Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of estimating transmitted symbols from received observations can be modeled as an in-context learning problem: Received observations are a noisy function of transmitted symbols, and this function can be represented by an unknown parameter whose statistics depend on an unknown latent context. This problem, which we term in-context estimation (ICE), has significantly greater complexity than the extensively studied linear regression problem. The optimal solution to the ICE problem is a non-linear function of the underlying context. In this paper, we prove that, for a subclass of such problems, a single-layer softmax attention transformer (SAT) computes the optimal solution of the above estimation problem in the limit of large prompt length. We also prove that the optimal configuration of such a transformer is indeed the minimizer of the corresponding training loss. Further, we empirically demonstrate the proficiency of multi-layer transformers in efficiently solving broader in-context estimation problems. Through extensive simulations, we show that solving ICE problems using transformers significantly outperforms standard approaches. Moreover, just with a few context examples, it achieves the same performance as an estimator with perfect knowledge of the latent context.

Linguistic steganography aims to conceal information within natural language text without being detected. An effective steganography approach should encode the secret message into a minimal number of language tokens while preserving the natural appearance and fluidity of the stego-texts. We present a new framework to enhance the embedding efficiency of stego-texts generated by modifying the output of a large language model (LLM). The novelty of our approach is in abstracting the sequential steganographic embedding process as a Constrained Markov Decision Process (CMDP), which takes into consideration the long-term dependencies instead of merely the immediate effects. We constrain the solution space such that the discounted accumulative total variation divergence between the selected probability distribution and the original distribution given by the LLM is below a threshold. To find the optimal policy, we first show that the functional optimization problem can be simplified to a convex optimization problem with a finite number of variables. A closed-form solution for the optimal policy is then presented to this equivalent problem. It is remarkable that the optimal policy is deterministic and resembles water-filling in some cases. The solution suggests that usually adjusting the probability distribution for the state that has the least random transition probability should be prioritized, but the choice should be made by taking into account the transition probabilities at all states instead of only the current state.

We consider the design of a modern uplink for supporting machine-type communication and the confluence of sensing, communication, and distributed learning. We demonstrate that grant-free multiple access is possible even in the presence of highly time-varying channels and high delay spread. Our approach is built on enhancing the 2 -step random access procedure of the 5GNR standard. This 2 -step procedure uses Zadoff-Chu (ZC) sequences as preambles that point to radio resources which are then used to upload data. ZC sequences are processed in the delay-Doppler (DD) domain rather than the time domain. We demonstrate that it is possible to detect multiple preambles in the presence of mobility and delay spread using a receiver with no knowledge of the channel other than the worst case delay and Doppler spreads. Our approach depends on the mathematical properties of ZC sequences in the DD domain. We derive a closed form expression for ZC pilots in the DD domain, we characterize the possible self-ambiguity functions, and we determine the magnitude of the possible cross-ambiguity functions. These mathematical properties combine with Zak-OTFS modulation to enable detection of multiple pilots through solution of a compressed sensing problem. The columns of the compressed sensing matrix are the translates of individual ZC pilots in delay and Doppler. We show that columns in the design matrix satisfy a coherence property that makes it possible to detect multiple preambles in a single Zak-OTFS subframe using One-Step Thresholding, which is an algorithm with low complexity.

It is well known that separation between lossy source coding and channel coding is asymptotically optimal under classical additive distortion measures. Recently, coding under a new class of quality considerations, often referred to as perception or realism, has attracted significant attention due to its close connection to neural generative models and semantic communications. In this work, we revisit source-channel separation under the consideration of distortion-perception. We show that when the perception quality is measured on the block level, i.e., in the strong sense, the optimality of separation still holds when common randomness is shared between the encoder and the decoder; however, separation is no longer optimal when such common randomness is not available. In contrast, when the perception quality is the average per-symbol measure, i.e., in the weak sense, the optimality of separation holds regardless of the availability of common randomness.

The design of reliable and efficient codes for channels with feedback remains a longstanding challenge in communication theory. While significant improvements have been achieved by leveraging deep learning techniques, neural codes often suffer from high computational costs, a lack of interpretability, and limited practicality in resource-constrained settings. We focus on designing low-complexity coding schemes that are interpretable and more suitable for communication systems. We advance both analytical and neural codes. First, we demonstrate that PowerBlast, an analytical coding scheme inspired by Schalkwijk-Kailath (SK) and Gallager-Nakiboğlu (GN) schemes, achieves notable reliability improvements over both SK and GN schemes, outperforming neural codes in high signal-to-noise ratio (SNR) regions. Next, to enhance reliability in low-SNR regions, we propose LightCode, a lightweight neural code that achieves state-of-the-art reliability while using a fraction of memory and compute compared to existing deep-learning-based codes. Finally, we systematically analyze the learned codes, establishing connections between LightCodeand PowerBlast, identifying components crucial for performance, and providing interpretation aided by linear regression analysis.

This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC), whose respective field size and section sizes are equal. For such codes, an efficient decoding algorithm is proposed based on approximate message passing (AMP) that dynamically shares soft information between inner and outer decoders. This dynamic exchange of information is facilitated by a denoiser that runs belief propagation (BP) on the factor graph of the outer LDPC code within each AMP iteration. It is shown that this BP denoiser falls within the framework of non-separable denoising functions and subsequently, that state evolution holds for the proposed AMP-BP algorithm. Leveraging the rich structure of SR-LDPC codes, this article proposes an efficient low-dimensional approximate state evolution recursion that can be used for efficient hyperparameter tuning, thus paving the way for future work on optimal code design. Finally, numerical simulations demonstrate that SR-LDPC codes outperform contemporary codes over the AWGN channel for parameters of practical interest. SR-LDPC codes are shown to be viable means for obtaining shaping gains over the AWGN channel.

Novel sparse regression LDPC (SR-LDPC) codes exhibit excellent performance over additive white Gaussian noise (AWGN) channels in part due to their natural provision of shaping gains. Though SR-LDPC-like codes have been considered within the context of single-user error correction and massive random access, they are yet to be examined as candidates for coordinated multi-user communication scenarios. This article explores this gap in the literature and demonstrates that SR-LDPC codes, when combined with coded demixing techniques, offer a new framework for efficient non-orthogonal multiple access (NOMA) in the context of coordinated multi-user communication channels. The ensuing communication scheme is referred to as MU-SR-LDPC coding. Empirical evidence suggests that MU-SR-LDPC coding can increase the sum-rate for a fixed Eb/N0 when compared to orthogonal multiple access (OMA) techniques such as time division multiple access (TDMA) or frequency division multiple access (FDMA). Importantly, MU-SR-LDPC coding enables a pragmatic solution path for user-centric cell-free communication systems with (local) joint decoding. Results are supported by numerical simulations.

Recent work has argued that federated learning over wireless channels can be accelerated by a factor of$K$(the numbers of users), by using computation over multiple-access channels to directly average the gradients. This implicitly presumes that timely channel state information is available at the transmitters, which may not be feasible for large$K$. This paper presents a simple scheduling algorithm that only uses channel state information at the receiver to activate a subset of the users for computation, and accelerates averaging by a factor of$K^{2/3}$.

Iterative decoding of graph-based codes and sparse recovery through approximate message passing (AMP) are two research areas that have seen monumental progress in recent decades. Inspired by these advances, this article introduces sparse regression LDPC codes (SR-LDPC codes) and their decoding. Sparse regression codes (SPARCs) are a class of error correcting codes that build on ideas from compressed sensing and can be decoded using AMP. In certain settings, SPARCs are known to achieve capacity; yet, their performance suffers at finite block lengths. Likewise, low-density parity-check (LDPC) codes can be decoded efficiently using belief propagation and can also be capacity achieving. This article introduces a novel concatenated coding structure that combines an LDPC outer code with a SPARC-inspired inner code. Efficient decoding for such a code can be achieved using AMP with a denoiser that performs belief propagation on the factor graph of the outer LDPC code. The proposed framework exhibits performance improvements over SPARCs and standard LDPC codes for finite block lengths and results in a steep waterfall in error performance, a phenomenon not observed in uncoded SPARCs.

In this work we demonstrate how a lack of synchronization can in fact be advantageous in the problem of random access. Specifically, we consider a multiple-access problem over a frame-asynchronous 2-user binary-input adder channel in the unsourced setup (2-UBAC). Previous work has shown that under perfect synchronization the per-user rates achievable with linear codes over the 2-UBAC are limited by 0.5 bit per channel use (compared to the capacity of 0.75). In this paper, we first demonstrate that arbitrary small (even single-bit) shift between the user’s frames enables (random) linear codes to attain full capacity of 0.75 bit/user. Furthermore, we derive density evolution equations for irregular LDPC codes, and prove (via concentration arguments) that they correctly track the asymptotic bit-error rate of a BP decoder. Optimizing the degree distributions we construct LDPC codes achieving per-user rates of 0.73 bit per channel use.

We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.

Unsourced random access emerged as a novel wireless paradigm enabling massive device connectivity on the uplink. We consider quasi-static Rayleigh fading wherein the access point has multiple receive antennas and every mobile device a single transmit antenna. The objective is to construct a coding scheme that minimizes the energy-per-bit subject to a maximum probability of error given a fixed message length and a prescribed number of channel uses. Every message is partitioned into two parts: the first determines pilot values and spreading sequences; the remaining bits are encoded using a polar code. The transmitted signal contains two distinct sections. The first features pilots and the second is composed of spread modulated symbols. The receiver has three modules: an energy detector, tasked with recovering the set of active pilot sequences; a bank of Minimum Mean Square Error (MMSE) estimators acting on measurements at the receiver; and a polar list-decoder, which seeks to retrieve the coded information bits. A successive cancellation step is applied to subtract recovered codewords, before the residual signal is fed back to the decoder. Empirical evidence suggests that an appropriate combination of these ideas can outperform state-of-the-art coding techniques when the number of active users exceeds one hundred.

We consider the design of low-delay joint source-channel coding (JSCC) schemes for the transmission of discrete-time analog sources over noisy channels based on deep neural networks. The design problem is addressed as optimization of an autoencoder model, and several scenarios are discussed. For point-to-point communication of independent and identically distributed (i.i.d) Gaussian sources and Gauss-Markov sources over additive-white Gaussian noise (AWGN) channels, the encoder and decoder are constructed using recurrent neural networks (RNNs). With minimum prior knowledge used for design, the performance of these RNNs-based models is optimized using fine tuning techniques during training. Sinusoidal representation networks (SIRENs)-based models are proposed and optimized for three JSCC problems namely, transmitting multivariate Gaussian sources over AWGN channels, transmitting i.i.d Gaussian sources with side information at the decoder, and for communicating correlated sources over orthogonal Gaussian channels. We show that these deep learning-based JSCC schemes perform comparably or better than state-of-the-art (SOTA) traditional schemes. The proposed scheme can extend flexibly to different pairs of source and channel dimensions. Moreover, the spontaneously learned encoder mappings exhibit structured patterns that are interpretable.

We introduce two generalizations to the paradigm of using Random Khatri-Rao Product (RKRP) codes for distributed matrix multiplication. We first introduce a class of codes called Sparse Random Khatri-Rao Product (SRKRP) codes which have sparse generator matrices. SRKRP codes result in lower encoding, computation and communication costs than RKRP codes when the input matrices are sparse, while they exhibit similar numerical stability to other state of the art schemes. We empirically study the relationship between the probability of the generator matrix (restricted to the set of non-stragglers) of a randomly chosen SRKRP code being rank deficient and various parameters of the coding scheme including the degree of sparsity of the generator matrix and the number of non-stragglers. Secondly, we show that if the master node can perform a very small number of matrix product computations in addition to the computations performed by the workers, the failure probability can be substantially improved.

