity when the channel is in the "bad" state. An optimal quantizer design algorithm for the general case where noisy state information is available both at the receiver and at the transmitter is derived. It is shown that using mixed strategies is necessary in order to achieve the optimal performance. Finally, the case where the observation is noisy is considered and it is shown that the optimal scheme in this case is to apply the algorithm for the "no observation noise" to the mean-squared estimate of the desired random variable from the noisy data.