We propose a semi-blind decision-directed joint channel estimation and decoding algorithm for low-density parity check (LDPC) coded Orthogonal Frequency Division Multiplexing (OFDM) systems. There are two novel aspects in our algorithm - (i) an enhanced semi-blind channel estimation algorithm that hypothesizes a small set of symbols as additional pilots and (ii) an edge strength-based metric to determine a small subset of decisions at the output of the LDPC decoder as being reliable. Our algorithm has an order of magnitude lower complexity than a recently proposed machine learning-based channel estimation algorithm, while their performances are comparable.

This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a sparse random multi-access graph conducive to joint decoding. This construction leverages the lessons learned from traditional IDMA into creating low-complexity schemes for the unsourced setting, while also accounting for inherent randomness. Under joint message-passing decoding, the proposed scheme offers good performance at a low computational complexity. Findings are supported by numerical simulations, and results are compared to existing alternatives.

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced random access with coded compressed sensing (CCS), as first demonstrated by Fengler, Jung, and Caire. Specifically, their approach employs a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In their original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. This scheme necessitates the redesign of the outer code as to enable belief propagation in a computationally tractable manner. The enhanced architecture exhibits significant performance benefits over a range of system parameters. The error performance of the proposed scheme can be accurately predicted through a set of equations known as state evolution of AMP. These findings are supported both analytically and through numerical methods.

This article seeks to advance coded compressed sensing (CCS) as a practical scheme for unsourced random access. The CCS algorithm features a concatenated structure where an inner code is tasked with support recovery and an outer code conducts message disambiguation. Recently, the CCS scheme was improved through the use of approximate message passing (AMP) with a dynamic denoiser that shares soft information between the inner and outer decoders. This significantly improves performance at the cost of additional complexity. This work shows how the spatial coupling generated by the outer code is sufficiently strong to justify relaxing certain constraints on the inner code. It is shown that a block diagonal sensing matrix with the aforementioned dynamic denoiser forms an effective means to get good performance at reduced complexity. This novel architecture can be used to scale CCS to dimensions that were previously impractical. Findings are supported by numerical simulations.

Abstract We propose two-stage adaptive pooling schemes, 2-STAP and 2-STAMP, for detecting COVID-19 using real-time reverse transcription quantitative polymerase chain reaction (RT-qPCR) test kits. Similar to the Tapestry scheme of Ghosh et al ., the proposed schemes leverage soft information from the RT-qPCR process about the total viral load in the pool. This is in contrast to conventional group testing schemes where the measurements are Boolean. The proposed schemes provide higher testing throughput than the popularly used Dorfman’s scheme. They also provide higher testing throughput, sensitivity and specificity than the state-of-the-art non-adaptive Tapestry scheme. The number of pipetting operations is lower than state-of-the-art non-adaptive pooling schemes, and is higher than that for the Dorfman’s scheme. The proposed schemes can work with substantially smaller group sizes than non-adaptive schemes and are simple to describe. Monte-Carlo simulations using the statistical model in the work of Ghosh et al . (Tapestry) show that 10 infected people in a population of size 961 can be identified with 70.86 tests on the average with a sensitivity of 99.50% and specificity of 99.62%. This is 13.5x, 4.24x, and 1.3x the testing throughput of individual testing, Dorfman’s testing, and the Tapestry scheme, respectively.

This article presents a novel enhancement to the random spreading based coding scheme developed by Pradhan et al. for the unsourced multiple access channel. The original coding scheme features a polar outer code in conjunction with a successive cancellation list decoder (SCLD) and a hard-input soft-output MMSE estimator. In contrast, the proposed scheme employs a soft-input soft-output MMSE estimator for multi-user detection. This is accomplished by replacing the SCLD based polar code with an LDPC code amenable to belief propagation decoding. This novel framework is leveraged to successfully pass pertinent soft information between the MMSE estimator and the outer code. LDPC codes are carefully designed using density evolution techniques to match the iterative process. This enhanced architecture exhibits significant performance improvements and represents the state-of-the-art over a wide range of system parameters.

We revisit the joint source-channel coding (JSCC) problem of transmitting correlated sources over the additive white Gaussian noise channel using deep learning methods. Specifically, we consider the design of JSCC schemes for transmitting multivariate Gaussian sources, and Gauss-Markov processes over noisy channels with bandwidth (BW) compression and low delay. We show that encoding and decoding schemes represented by deep neural networks can be optimized jointly to obtain good JSCC schemes. Specifically, we adopt sinusoidal representation networks (SIRENs) for the transmission of multivariate Gaussian sources. The new architecture not only provides similar performance as the state-of-the-art (SOTA) with higher flexibility, but also results in interpretable encoder mappings. For the transmission of Gauss-Markov sources, recurrent neural networks (RNNs) are implemented to extract temporal information without resorting to explicit decorrelation prior to transmission. Experimental results show improved performance compared with traditional schemes.

We consider the approximate support recovery (ASR) task of inferring the support of a$K$-sparse vector$\mathrm{x}\in \mathbb{R}^{n}$from$m$noisy measurements. We examine the case where$n$is large, which precludes the application of standard compressed sensing solvers, thereby necessitating solutions with lower complexity. We design a scheme for ASR by leveraging techniques developed for unsourced multiple access. We present two decoding algorithms with computational complexities$\mathcal{O}(K^{2}\log n+ K\log n\log\log n)$and$\mathcal{O}(K^{3}+K^{2}\log n+K\log n\log \log n)$per iteration, respectively. When$K\ll n$, this is much lower than the complexity of approximate message passing with a minimum mean squared error denoiser, which requires$\mathcal{O}(mn)$operations per iteration. This gain comes at a slight performance cost. Our findings suggest that notions from multiple access can play an important role in the design of measurement schemes for ASR.

We introduce a class of codes, called Squeezed Random Khatri-Rao Product (RKRP) codes, for coded matrix multiplication when each worker node can perform multiple submatrix products. The proposed codes are a generalization of RKRP codes in [1] and are built on the idea of squeezed polynomial codes in [2]. We show that squeezed RKRP codes are maximum distance separable with probability 1. They have the same communication cost as that of squeezed polynomial codes while offering better numerical stability.

Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to machine-type communications. Coded compressed sensing uses a divide-and-conquer approach to break the sparse recovery task into sub-components whose dimensions are amenable to conventional compressed sensing solvers. The recovered fragments are then stitched together using a low complexity decoder. This article introduces an enhanced decoding algorithm for coded compressed sensing where fragment recovery and the stitching process are executed in tandem, passing information between them. This novel scheme leads to gains in performance and a significant reduction in computational complexity. This algorithmic opportunity stems from the realization that the parity structure inherent to coded compressed sensing can be used to dynamically restrict the search space of the subsequent recovery algorithm.

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In this paper, we advocate learning implicit latent representations using semi-implicit variational inference to further increase model flexibility. Semi-implicit stochastic recurrent neural network (SIS-RNN) is developed to enrich inferred model posteriors that may have no analytic density functions, as long as independent random samples can be generated via reparameterization. Extensive experiments in different tasks on real-world datasets show that SIS-RNN outperforms the existing methods.

This article presents a novel transmission scheme for the unsourced, uncoordinated Gaussian multiple access problem. The proposed scheme leverages notions from single-user coding, random spreading, minimum-mean squared error (MMSE) estimation, and successive interference cancellation. Specifically, every message is split into two parts: the first fragment serves as the argument to an injective function that determines which spreading sequence should be employed, whereas the second component of the message is encoded using a polar code. The latter coded bits are then spread using the sequence determined during the first step. The ensuing signal is transmitted through a Gaussian multiple-access channel (GMAC). On the receiver side, active sequences are detected using a correlation-based energy detector, thereby simultaneously recovering individual signature sequences and their generating information bits in the form of preimages of the sequence selection function. Using the set of detected active spreading sequences, an MMSE estimator is employed to produce log-likelihood ratios (LLRs) for the second part of the messages corresponding to these detected users. The LLRs associated with each detected user are then passed to a list decoder of the polar code, which performs single-user decoding to decode the second portion of the message. This decoding operation proceeds iteratively by subtracting the interference due to the successfully decoded messages from the received signal, and repeating the above steps on the residual signal. At this stage, the proposed algorithm outperforms alternate existing low-complexity schemes when the number of active uses is below 225.

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning themas model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. GNN training with adaptive connection sampling is shown to be mathematically equivalent to an efficient approximation of training BayesianGNNs. Experimental results with ablation studies on benchmark datasets validate that adaptively learning the sampling rate given graph training data is the key to boost the performance of GNNs in semi-supervised node classification, less prone to over-smoothing and over-fitting with more robust prediction.

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced access with coded compressed sensing (CCS), as first pointed out by Fengler, Jung, and Caire. More specifically, their approach uses a concatenated coding framework with an inner AMP decoder followed by an outer tree decoder. In the original implementation, these two components work independently of each other, with the tree decoder acting on the static output of the AMP decoder. This article introduces a novel framework where the inner AMP decoder and the outer tree decoder operate in tandem, dynamically passing information back and forth to take full advantage of the underlying CCS structure. The enhanced architecture exhibits significant performance benefit over a range of system parameters.

We propose two coding schemes for distributed matrix multiplication in the presence of stragglers. These coding schemes are adaptations of Luby Transform (LT) codes and Raptor codes to distributed matrix multiplication and are termedFactored LT (FLT) codesandFactored Raptor (FRT) codes. We show that all nodes in the Tanner graph of a randomly sampled code have a tree-like neighborhood with high probability. This ensures that the density evolution analysis gives a reasonable estimate of the average recovery threshold of FLT codes. The recovery threshold of the proposed FLT codes is asymptotically optimal when the output degree distribution is Soliton. Empirically, we show that FRT codes have an excellent recovery threshold while the number of worker nodes is moderately large. In addition, using Azuma–Hoeffding inequality, we derive concentration results to show that the recovery threshold of a randomly chosen FLT code is close to the ensemble average. FLT and FRT codes have better recovery thresholds when compared to Product codes and they are expected to have better numerical stability when compared to Polynomial codes, while they can also be decoded with a low-complexity decoding algorithm. Finally, the proposed codes are better matched to the practically important case of sparse matrix-matrix multiplication as compared to many previous schemes.

This work considers the distributed multivariate polynomial evaluation (DMPE) problem using a master-worker framework, which was originally considered by Yu et al., where Lagrange Coded Computing (LCC) was proposed as a coded computation scheme to provide resilience against stragglers for the DMPE problem. In this work, we propose a variant of the LCC scheme, termed Product Lagrange Coded Computing (PLCC), by combining ideas from classical product codes and LCC. The main advantage of PLCC is that they are more numerically stable than LCC; however, their resilience to stragglers is sub-optimal.

High-throughput molecular profiling technologies have produced high-dimensional multi-omics data, enabling systematic understanding of living systems at the genome scale. Studying molecular interactions across different data types helps reveal signal transduction mechanisms across different classes of molecules. In this paper, we develop a novel Bayesian representation learning method that infers the relational interactions across multi-omics data types. Our method, Bayesian Relational Learning (BayReL) for multi-omics data integration, takes advantage of a priori known relationships among the same class of molecules, modeled as a graph at each corresponding view, to learn view-specific latent variables as well as a multi-partite graph that encodes the interactions across views. Our experiments on several real-world datasets demonstrate enhanced performance of BayReL in inferring meaningful interactions compared to existing baselines.

This article introduces a novel scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent advances in compressed sensing and forward error correction to produce a novel uncoordinated access paradigm, along with a computationally efficient decoding algorithm. Within this framework, every active device partitions its data into several sub-blocks and, subsequently, adds redundancy using a systematic linear block code. Compressed sensing techniques are then employed to recover sub-blocks up to a permutation of their order, and the original messages are obtained by stitching fragments together using a tree-based algorithm. The error probability and computational complexity of this access paradigm are characterized. An optimization framework, which exploits the tradeoff between performance and computational complexity, is developed to assign parity-check bits to each sub-block. In addition, two emblematic parity bit allocation strategies are examined and their performances are analyzed in the limit as the number of active users and their corresponding payloads tend to infinity. The number of channel uses needed and the computational complexity associated with these allocation strategies are established for various scaling regimes. Numerical results demonstrate that coded compressed sensing outperforms other existing practical access strategies over a range of operational scenarios.

Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes defined on the vertices of graphs. It has been shown that well-known spectral graph kernel methods assume that the underlying random process over a graph is stationary. While many approaches have been proposed, both in machine learning and signal processing literature, to model stationary random processes over graphs, they are too restrictive to characterize real-world datasets as most of them are non-stationary processes. In this paper, to well-characterize a non-stationary process over graph, we propose a novel model and a computationally efficient algorithm that partitions a large graph into disjoint clusters such that the process is stationary on each of the clusters but independent across clusters. We evaluate our model for traffic prediction on a large-scale dataset of fine-grained highway travel times in the Dallas-Fort Worth area. The accuracy of our method is very close to the state-of-the-art graph based deep learning methods while the computational complexity of our model is substantially smaller.

This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a sparse random multi-access graph conducive to joint decoding. This construction leverages the lessons learned from traditional IDMA into creating low- complexity schemes for the unsourced setting and its inherent randomness. Under joint message- passing decoding, the proposed scheme offers superior performance compared to existing low- complexity alternatives. Findings are supported by numerical simulations.

The neighbor discovery paradigm finds wide application in Internet of Things networks, where the number of active devices is orders of magnitude smaller than the total device population. Designing low-complexity schemes for asynchronous neighbor discovery has recently gained significant attention from the research community. Concurrently, a divide-and-conquer framework, referred to as coupled compressive sensing, has been introduced for the synchronous massive random access channel. This work adapts this novel algorithm to the problem of asynchronous neighbor discovery with unknown transmission delays. Simulation results suggest that the proposed scheme requires much fewer transmissions to achieve a performance level akin to that of state-of-the-art techniques.

This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of N items among which K items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the result of a test reveals the number of defective items in the tested group. In this work, we propose a non-adaptive QGT scheme using sparse graph codes over bi-regular bipartite graphs and binary t-error-correcting BCH codes. The proposed scheme provides exact recovery with probabilistic guarantee, i.e. recovers all the defective items with high probability. In particular, we show that for the sub-linear regime where K vanishes as K, N → ∞, the proposed scheme requires at most m ≈ 1.19K log2(4.74 N/K) tests to recover all the defective items with probability approaching one as K, N → ∞. This bound can be achieved by t = 2. The testing and recovery algorithms of the proposed scheme for any t ≤ 4 have the computational complexity of O(K log2N/K) and O(K log N/K), respectively. Our simulation results also show that the proposed scheme significantly outperforms a non-adaptive semi-quantitative group testing scheme recently proposed by Abdalla et al. in terms of the required number of tests for identifying all the defective items with high probability.

We show that Polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Generalized Reed-Solomon codes and hence, can be collaboratively decoded. We consider a fault-tolerant setup where t out of N workers return erroneous values. For an additive random Gaussian error model, we show that for any t ≤ N - K - 1, where K is the effective dimension of the code, all errors can be corrected with probability 1 while the decoding complexity is O(( L/L+1)4(N - K)4+ LN) for any L ≥ N - K - 1.

Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph recurrent neural network (GRNN) to capture both topology and node attribute changes in dynamic graphs. We argue that the use of high-level latent random variables in this variational GRNN (VGRNN) can better capture potential variability observed in dynamic graphs as well as the uncertainty of node latent representation. With semi-implicit variational inference developed for this new VGRNN architecture (SI-VGRNN), we show that flexible non-Gaussian latent representations can further help dynamic graph analytic tasks. Our experiments with multiple real-world dynamic graph datasets demonstrate that SI-VGRNN and VGRNN consistently outperform the existing baseline and state-of-the-art methods by a significant margin in dynamic link prediction.

Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. SIG-VAE integrates a carefully designed generative model, well suited to model real-world sparse graphs, and a sophisticated variational inference network, which propagates the graph structural information and distribution uncertainty to capture complex posteriors. SIG-VAE clearly outperforms a simple combination of VGAE with variational inference, including semi-implicit variational inference~(SIVI) or normalizing flow (NF), which does not propagate uncertainty in its inference network, and provides more interpretable latent representations than VGAE does. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.

This work introduces a novel coding paradigm for the unsourced multiple access channel model. The envisioned framework builds on a select few key components. First, the transmission period is partitioned into a sequence of sub-blocks, thereby yielding a slotted structure. Second, messages are split into two parts. A portion of the data is encoded using spreading sequences or codewords that are designed to be recovered by a compressed sensing type decoder. In addition to being an integral part of the data, the information bits associated with this first part also determine the parameters of the low-density parity check code employed during the subsequent stages of the communication process. The other portion of the message is encoded using the aforementioned low-density parity check code. The data embedded in this latter stage is decoded using a joint message passing algorithm designed for the T-user binary input real adder channel. Finally, devices repeat their codeword in multiple sub-blocks, with the transmission pattern being a deterministic function of message content independent of the identity of the device. When combined with successive interference cancellation, the ensuing communication infrastructure offers significant performance improvement compared to coding schemes recently published in the literature for unsourced random access.

This article introduces a novel paradigm for the unsourced multiple-access communication problem. This divide-and-conquer approach leverages recent advances in compressive sensing and forward error correction to produce a computationally efficient algorithm. Within the proposed framework, every active device first partitions its data into several subblocks, and subsequently adds redundancy using a systematic linear block code. Compressive sensing techniques are then employed to recover sub-blocks, and the original messages are obtained by connecting pieces together using a low-complexity tree-based algorithm. Numerical results suggest that the proposed scheme outperforms other existing practical coding schemes. Measured performance lies approximately 4.3 dB away from the Polyanskiy achievability limit, which is obtained in the absence of complexity constraints.

The frame error rate (FER) of spatially-coupled irregular low-density parity-check (SC-iLDPC) code ensemble in error floor region is estimated. First, the number of codewords of each weight is calculated by the permutations of all the sub-codewords at their coupling positions. Second, the FER is estimated by these numbers of the codewords of each weight. Numerical results show that the FER performances in the error floor regions of the SC-iLDPC code ensembles are superior to the conventional irregular LDPC code ensembles at almost identical belief-propagation (BP) thresholds.

We evaluate a new MAC layer algorithm based on slotted ALOHA with successive interference cancellation(SIC) for IEEE 802.11p vehicular communications standard and test it by taking into consideration the performance of underlying physical layer in the presence of a realistic empirical fading channel model. The performance of slotted ALOHA-SIC MAC scheme with respect to average packet loss ratio, throughput, and channel access delay is studied. This scheme can significantly improve the channel access delay and throughput performance in vehicular networks when compared to the carrier sense multiple access scheme proposed in 802.11.

This paper introduces a high rate error-correcting coding scheme called symmetric block-wise concatenated Bose-Chaudhuri-Hocquenghem (symmetric BC-BCH) codes tailored for storage devices with hard-decision outputs, e.g., storage devices based on NAND flash memory. It will be shown that a careful integration of the symmetry and 2-D block-wise concatenation is especially beneficial to achieve improvements of error-rate performance when an iterative hard-decision-based decoding (IHDD) is assumed. The claim is substantiated by proving that the proposed symmetric concatenation is optimal in terms of error-rate performance in the low error-rate regime over other 2-D block-wise concatenations. Besides, this paper proposes a novel way to design constituent codes, which enables us to enjoy advantages of primitive BCH codes and to efficiently break stopping sets associated with the IHDD in the low error-rate regime. We consider error-control systems made up of a symmetric BC-BCH code, the IHDD, and simple auxiliary decoders specifically targeting to break stopping sets caused in the IHDD. It will be shown that the auxiliary decoders significantly improve error-rate performance at a negligible amount of extra complexity. Performance comparisons are also carried out between error-control systems with the proposed and other coding schemes such as BCH codes, quasi-primitive BC-BCH codes, and low-density parity-check codes.

In this paper, we extend Construction A of lattices to the ring of algebraic integers of a general imaginary quadratic field that may not form a principal ideal domain (PID). We show that such a construction can produce good lattices for coding in the sense of Poltyrev and for MSE quantization. As an application, we then apply the proposed lattices to the compute-and-forward paradigm with limited feedback. Without feedback, compute-and-forward is typically realized with lattice codes over the ring of integers, the ring of Gaussian integers, or the ring of Eisenstein integers, which are all PIDs. A novel scheme called adaptive compute-and-forward is proposed to exploit the limited feedback about the channel state by working with the best ring of imaginary quadratic integers. Simulation results show that by adaptively choosing the best ring among the considered ones according to the limited feedback, the proposed adaptive compute-and-forward provides a better performance than that provided by the conventional compute-and-forward scheme which works over Gaussian or Eisenstein integers solely.

We consider a joint source-channel decoding (JSCD) problem where the source encoder leaves residual redundancy in the source. We first model the redundancy in the source encoder output as the output of a side information channel at the channel decoder, and show that this improves random error exponent. Then, we consider the use of polar codes in this framework when the source redundancy is modeled using a sequence of t-erasure correcting block codes. For this model, the rate of polar codes can be improved by unfreezing some of originally frozen bits and that the improvement in rate depends on the distribution of frozen bits within a codeword. We present a proof for the convergence of that distribution, as well as the convergence of the maximum rate improvement. The significant performance improvement and improved rate provide strong evidences that polar code is a good candidate to exploit the benefit of source redundancy in the JSCD scheme.

We propose a novel coding scheme for the unsourced multiple access channel model introduced by Polyanskiy [1]. This new paradigm is composed of four main ingredients: (i) the transmission period is partitioned into sub-blocks, thereby instituting a slotted framework; (ii) The message (data) is split into two parts and one part chooses an interleaver for a low density parity check (LDPC) type code. This part of the message is encoded using spreading sequences or codewords that are designed to be decoded by a compressed sensing type decoder; (iii) The other part of the message is encoded using a low density parity check (LDPC) type code and decoded using a joint message passing decoding algorithm designed for the T-user binary input real adder channel; (iv) users repeat their codeword in multiple sub-blocks, with the transmission pattern being a deterministic function of message content and independent of the identity of the user. When this coding scheme is combined with serial interference cancellation, the ensuing communication infrastructure can offer significant performance improvements compared to the recently proposed coding scheme in [2] and results in the best performing coding scheme to date.

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of L linear codes over Fp1,..., FpL, respectively, and hence is referred to as Construction πA. The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction πAlattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction πDis also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction πAas special cases.

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability decoding of their component codes. In this paper, we show that one can approach capacity at high rates using iterative hard-decision decoding (HDD) of generalized product codes. Specifically, a class of spatially coupled generalized LDPC codes with Bose-Chaudhuri-Hocquengham component codes is considered, and it is observed that, in the high-rate regime, they can approach capacity under the proposed iterative HDD. These codes can be seen as generalized product codes and are closely related to braided block codes. An iterative HDD algorithm is proposed that enables one to analyze the performance of these codes via density evolution.

We propose a joint list decoder and language decoder that exploits the redundancy of language- based sources during polar decoding. By judging the validity of decoded words in the decoded sequence with the help of a dictionary, the polar list decoder constantly detects erroneous paths after the decoding of every few bits. This path-pruning technique based on joint decoding has advantages over stand-alone polar list decoding in that most decoding errors in early stages are corrected. We show that if the language structure can be modeled as erasure correcting outer block codes, the rate of inner polar code can be increased while still guaranteeing a vanishing probability of error. To facilitate practical joint decoding, we first propose a construction of a dynamic dictionary using a trie and show an efficient way to trace the dictionary during decoding. Then we propose a joint decoding scheme for polar codes taking into account both information from the channel and the source. The proposed scheme has the same decoding complexity as the list decoding of polar codes. A list-size adaptive joint decoding is further implemented to largely reduce the decoding complexity. Simulation results show that the joint decoding schemes outperform stand-alone polar codes with CRC-aided successive cancellation list decoding by over 0.6 dB.

We consider the problem of physical-layer network coding when the channel exhibits block fading. Specifically, we focus on the use of lattice codes in a compute-and-forward framework for realizing physical-layer network coding. We construct a novel lattice ensemble called the root-Low-Density Construction-A (root-LDA) ensemble which uses Construction A with root-low-density parity check (LDPC) codes. Using extensive simulations, we show that the proposed lattice codes exhibit full diversity when used over the block fading channels. In addition, their performance is comparable to the performance of LDA lattice codes optimized by the progressive edge growth algorithm over the additive white Gaussian noise AWGN channel. This suggests that root-LDA lattice codes provide a robust solution to the problem of implementing physical layer network coding over fading channels.

Future wireless access points may have to support sporadic transmissions from a massive number of unattended machines. Recently, there has been a lot of interest in the design of massive uncoordinated multiple access schemes for such systems based on clever enhancements to slotted ALOHA. A close connection has been established between the design of the multiple access scheme and the design of low density generator matrix codes. Based on this connection, optimal multiple access schemes have been designed based on slotted ALOHA and successive interference cancellation, assuming that the number of users in the network is known at the transmitters. In this paper, we extend this work and consider the design of universal uncoordinated multiple access schemes that are agnostic to the number of users in the network. We design Markov chain based transmission policies and numerical results show that substantial improvement to slotted ALOHA is possible.

In [1], [2], two schemes have been proposed to recover the support of a K-sparse N-dimensional signal from noisy linear measurements. Both schemes use left-regular sparse-graph code based sensing matrices and a simple peeling-based decoding algorithm. Both the schemes require O(K logN) measurements and the first scheme require O(N logN) computations whereas the second scheme requires O(K logN) computations (sub-linear time complexity when K is sub-linear in N). We show that by replacing the left-regular ensemble with left and right regular ensemble, we can reduce the number of measurements required of these schemes to the optimal order of O(K log N/K) with decoding complexities of O(K log N/K) and O(N log N/K), respectively.

We analyze interleaved concatenation schemes of polar codes with outer binary BCH codes and convolutional codes. We show that both BCH-polar and Conv-polar codes can have a frame error rate that decays exponentially with the code length for all rates up to capacity, which is a substantial improvement in the error exponent over stand-alone polar codes. Interleaved concatenation with long constraint length convolutional codes is an effective way to leverage the fact that polarization increases the cutoff rate of the channel. Simulation results show that Conv-polar codes when decoded with the proposed soft-output multistage iterative decoding algorithm can outperform stand-alone polar codes decoded with successive cancellation or belief propagation decoding. It may be comparable to stand-alone polar codes with list decoding in the high SNR regime. In addition to this, we show that the proposed concatenation scheme requires lower memory and decoding complexity in comparison to belief propagation and list decoding of polar codes. Practically, the scheme enables rate compatible outer codes which ease hardware implementation. Our results suggest that the proposed method may strike a better balance between performance and complexity compared to existing methods in the finite-length regime.

We study the capacity region of the parallel Gaussian bidirectional relay channel with L independent subchannels and propose efficient coding schemes for approaching the capacity limit within a constant gap. A two-step approach is considered. First, the corresponding finite field linear deterministic model is studied, for which linear network coding across sub-channels is shown to achieve the capacity region of the channel. Next, based on the insight obtained, a lattice-based compute-and-forward scheme together with simple linear network coding across sub-channels is proposed and is shown to achieve the capacity region of the Gaussian model to within L bits per user regardless of the channel parameters. Even though coding across different sub-channels is necessary for approaching the capacity region, it is shown that this can be realized through a simple linear network coding scheme (across different sub-channels) at the relay.

We consider the compute-and-forward relay network with limited feedback. A novel scheme called adaptive compute-and-forward is proposed to exploit the channel knowledge by working with the best ring of imaginary quadratic integers. This is enabled by generalizing Construction A lattices to other rings of imaginary quadratic integers which may not form principal ideal domains and by showing such construction can produce good lattices for coding in the sense of Poltyrev and for MSE quantization. Since there are channel coefficients (complex numbers) which are closer to elements of rings of imaginary quadratic integers other than Gaussian and Eisenstein integers, by always working with the best ring among them, we can obtain better performance than that provided by working over Gaussian or Eisenstein integers.

Communication in the presence of bounded timing asynchronism, which is known to the receiver but cannot be easily compensated, is studied. Examples of such situations include point-to-point communication over intersymbol interference (ISI) channels and asynchronous wireless networks. In these scenarios, although the receiver may know all the delays, it is often not an easy task for the receiver to compensate the delays as the signals are mixed together. A novel framework, which is called interleave/deinterleave transform (IDT), is proposed to deal with this problem. It is shown that the IDT allows one to design the delays so that quasi-cyclic (QC) codes with a proper shifting constraint can be used accordingly. When used in conjunction with QC codes, IDT provides significantly better performance than existing schemes relying solely on cyclic codes. Two instances of asynchronous physical-layer network coding, namely, the integer-forcing equalization for ISI channels and asynchronous compute-and-forward, are then studied. For integer-forcing equalization, the proposed scheme provides improved performance over using cyclic codes. For asynchronous compute-and-forward, the proposed scheme shows that there is no loss in the achievable information rates due to delays that are integer multiples of the symbol duration. Furthermore, the proposed approach shows that delays introduced by the channel can sometimes be exploited to obtain higher information rates than those obtainable in the synchronous case. The proposed IDT can be thought of as a generalization of the interleaving/deinterleaving idea proposed by Wang et al., which allows the use of QC codes, thereby substantially increasing the design space.

In this paper, we consider the use of lattice codes over Eisenstein integers for implementing a compute and-forward protocol in wireless networks when channel state information is not available at the transmitter. We extend the compute-and-forward paradigm of Nazer and Gastpar to decoding Eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over Eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the Poltyrev limit. Using this result, we show that both the outage performance and error-correcting performance of the nested lattice codebooks over Eisenstein integers surpass those of lattice codebooks over integers considered by Nazer and Gastpar with no additional computational complexity.

Communication in the presence of bounded timing asynchronism which is known to the receiver but cannot be easily compensated is studied. Examples of such situations include point-to-point communication over inter-symbol interference (ISI) channels and asynchronous wireless networks. In these scenarios, although the receiver may know all the delays, it may not be an easy task for the receiver to compensate the delays as the signals are mixed together. A novel framework called interleave/deinterleave transform (IDT) is proposed to deal with this problem. It is shown that the IDT allows one to design the delays so that quasi-cyclic (QC) codes with a proper shifting constraint can be used accordingly. When used in conjunction with QC codes, IDT provides significantly better performance than existing schemes relying solely on cyclic codes. Two instances of asynchronous physical-layer network coding, namely the integer-forcing equalization for ISI channels and asynchronous compute-and-forward, are then studied where the gap-to-capacity can be bridged for the former and significant gains can be obtained for the later. The proposed IDT can be thought of as a generalization of the interleaving/deinterleaving idea in [1] which allows the use of QC codes thereby substantially increasing the design space.

Product construction with two levels proposed in [1] is a lattice construction which can be thought of as Construction A with codes that can be represented as the Cartesian product of two linear codes. This paper first generalizes the product construction to arbitrary number of levels. More importantly, the existence of a sequence of such lattices that are good for quantization and Poltyrev-good under multistage decoding is proved. This family of lattices is then used to generate a sequence of nested lattice codes based on the recent construction of Ordentlich and Erez. This allows one to achieve the same computation rate of Nazer and Gastpar for compute-and-forward with multistage decoding, which is termed multistage compute-and-forward.

For compound LDGM/LDPC codes with maximum a posteriori (MAP) processing, Wainwright and Martinian showed that the information-theoretic rate regions of the Wyner-Ziv (WZ) and Gelfand-Pinsker (GP) problems are achievable. For the same ensemble, these rates do not appear to be achievable with message-passing guided decimation (GD). Fortunately, spatially-coupled (SC) codes seem to provide an elegant remedy when iterative decoding falls short of MAP decoding. In particular, Aref et al. recently introduced SC LDGM codes that approach the rate-distortion region with belief-propagation guided decimation (BPGD). In this paper, we show that SC compound LDGM/LDPC codes with BPGD can approach the rate regions of the WZ and GP problems.

We propose a class of lattices constructed using Construction D where the underlying linear codes are nested binary spatially-coupled low-density parity-check codes (SC-LDPC) codes with uniform left and right degrees. By leveraging recent results on the optimality of spatially-coupled codes for binary input memoryless channels and Forney et al.'s earlier results on the optimality of construction D, we show that the proposed lattices achieve the Poltyrev limit under multistage belief propagation decoding. Lattice codes constructed from these lattices are shown to provide excellent performance for the three user symmetric interference channel. They can also be naturally used in applications such as integer-forcing and compute-and-forward.

In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D, and Construction πA(previously called product construction) recently proposed by the authors. While most of the results in this paper have been available in the literature, we discuss two generalizations where the first one is a general construction of lattices named Construction πDsubsuming the above three constructions as special cases and the second one is to go beyond principal ideal domains and build lattices over algebraic integers.

Designing error-correcting codes for optical communication is challenging mainly because of the high data rates (e.g., 100 Gbps) required and the expectation of low latency, low overhead (e.g., 7% redundancy), and large coding gain (e.g., >9dB). Although soft-decision decoding (SDD) of low-density parity-check (LDPC) codes is an active area of research, the mainstay of optical transport systems is still the iterative hard-decision decoding (HDD) of generalized product codes with algebraic syndrome decoding of the component codes. This is because iterative HDD allows many simplifications and SDD of LDPC codes results in much higher implementation complexity. In this paper, we use analysis and simulation to evaluate tightly-braided block codes with BCH component codes for high-speed optical communication. Simulation of the iterative HDD shows that these codes are competitive with the best schemes based on HDD. Finally, we suggest a specific design that is compatible with the G.709 framing structure and exhibits a coding gain of >9.35 dB at 7% redundancy under iterative HDD with a latency of approximately 1 million bits.

A novel construction of lattices is proposed. This construction can be thought of as Construction A with linear codes that can be represented as the Cartesian product of two linear codes over Fq; hence, is referred to as the product construction. The existence of a sequence of Poltyrev-good lattices generated by the product construction under some conditions is shown. This family of lattices is then used to generate signal constellations with q2elements which can be used in conjunction with multilevel coding with channel codes over Fqinstead of Fq2to design good coded modulation schemes for compute-and-forward.

We consider a class of lattices built using Construction A, where the underlying code is a non-binary spatially-coupled low density parity check code. We refer to these lattices as spatially-coupled LDA (SCLDA) lattices. SCLDA lattices can be constructed over integers, Gaussian integers and Eisenstein integers. We empirically study the performance of SCLDA lattices under belief propagation (BP) decoding. Ignoring the rate loss from termination, simulation results show that the BP thresholds of SCLDA lattices over integers is 0.11 dB (0.34 dB with the rate loss) and the BP thresholds for SCLDA lattices over Eisenstein integers are 0.08 dB from the Poltyrev limit (0.19 dB with the rate loss). Motivated by this result, we use SCLDA lattice codes over Eisenstein integers for implementing a compute-and-forward protocol. For the examples considered in this paper, the thresholds for the proposed lattice codes are within 0.28 dB from the achievable rate of this coding scheme and within 1.06 dB from the achievable computation rate of Nazer and Gastpar's coding scheme in [6] extended to Eisenstein integers.

We provide inner and outer bounds on the capacity region for the Gaussian bi-directional relaying over inter-symbol interference channels. The outer bound is obtained by the conventional cut-set argument. For the inner bound, we propose a compute-and-forward coding scheme based on lattice partition chains and study its achievable rate. The coding scheme is a time-domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords. The proposed compute-and-forward coding scheme substantially outperforms decode-and-forward schemes. While it is well known that for the point-to-point communication case, both independent coding along sub-channels and time-domain coding can approach the capacity limit, as a byproduct of the proposed scheme, we show that for the bi-directional relay case, independent coding along sub-channels is not optimal in general and joint coding across sub-channels can improve the capacity for some channel realizations.

We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded (using codes of fixed rate) and transmitted over two independent binary memoryless symmetric channels. The capacity of each channel is characterized by a single parameter that is not known at the transmitter. System performance is evaluated by computing the set of channel parameters for which the system can successfully decode. This set is called the achievable channel parameter region (ACPR). The goal is to design systems whose ACPRs are as large as possible. The main result is the design of irregular low-density parity-check (LDPC) ensembles whose ACPRs are significantly larger than previous designs. Some previous attempts to achieve large ACPRs with LDPC codes failed because systematic codes were used. In this work, we start with systematic encoders but puncture all the systematic bits before transmission. We also show that additional gains are possible using a staggered structure which enables codes optimized for single-user channels to perform well under symmetric channel conditions. The main analysis tool is a generic density-evolution framework for the analysis of joint iterative decoding for this problem.

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute-and-forward paradigm, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be computed (or decoded) is then chosen depending on the channel realization. We define such a class of functions which can be decoded at the relay using the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme results in substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields.

We study modulo-sum computation of two binary source sequences over a two-user erasure multiple access channel. The channel is modeled as a binary-input, erasure multiple access channel, which can be in one of three states-either the channel output is a modulo-sum of the two input symbols, or the channel output equals the input symbol on the first link and an erasure on the second link, or vice versa. The associated state sequence is independent and identically distributed. Unlike previously studied multiple-access channels, the proposed channel is not matched to the modulo-sum function and therefore we expect simple cut-set upper bounds to be far from capacity. In this paper, we establish a new upper bound on the modulo-sum capacity that is tighter than the cut-set bound. The key step in establishing this new bound is to provide suitable side information to the encoders to reduce the setup to a compound multiple-access channel and then capture the tension across multiple receivers required to compute the modulo-sum function. In our lower bound, it suffices to use identical linear codebooks at the two encoders. When a (strictly) causal feedback of the channel state is available to the encoders, we present a simple coding scheme that can achieve a rate larger than our upper bound for the case without feedback. This shows that the modulo-sum capacity is increased with feedback. An extension to the case of lossy reconstruction is also treated briefly.

This paper considers the relationship between code-rate selection and queueing performance for communication systems subject to time-varying channel conditions. While error-correcting codes offer protection against channel uncertainties, there exists a natural tradeoff between the enhanced protection of low-rate codes and the rate penalty imposed by additional redundancy. In the limiting regime where codewords are asymptotically long, this tradeoff is well understood and characterized by the Shannon capacity. However, for delay-sensitive communication systems and finite block lengths, a complete characterization of this tradeoff is not fully developed. This paper offers a new perspective on the queueing performance of communication systems with finite block lengths operating over correlated erasure channels. A rigorous framework that links code rate to overall system performance for random codes is presented. Guidelines for code-rate selection in delay-sensitive systems are identified. These findings are supported by a numerical study.

We consider the design and analysis of coding schemes for the binary input two way relay channel with erasure noise. We focus on reliable physical layer network coding as described in [1] in which the relay performs perfect error correction prior to forwarding messages. The best known achievable rates for this problem can be achieved through either decode and forward or compute and forward relaying. We consider a decoding paradigm called joint compute and forward which we numerically show can achieve the best of these rates with a single encoder and decoder. This is accomplished by deriving the exact performance of a message passing decoder based on joint compute and forward for spatially coupled LDPC ensembles.

Recently, it has been observed that terminated low-density-parity-check (LDPC) convolutional codes (or spatially-coupled codes) appear to approach the capacity universally across the class of binary memoryless channels. This is facilitated by the “threshold saturation” effect whereby the belief-propagation (BP) threshold of the spatially-coupled ensemble is boosted to the maximum a-posteriori (MAP) threshold of the underlying constituent ensemble. In this paper, we consider spatially-coupled codes over intersymbol-interference (ISI) channels under joint iterative decoding where we empirically show that threshold saturation also occurs. This can be observed by first identifying the GEXIT curve that naturally obeys the general area theorem. From this curve, the corresponding MAP and the BP threshold estimates are then numerically obtained. Given the fact that regular LDPC codes can achieve the symmetric information rate (SIR) under MAP decoding, we conjecture that spatially-coupled codes with joint iterative decoding can universally approach the SIR of ISI channels.

A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with message-passing decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. In this paper, we analyze a class of spatially-coupled generalized LDPC codes and observe that, in the high-rate regime, they can approach capacity under iterative hard-decision decoding. These codes can be seen as generalized product codes and are closely related to braided block codes.

We study computation of a modulo-sum of two binary source sequences over a two-user erasure multiple access channel. Each sender observes an independent and equiprobable binary sequence and the receiver is interested in computing the modulo-sum of these two sequences. The channel is modelled as a binary-input, erasure multiple access channel, which can be in one of three states - either the channel output is a modulo-sum of the two input symbols, or the channel output equals the input symbol on the first link and an erasure on the second link, or it equals the input symbol on the second link and an erasure on the first link. The associated state sequence is independent and identically distributed. We establish upper and lower bounds on the modulo-sum capacity. Our coding scheme uses either the compute-and-forward or the decode-and-forward techniques. The upper bound is obtained by a genie aided argument that reduces the setup to a compound multiple-access channel. It is in general is tighter than a simple upper bound obtained by revealing one of the messages to the decoders. We also briefly consider the case when a strictly causal state feedback is available to the encoders and establish that such feedback can increase the modulo-sum capacity.

A fundamental connection between the belief propagation (BP) and maximum a posteriori (MAP) decoding thresholds was derived by Méasson, Montanari, and Urbanke using the area theorem for extrinsic information transfer (EXIT) curves. This connection allows the MAP threshold, for the binary erasure channel, to be evaluated efficiently via an upper bound that can be shown to be tight in some cases. In this paper, a similar analysis is used to extend these results to several multiuser systems, namely a noisy Slepian-Wolf problem and a multiple-access channel with erasures. The simplicity of these channel models allows for rigorous analysis and enables the derivation of upper bounds on the MAP thresholds using EXIT area theorems. In some cases, one can also show these bounds are tight. One interesting application is that the MAP thresholds can be compared with the BP thresholds of spatially-coupled codes to verify threshold saturation for the corresponding systems.

We study the joint source-channel coding problem of transmitting a discrete-time analog source over an additive white Gaussian noise (AWGN) channel with interference known at transmitter. We consider the case when the source and the interference are correlated. We first derive an outer bound on the achievable distortion and then, we propose two joint source-channel coding schemes. The first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a Wyner-Ziv encoder and a dirty paper encoder. In the second scheme, the digital part is replaced by the hybrid digital and analog scheme proposed by Wilson et al. When the channel signal-to-noise ratio (SNR) is perfectly known at the transmitter, both proposed schemes are shown to provide identical performance which is substantially better than that of existing schemes. In the presence of an SNR mismatch, both proposed schemes are shown to be capable of graceful enhancement and graceful degradation. Interestingly, unlike the case when the source and interference are independent, neither of the two schemes outperforms the other universally. As an application of the proposed schemes, we provide both inner and outer bounds on the distortion region for the generalized cognitive radio channel.

We propose two compute-and-forward coding schemes for the bi-directional relay channel with inter- symbol interference (ISI) based on lattice codes and study their achievable rates. The first coding scheme is similar in spirit to coded orthogonal frequency division multiplexing (OFDM) with independent coding across sub-carriers and uses nested-lattice code with a power allocation strategy that can exploit the group property of lattices. The second coding scheme is a time-domain coding scheme which uses a novel precoding scheme at the transmitter in combination with lattice precoding and a minimum mean squared error receiver to recover linear combinations of lattice codewords. The proposed compute-and-forward coding schemes substantially outperform decode-and-forward schemes. While it is well known that for the point-to-point communication case, both the coded OFDM approach and the time-domain coding scheme can approach the capacity limit, we show that for the bi-directional relaying case, the performance of the two coding schemes are different. Particularly, we show that independent coding across sub-channels is not optimal and joint coding across sub-channels can improve the exchange capacity for some channel realizations.

We present a new coding scheme based on concatenating a newly introduced class of lattice codes called signal codes with interleaved Low Density Parity Check (LDPC)codes. These codes are shown to possess a special algebraic structure which makes them suitable for recovering linear combinations (over a finite field) of the transmitted signals in a multiple access channel. This facilitates their use as a coding scheme for the recently proposed compute and forward paradigm. The decoding algorithm is based on an appropriate combination of the stack decoder with a message passing algorithm. Simulation results show that our proposed scheme can approach the uniform input AWGN capacity within 1.5 db, which is a 2 db improvement compared to using only signal codes when decoding using a stack algorithm with the same stack size. Simulation results for our proposed scheme applied to compute and forward are also presented.

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits the recovery of a class of functions at the relay. We define such a class of functions and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that substantially higher rates are achievable with our proposed approach than those achievable by always using a fixed function or adapting the function at the relay but coding over GF(4).

In this paper, we study the joint source-channel coding problem of transmitting a discrete-time analog source over an additive white Gaussian noise (AWGN) channel with interference known at transmitter. We consider the case when the source and the interference are correlated. We first derive an outer bound on the achievable distortion and then, we propose two joint source-channel coding schemes to make use of the correlation between the source and the interference. The first scheme is the superposition of the uncoded signal and a digital part which is the concatenation of a Wyner-Ziv encoder and a dirty paper encoder. In the second scheme, the digital part is replaced by a hybrid digital and analog scheme so that the proposed scheme can provide graceful degradation in the presence of (signal-to-noise ratio) SNR mismatch. Interestingly, unlike the independent interference setup, we show that neither of both schemes outperform the other universally in the presence of SNR mismatch.

We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded and transmitted over two independent binary memoryless symmetric channels. Each channel capacity is assumed to be characterized by a single parameter which is not known at the transmitter. The receiver has knowledge of both the source correlation and the channel parameters. We call a system universal if it retains near-capacity performance without channel knowledge at the transmitter. Kudekar et al. recently showed that terminated low-density parity-check (LDPC) convolutional codes (a.k.a. spatially-coupled LDPC ensembles) can have belief-propagation thresholds that approach their maximum a-posteriori thresholds. This was proven for binary erasure channels and shown empirically for binary memoryless symmetric channels. They also conjectured that the principle of spatial coupling is very general and the phenomenon of threshold saturation applies to a very broad class of graphical models. In this work, we derive an area theorem for the joint decoder and empirically show that threshold saturation occurs for this problem. As a result, we demonstrate near-universal performance for this problem using the proposed spatially-coupled coding system. A similar result is also discussed briefly for the 2-user multiple-access channel.

One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the best set of erasure patterns also turns into a covering problem that can be solved asymptotically by RD theory. Thus, the proposed approach can be used to understand the asymptotic performance-versus-complexity tradeoff of multiple errors-and-erasures decoding of RS codes. This initial result is also extended a few directions. The rate-distortion exponent (RDE) is computed to give more precise results for moderate blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are analyzed using this framework. Analytical and numerical computations of the RD and RDE functions are also presented. Finally, simulation results show that sets of erasure patterns designed using the proposed methods outperform other algorithms with the same number of decoding trials.

Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion theory, as proposed previously by the authors, currently provides the best performance-versus-complexity trade-off. In this paper, an analysis based on the rate-distortion exponent is used to directly minimize the exponential decay rate of the error probability. This enables rigorous bounds on the error probability for finite-length RS codes and leads to modest performance gains. As a byproduct, a numerical method is derived that computes the rate-distortion exponent for independent non-identical sources. Analytical results are given for errors/erasures decoding.

This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters. This gives a framework that allows a rigorous analysis of the queue as a function of the code rate. Most prior work in this area either ignores block-length (e.g., fluid models) or assumes error-free communication using finite codes. This work enables one to determine when such assumptions provide good, or bad, approximations of true behavior. Moreover, it offers a new approach to optimize parameters and evaluate performance. This can be valuable for delay-sensitive systems that employ short block lengths.

The problem of transmitting a Gaussian source over an additive white Gaussian noise (AWGN) channel when the channel signal-to-noise ratio (SNR) is unknown at the transmitter and is known at the receiver is considered. The performance metric used is distortion SNR exponent which is defined as the rate of decay of mean-squared error (MSE) distortion with SNR. The optimal exponent is shown to be equal to the ratio of the number of channel uses to number of source samples. A superposition-based scheme is proposed that can achieve an exponent arbitrarily close to the optimal value.

We study the joint source-channel coding problem of transmitting a Gaussian source over a Gaussian channel in two cases: (i) the presence of interference known only to the transmitter and (ii) in the presence of side information about the source known only to the receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. We present the random coding counterpart of schemes based on lattices proposed by Kochman and Zamir. Then, we discuss applications of the hybrid digital analog schemes in the case of channel signal-to-noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression.

We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1/2 log(1 + snr) bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel. We show that, using lattice codes and lattice decoding, we can obtain a rate of 1/2 log(1/2 + snr) bits per transmitter, which is essentially optimal at high SNR. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1/2 log(1/2 + snr). The proposed scheme can be thought of as a joint physical-layer network-layer code which outperforms other recently proposed analog network coding schemes.

We consider a communication system where two transmitters wish to exchange information through a half-duplex relay in the middle. The channels between the transmitters and the relay have asymmetric channel gains. More specifically, the channels are assumed to be synchronized with complex inputs and complex fading coefficients with an average power constraint on the inputs to the channels. The noise at the receivers have the same power spectral density and are assumed to be white and Gaussian. We restrict our attention to transmission schemes where information from the two nodes are simultaneously sent to the relay during a medium access phase followed by a broadcast phase where the relay broadcasts information to both the nodes. An upper bound on the capacity for the two phase protocol under a sum power constraint on the transmit power from all the nodes is obtained as a solution to a convex optimization problem. We show that a scheme using channel inversion with lattice decoding can obtain a rate a small constant 0:09 bits from the upper bound at high signal-to-noise ratios. Numerical results show that the proposed scheme can perform very close to the upper bound.

The fifteen articles in this special issue are devoted to new equalization techniques for wireless communications, including new the latest theories and applications.

We consider the problem of joint source-channel coding for transmitting K samples of a complex Gaussian source overT bK uses of a block-fading multiple-input multiple-output (MIMO) channel with M transmit and N receive antennas. We consider the case when we are allowed to code over L blocks. The channel gain is assumed to be constant over a block and channel gains for different blocks are assumed to be independent. The performance measure of interest is the rate of decay of the expected mean-squared error with the signal-to-noise ratio (SNR), called the distortion SNR exponent. We first show that using a broadcast strategy similar to that of Gunduz and Erkip, but with a different power and rate allocation policy, the optimal distortion SNR exponent can be achieved for 0 les b les (|N - M| + 1)/ min(M,N) and for b > MNL2. This is the first time the optimal exponent is characterized for 1/min(M, N) < b < (|N - M| + 1)/min(M, N). Then, we propose a digital layered transmission scheme that uses both time layering and superposition. The new scheme is at least as good as currently known schemes for the entire range of bandwidth expansion factors b, whereas at least for some M, N, and b, it is strictly better than the currently known schemes.

The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies for algebraic soft-decision decoding (SDD) with infinite cost are first studied over erasure channels and the binary-symmetric channel. The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The multiplicity assignment strategy and the corresponding performance analysis are then generalized to characterize the decoding region of algebraic SDD over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed multiplicity assignment strategy is shown to be significantly larger than that of conventional Berlekamp-Massey decoding. As an application, a bit-level generalized minimum distance decoding algorithm is proposed. The proposed decoding compares favorably with many other Reed-Solomon SDD algorithms over various channels. Moreover, owing to the simplicity of the proposed bit-level generalized minimum distance decoding, its performance can be tightly bounded using order statistics.

We consider the problem of broadcasting kldr samples of an independent identically distributed (i.i.d) Gaussian source to two users in n = lambdakldr uses of an AWGN channel. We develop a framework which shows a duality between a source-channel coding scheme for the case of lambda > 1 and that for lambda < 1. Using this duality, we derive a scheme for the case of lambda < 1, which is the dual of a scheme proposed by Reznic, Zamir and Feder (2006). This scheme, which provides the largest known achievable distortion region currently known, is also the same as that proposed by Prabhakaran et al (2005) specialized to the case of an i.i.d source with lambda < 1. We also provide an explanation for why this scheme performs well by first analyzing the performance of source-channel coding schemes in the presence of a signal-to- noise ratio mismatch.

An alternative to extrinsic information transfer (EXIT) charts called mean-square error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean-square error (MMSE) for the additive white Gaussian noise (AWGN) channel, a relationship between the rate of any code and the area under a plot of MMSE versus signal-to-noise ratio (SNR) is obtained, when the a priori log-likelihood ratio (LLR) is from a binary input Gaussian channel. Using this result, a justification is provided for designing concatenated codes by matching the EXIT curves of the inner and outer decoder, when the LLRs are assumed to be Gaussian which is also the typical assumption used for code design using EXIT charts. Even though the Gaussian assumption is almost never true, the results presented in this paper represent a step toward the analysis of iterative decoding schemes using a single parameter. Finally, for the special case of AWGN channel it is shown that any capacity-achieving code has an EXIT curve that is a step function

We consider the transmission of a real independent and identically distributed (i.i.d.) "analog" source over a quasi-static M-input N-output multiple-input multiple-output (MIMO) block-fading channel. The relevant performance criterion is end-to-end average quadratic distortion D versus channel signal-to-noise ratio (SNR), for given spectral efficiency eta, defined as the ratio of the source bandwidth over the channel bandwidth. In the limit of high SNR, we define the distortion SNR exponent a*(eta) as the largest a such that D esdot snr-a, over all possible source-channel coding schemes of spectral efficiency eta. We find a simple upper bound on a*(eta), an achievable lower bound asep(eta) achievable by separated (tandem) source-channel coding, and a tighter lower bound ahybrid(eta) achievable by new hybrid digital analog space-time coding schemes. As a corollary, we have that a*(eta) is completely determined for the scalar case M = N = 1 and for the "bandwidth compression" case eta ges 2 min{M, N}. Expiicit and simple construction of hybrid space-time codes achieving ahybrid(eta) are also given.

We consider a system with parallel flat-fading subchannels for transmission of data, similar to a multicarrier system, where the sub-channel states are known perfectly to both the transmitter and the receiver. The results presented so far in literature for this system have only considered maximizing the sum-rate with Gaussian constellations which is not realizable in practice. In this paper, we consider practical QAM constellations for transmission, the size of which can be varied across subchannels. Under this constraint, we derive the maximum sum-information-rate of the overall system and the power/rate allocation algorithm to achieve it, which has not been attempted before. A practical MIMO system can be resolved into parallel subchannels and we then extend the allocation algorithm to a MIMO case. We further constrain the system to use a single overall codebook which is more practical and optimize the proposed power/rate allocation algorithm under this constraint. The simulations with an LDPC code show that the proposed power/rate allocation method is very robust and the code performance is within 2dB of even the unconstrained Gaussian sum-rate limit for both cases.

We consider coding schemes for channels with non-uniform inputs (NUI), where standard linear block codes can not be applied directly. We show that multilevel coding (MLC) with a set of linear codes and a deterministic mapper can achieve the information rate of the channel with NUI. The mapper, however, does not have to be one-to-one. As an application of the proposed MLC scheme, we present a rateless transmission scheme over the binary symmetric channel (BSC)

The common practice for achieving unequal error protection (UEP) in scalable multimedia communication systems is to design rate-compatible punctured channel codes before computing the UEP rate assignments. This paper proposes a new approach to designing powerful irregular repeat accumulate (IRA) codes that are optimized for the multimedia source and to exploiting the inherent irregularity in IRA codes for UEP. Using the end-to-end distortion due to the first error bit in channel decoding as the cost function, which is readily given by the operational distortion-rate function of embedded source codes, we incorporate this cost function into the channel code design process via density evolution and obtain IRA codes that minimize the average cost function instead of the usual probability of error. Because the resulting IRA codes have inherent UEP capabilities due to irregularity, the new IRA code design effectively integrates channel code optimization and UEP rate assignments, resulting in source-optimized channel coding or joint source-channel coding. We simulate our source-optimized IRA codes for transporting SPIHT-coded images over a binary symmetric channel with crossover probability p. When p = 0.03 and the channel code length is long (e.g., with one codeword for the whole 512 x 512 image), we are able to operate at only 9.38% away from the channel capacity with code length 132380 bits, achieving the best published results in terms of average peak signal-to-noise ratio (PSNR). Compared to conventional IRA code design (that minimizes the probability of error) with the same code rate, the performance gain in average PSNR from using our proposed source-optimized IRA code design is 0.8759 dB when p = 0.1 and the code length is 12800 bits. As predicted by Shannon's separation principle, we observe that this performance gain diminishes as the code length increases.

Along with inter-symbol interference (ISI), many communication channels also suffer from timing errors. Traditionally, timing errors are meditated through dedicated timing recovery circuitry. In this paper, we extend a recently introduced BCJR-DFE receiver to accomplish timing recovery, ISI equalization and decoding concurrently using per-survivor processing technique. We show that the proposed BCJR-DFE receiver offers many advantages over other receiver structures, such as iterative timing recovery and detection.

We present a memory efficient serial low density parity check (LDPC) decoder that implements a modified sum product algorithm (SPA). The modification is similar to the approximate min constraint presented by C. Jones et al. (see IEEE Conf. Military Commun., MILCOM 2003, p.157-162, 2003) but differs in hardware implementation to suit a serial architecture. Our main contribution is the proposed architecture that exploits the min constraint to reduce the storage of extrinsic messages which forms the bulk of the hardware. The least reliable bit to check input along with the check sum are the only quantities stored in the decoder. Extrinsic message memory reduction increases with the rate of the code and up to 68% saving is achieved for a rate 9/10 code. Simulation results show that the proposed changes do not degrade the bit error rate performance.

Maximal length linear congruential sequence (MLLCS) based LDPC codes have the advantage that the LDPC code graph can be generated at the receiver without having to explicity store the graph. Hence, these codes are advantageous when the same hardware needs to be used for different sets of rates and lengths. In this paper, we reveal an inherent structure in these codes that facilitates parallel implementation of the decoding algorithm. Based on this, we present an architecture for the MLLCS-LDPC decoder that facilitates parallel scalable implementation and joint code-decoder design.

In this paper, we characterize the decoding region of algebraic soft decoding (ASD) [4] of Reed-Solomon (RS) codes over erasure channels and binary symmetric channel (BSC). Optimal multiplicity assignment strategies (MAS) are investigated and tight bounds are derived to show the ASD can significantly outperform conventional Berlekamp Massey (BM) decoding over these channels for a wide code rate range. The analysis technique can also be extended to other channel models, e.g., RS coded modulation over erasure channels

We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost multicast

A discrete-time single-user channel with temporally correlated Rayleigh fading is considered. Neither the transmitter nor the receiver has channel side information (CSI), and both peak and average power constraints are placed on the inputs. Two lower bounds to the capacity are presented. One is motivated by the technique of decision feedback decoding. The other is related to the information rate with side information present, minus a penalty term to account for the information about the channel that is learned at the receiver. The second lower bound is a slight variation of a bound of Shamai and Marzetta. The bounds are compared numerically to two upper bounds for a channel with Gauss Markov Rayleigh fading. One upper bound is the capacity for complete CSI, with the peak constraint ignored, and the other is based on the capacity per unit energy. In general, the gap between the upper and lower bounds depends on the channel memory, but is quite small for low SNR

This paper proposes two low-complexity coding schemes for intersymbol interference (ISI) channels that perform close to the channel capacity. The first scheme is a serial concatenation of an outer code and a spectral shaping inner code. The second scheme is a parallel concatenation of two component trellis codes that are designed to be spectrally matched to the channel. Analysis using extrinsic information transfer (EXIT) functions and bit-error-rate (BER) simulations shows that both schemes surpass the independent identically distributed (i.i.d.) channel capacity and outperform other existing schemes.

We consider the analysis and design of low-density parity check (LDPC) codes for intersymbol interference (ISI) channels when used with soft interference cancellation plus linear minimum mean-square error filtering (SIC-MMSE) turbo equalization. We discuss techniques to compute the probability density function (pdf) of the extrinsic information at the output of the SIC-MMSE equalizer as a function of pdf of the input extrinsic information, channel impulse response, and the signal-to-noise ratio. For static ISI channels, we show that the output pdf can be modeled as symmetric Gaussian, and show that the mean can be evaluated without simulating the equalizer. For channels with long memory, we propose to use the unscented transform technique to compute the mean, which significantly reduces the computation required. Finally, for fading channels, we model the pdf by a mixture of symmetric Gaussian densities. Using these techniques, we are able to fairly accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds and the designed irregular LDPC codes outperform regular ones significantly.

This paper presents a Slepian-Wolf coding of n correlated m-ary sources for LDPC codes. On applying the syndrome concept, multilevel codes with low-density parity-check (LDPC) codes can be used to approach the Slepian-Wolf limit at each level. The advantage of LDPC codes is that they can be designed for different correlation models between source outputs and the side information and approach the Slepian-Wolf limits. Specifically, for Slepian-Wolf coding of three sources, a design rule of rates for coding each source, which facilitates code design and allows multistage decoding was proposed.

In this paper, we propose a simple design of LDPC codes which combines the good properties of multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes with Gray-mapped PAM constellations and one-shot demodulation. Through simulations, we show that it performs better than MLC/parallel independent decoding for short-medium lengths, which is required for most applications, on AWGN and block-fading channels. Since 2/sup m/-PAM represents one quadrature component of 2/sup 2m/-QAM, the optimization holds true for QAM too. In general, this idea can be extended to other modulation schemes like 2/sup m/-PSK very easily.

We present a soft decision decoding algorithm for Reed Solomon (RS) codes using their binary image representations. The novelty of the proposed decoding algorithm is in reducing the submatrix corresponding to the less reliable bits to a sparse nature prior to each decoding iteration and in adapting the parity check matrix from one iteration to another. Simulation results show that the new method provides significant gain over hard decision decoding (HDD) and compares favorably with other popular soft decision decoding methods [R. Koetter et al., 2003].

This paper considers designing and applying punctured irregular repeat-accumulate (IRA) codes for scalable image and video transmission over binary symmetric channels. IRA codes of different rates are obtained by puncturing the parity bits of a mother IRA code, which uses a systematic encoder. One of the main ideas presented here is the design of the mother code such that the entire set of higher rate codes obtained by puncturing are good. To find a good unequal error protection for embedded bit streams, we employ the fast joint source-channel coding algorithm in Hamzaoui et al. to minimize the expected end-to-end distortion. We test with two scalable image coders (SPIHT and JPEG-2000) and two scalable video coders (3-D SPIHT and H.26L-based PFGS). Simulations show better results with IRA codes than those reported in Banister et al. with JPEG-2000 and turbo codes. The IRA codes proposed here also have lower decoding complexity than the turbo codes used by Banister et al.

We present an efficient algorithm to compute the distance spectrum of a general finite intersymbol interference (ISI) channel, whose complexity is lower than those of existing methods. Closed-form expressions are derived for both input-output Euclidean distance enumerators and asymptotic distance spectrum shapes for 2-tap and 3-tap ISI channels. Coded and/or precoded ISI channels are also discussed.

Low-density parity-check (LDPC) codes perform very close to capacity for long lengths on several channels. However, the amount of memory (fixed-point numbers that need to be stored) required for implementing the message-passing algorithm increases linearly as the number of edges in the graph increases. In this letter, we propose a decoding algorithm for decoding LDPC codes that reduces the memory requirement at the decoder. The proposed decoding algorithm can be analyzed using density evolution; further, we show how to design good LDPC codes using this. Results show that this algorithm provides almost the same performance as the conventional sum-product decoding of LDPC codes.

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

We consider the analysis and design of low density parity check (LDPC) codes for turbo multiuser detection in multipath code-division multiple-access (CDMA) channels. We develop techniques to compute the probability density function (pdf) of the extrinsic information at the output of the multiuser detector. We show that the output pdf can be modeled as symmetric Gaussian for synchronous CDMA in additive white Gaussian noise (AWGN) channel and as a mixture of symmetric Gaussian densities for asynchronous CDMA system over fading channel. The expectation-maximization (EM) algorithm can be used to compute the parameters of this mixture. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds and the designed irregular LDPC codes outperform regular ones significantly.

We consider the design of convolutional codes and low density parity check (LDPC) codes with minimum-shift keying (MSK) when the receiver employs iterative decoding and demodulation. The main idea proposed is the design of coded schemes that are well matched to the iterative decoding algorithm being used rather than to hypothetical maximum-likelihood decoding. We first show that the design is crucially dependent on whether the continuous phase encoder (CPE) is realized in recursive form or in nonrecursive form. We then consider the design of convolutionally coded systems and low density parity check codes with MSK to obtain near-capacity performance. With convolutional codes, we show that it is possible to improve the performance significantly by using a mixture of recursive and nonrecursive realizations for the CPE. For low density parity check codes, we show that codes designed for binary phase shift keying are optimal for MSK only if the nonrecursive realization is used; for the recursive realization, we design new LDPC codes based on the concept of density evolution. We show that these codes outperform the best known codes for MSK and have lower decoding complexity.

We propose a class of codes which combine the principles of turbo coding and space-time trellis codes. It is first shown that several classes of space-time codes have an equivalent recursive realization. This fact is then exploited to design serial concatenated coding schemes with an outer code, interleaver, and an inner recursive space-time encoder. Two solutions are proposed in this paper - the use of convolutional outer codes aimed mainly to improve the power efficiency and the use of very high-rate outer codes to obtain significant improvement in power efficiency with a marginal decrease in spectral efficiency. We show that single parity check based turbo product codes are a good candidate for very high-rate outer codes. Finally, we propose an automatic repeat request scheme based on recursive realizations of space-time codes and show that the proposed scheme provides significant reduction in frame error rate.

The problem of designing codes with close-to-capacity performance on the multiple-input multiple-output (MIMO) quasi-static fading channel (QSFC) is addressed. We consider three different coding schemes - namely, direct transmission of random-like codes, concatenation with linear processing orthogonal space-time block codes (o-STBC) and concatenation with space-time trellis codes (STTC). The constrained modulation outage capacity of each of these schemes is computed. It is shown how low-density parity check (LDPC) codes may be used to approach capacity in these cases. For the STTC, the serial concatenation scheme of Gulati et al. (2001) turns out to have close to capacity performance.

It is well-known that iterative equalization/decoding offers good coding gains for intersymbol interference (ISI) channels. Recently, precoded ISI channels have been considered with turbo equalization which results in significant interleaving gains due to the recursive nature of precoded ISI channels. This paper presents new results pertaining to the design of codes for precoded ISI channels. An analytical proof is presented to show that precoding results in a loss in reliability during the first iteration for all 2-tap ISI channels. We compute the ratio of probability of error between nonprecoded and precoded ISI channels, which is closely related to the reliability, via a recursion. Based on this and the convergence properties of precoded and non-precoded channels, it is shown that by using a mixture of precoded and non-precoded parts, better performance can be achieved. Due to the recursiveness introduced from precoding, the codes required to achieve good performance are very simple codes and, hence, the resulting schemes provide good bit error rate performance at low receiver complexity.

This paper considers designing and applying rate-compatible irregular repeat accumulate (IRA) codes for scalable image transmission over binary symmetric channels. IRA codes of different rates are obtained by puncturing the parity bits of a mother IRA code which uses a systematic encoder. One of the main ideas presented here is the design of the mother code such that the entire set of higher rate codes obtained by puncturing are good. Using the Viterbi algorithm for finding the optimal unequal error protection of JPEG2000 bit streams, we present better results with IRA codes than those reported with turbo codes. The proposed IRA codes also have lower decoding complexity than the turbo codes.

We discuss techniques to characterize the probability density function of the extrinsic information at the output of a soft interference canceler based equalizer when used in a turbo equalizer. Then, we show how to use this to compute thresholds for low density parity check (LDPC) codes and to design good LDPC code ensembles for static and time-varying intersymbol interference channels. For other types of equalizers, we propose to design LDPC codes whose extrinsic information transfer (EXIT) diagram is matched to that of the equalizer.

We study packet combining techniques for retransmission schemes over intersymbol interference (ISI) channels. Two types of combining schemes are investigated, namely, maximum-likelihood combining (MLC) and iterative combining (IC). By first employing a precoding technique and then by interpreting the ISI channel as a trellis code, the transmissions of the same data packet at different times through the channel can be treated as the parallel concatenation of recursive trellis codes. If interleavers are used in between retransmissions, "turbo" coding gains can be achieved by iterative equalization. It is shown that IC provides excellent performance and outperforms other forms of combining in terms of frame error rate performance both analytically and through simulations.

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on. the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes.

We consider a space-time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. It is shown that the product of the time-selectivity order and the frequency-selectivity order is a key parameter to characterize the outage capacity of the correlated fading channel. It is also observed that STCs with large effective lengths and ideal built-in interleavers are more effective in exploiting the natural diversity in multiple-antenna correlated fading channels. We then propose a low-density parity-check (LDPC)-code-based STC-OFDM system. Compared with the conventional space-time trellis code (STTC), the LDPC-based STC can significantly improve the system performance by exploiting both the spatial diversity and the selective-fading diversity in wireless channels. Compared with the previously proposed turbo-code-based STC scheme, LDPC-based STC exhibits lower receiver complexity and more flexible scalability. We also consider receiver design for LDPC-based STC-OFDM systems in unknown fast fading channels and propose a novel turbo receiver employing a maximum a posteriori expectation-maximization (MAP-EM) demodulator and a soft LDPC decoder, which can significantly reduce the error floor in fast fading channels with a modest computational complexity. With such a turbo receiver, the proposed LDPC-based STC-OFDM system is a promising solution to highly efficient data transmission over selective-fading mobile wireless channels.

We consider maximal-length linear congruential sequences generated using a simple recursion to generate the bipartite graph of a low-density parity-check (LDPC) code. The main advantage is that the graph structure of the codes (edge connections) can be generated using a recursion, rather than having to store the graph connections in memory, which facilitates hardware implementation of the decoder. For this class of codes, sufficient conditions on the recursion parameters are derived, such that regular LDPC codes can be constructed with no cycles of length four or less. Simulation results show that these codes provide almost the same performance of a constrained pseudorandom construction that explicitly avoids cycles of length less than or equal to four.

Following the trend of turbo codes and low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) are being seriously considered for application in future high-density recording systems. Recent work on TPC/SPC codes has focused on ideal partial response channels with additive white Gaussian noise. This work extends the investigation to a more realistic equalized Lorentzian channel model where imperfect channel shaping, colored noise and recording density effect are taken into consideration. The effect of precoding is discussed and the interleaving gain is quantified. Simulation results of the turbo decoding system with both channel models are presented. A comprehensive evaluation is conducted, including BER performance, code rate selection, equalization targets and error statistics, which demonstrate TPC/SPC codes to be a promising candidate for future high-density recording systems.

Product accumulate (PA) codes were proposed and shown by Li, Narayanan and Georghiades (see Proc. Intl.. Symp. Inform. Theory, Washington DC, p.122-22, June 2001, and IEEE Tran. Info. Theory) to be a class of simple and provably good codes for rate R/spl ges/1/2. This work investigates the generalized product accumulate (GPA) codes which have rates over the entire range and which are also "good" both in the maximum likelihood (ML) sense and under the iterative approach. Analysis concentrates on the weight distribution over the code ensemble, the ML bounds, and the existence and computation of threshold phenomenon in the iterative decoding. A tight upper bound due to Divsalar (see Proc. 1998 Allerton Conf. Commun. and Control, Sept. 1998, p.201-10) and the thresholds computed using density evolution are examined. Simulations are presented and evaluated, especially for rate R/spl les/1/2.

This paper proposes an efficient graph-based sum-product algorithm for decoding 1/(1+D/sup n/) code, whose Tanner (1981) graph is cycle-free. A rigorous proof is given which shows the proposed algorithm is equivalent to the MAP decoding implementing the BCJR algorithm, but with a lower complexity magnitude. The paper presents an explicit example which confirms the claim that the sum-product algorithm is optimal on cycle-free graphs. A parallel realization is then discussed and shown to resemble low density parity check (LDPC) decoding. The paper further proposes a min-sum algorithm which is equivalent to the max-log-MAP algorithm. Prospective applications which can take advantage of the proposed decoding algorithms are discussed and simulations are provided.

We investigate serial concatenation of low-density parity check (LDPC) codes and minimum shift keying (MSK) with iterative decoding. We show that the design of LDPC codes is crucially dependent on the realization of the MSK modulator. For MSK modulators with nonrecursive continuous phase encoders (CPEs), optimal codes for BPSK are optimal, whereas for MSK modulators with recursive CPEs, the BPSK codes are not optimal. We show that for nonrecursive CPEs, iterative demodulation and decoding is not required even though the CPE has memory. However, iterative demodulation is essential for recursive CPEs. For recursive CPEs, we design LDPC codes using density evolution and differential evolution considering iterative demodulation and decoding. The resulting codes provide significantly improved performance over the existing codes.

We investigate the performance of low density parity check (LDPC) codes, single-parity turbo product codes (TPC/SPC) and multi-parity turbo product codes (TPC/MPC) over various partial response channels (PR) encountered in magnetic and magneto-optical (MO) recording systems, like PR4/EPR4 and PR1/PR2 channels. The codes have similarity in structures and can be decoded using simple message-passing algorithms. We show that the combination of a TPC/SPC code and a precoded PR channel results in good distance spectrum due to interleaving gain. Density evolution is then used to compute the thresholds for TPC/SPC and LDPC codes over PR channels. Through analysis and through simulations, we show the three types of codes yield comparable bit error rate performance with similar complexity, but they exhibit quite different error statistics, which in turn may result in sharp differences in block failure rate after the Reed-Solomon error correction code (RS-ECC).

A new class of codes, named product accumulate codes, which are the concatenation of an outer product code and an inner rate-1 differential encoder (or accumulator) is proposed. We show that these codes can perform within a few tenths of a dB from the Shannon limit for rates/spl ges/1/2. For practical block lengths, these codes provide similar performance to turbo codes but with significantly lower decoding complexity.

The effect of the precoder on the convergence of turbo equalization for precoded partial response channels is studied. The idea is to consider the turbo decoding algorithm as a one-parameter dynamical system and to study the effect of the precoder on the fixed points of the system. It is showed that precoding results in a loss in fidelity during the first iteration and that this loss depends on the precoder. Further, the rate at which the extrinsic information increases with iterations is also dependent on the precoder. The net result of these two effects is used to explain several existing results in the literature about the performance of different precoders. A design criteria based on the convergence is then proposed, and the impact of precoding on the design of the outer code is then studied. Finally, the design of precoders in the presence of an error correcting code, such as a Reed-Solomon code, is studied.

Interleaved trellis-coded systems with full response continuous-phase modulation (CPM) are considered. Upper bounds on the bit-error rate performance are derived for coherent detection on the additive white Gaussian noise and flat Rayleigh fading channels by considering the trellis code, interleaver, and CPM modulator as a serially concatenated convolutional code. A coherent receiver that performs iterative demodulation and decoding is shown to provide good bit error performance. Finally, a noncoherent iterative receiver is proposed and is shown to perform close to the coherent iterative receiver.

The effect of the precoder on the convergence of turbo equalization for precoded partial response channels is studied. The idea is to consider the turbo decoding algorithm as a one parameter dynamical system and to study the effect of the precoder on the fixed points of the system. It is shown that precoding results in a loss in reliability during the first iteration and that this loss depends on the precoder. Further, the rate at which the extrinsic information increases is also dependent on the precoder. The net result of these two effects is used to explain several existing results in the literature about the performance of different precoders. A design criteria based on the convergence is then proposed. The impact of precoding on the design of the outer code is then studied. Finally, the design of precoders when an error correcting code such as a Reed-Solomon code is studied.

We consider the design of convolutionally coded systems and low complexity receivers for communicating through intersymbol interference (ISI) channels when iterative equalization and decoding is employed in the receiver. We first introduce a binary precoding technique that makes a non-recursive ISI channel 'appear' recursive to the outer code and, hence, provides excellent bit error rate (BER) performance. Then, a low complexity soft output algorithm based on the M and T-algorithms is proposed for soft-output equalization of channels with long memory.

Iterative demodulation and decoding of convolutionally encoded data is treated as a special case of the previously proposed serial concatenation of interleaved codes. It is shown that by exploiting the recursive nature of the differential modulation schemes (for example, DBPSK, DQPSK, CPM, etc.), large interleaving gains can be achieved similar to serial concatenation schemes. We also show that when memoryless modulation is used, precoding can be used to create a rate-1 recursive inner code in order to obtain interleaving gains without adding redundancy from the inner code.

List decoding of turbo codes is analyzed under the assumption of a maximum-likelihood (ML) list decoder. It is shown that large asymptotic gains can be achieved on both the additive white Gaussian noise (AWGN) and fully-interleaved flat Rayleigh fading channels. It is also shown that the relative asymptotic gains for turbo codes are larger than those for convolutional codes. Finally, a practical list decoding algorithm based on the list output Viterbi algorithm (LOVA) is proposed as an approximation to the ML list decoder. Simulation results show that the proposed algorithm provides significant gains corroborating the analytical results. The asymptotic gain manifests itself as a reduction in the bit error rate (BER) and frame error rate (FER) floor of turbo codes.

List decoding of turbo codes is analyzed under the assumption of a maximum-likelihood (ML) list decoder. It is shown that large asymptotic gains can be achieved on both the additive white Gaussian noise (AWGN) and fully interleaved flat Rayleigh-fading channels. It is also shown that the relative asymptotic gains for turbo codes are larger than those for convolutional codes. Finally, a practical list decoding algorithm based on the list output Viterbi algorithm (LOVA) is proposed as an approximation to the ML list decoder. Simulation results show that the proposed algorithm provides significant gains corroborating the analytical results. The asymptotic gain manifests itself as a reduction in the bit-error rate (BER) and frame-error rate (FER) floor of turbo codes.

A method is presented for enhancing the narrow-band interference rejection capability of direct-sequence spread-spectrum systems employing an adaptive notch filter. The method, based on projection onto convex sets, restores that part of the spread-spectrum signal distorted by the filter. Simulation results are presented which show the output bit-error rate (BER) improvement gained by using the signal restoration scheme.