Different algorithms were proposed in recent years for achieving the overall goal of identifying a sparse approximation of a measured signal with high accuracy and relatively low computational complexity. Of paramount interest to the current work is the known Sparse Learning via Iterative Minimization (SLIM) algorithm, which is a maximum a-posteriori (MAP)-based approach for sparse signal recovery, originally proposed for multiple-input multiple-output (MIMO) radar imaging. The current work aims at introducing a modification to SLIM, termed Extended Sparse Learning via Iterative Minimization (ESLIM). This includes formulation of an extended cost function and derivation of an iterative optimization backed by proof-of-convergence. The extended algorithm aims to provide accurate sparse signal estimates for various applications and in different settings, e.g., a correlated dictionary (that is, a collection of signals composed of elementary signals similar to “choose” from) and short observation times. The solutions provided by the proposed algorithm, demonstrating its superiority and accuracy, are compared to several state-of-the-art sparse recovery algorithms, while focusing on MIMO radar imaging.

Increasing network capacity is undoubtedly a critical aspect of modern communication systems . In this paper, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is introduced for single-source multiple-sinks finite acyclic networks. This methodology offers a modification to existing LNC so that the source transmits its messages in a manner in which a given set of sinks (termed sub-rate sinks), whose max-flow is smaller than the source’s message-rate, can still decode a portion of the transmitted messages, without degrading the maximum achievable rate of LNC sinks whose max-flow is equal (or greater) than the source rate. The paper sets the conditions which a set of sub-rate sinks has to satisfy in order for that methodology to be applicable.

Various techniques have been proposed to address the problem of resource allocation in multi-carrier communications. These techniques, for the most part, arise from information-theoretic measures or otherwise associated with the channel behavior, which does not necessarily model the coding being employed. In this paper, an optimization technique is tailored for low density parity-check (LDPC) coded orthogonal frequency-division multiplexing (OFDM) systems, by employing the so-called general stability condition introduced by Richardson et al. The latter formulates a necessary condition for the belief-propagation decoder to perfectly decode a received vector with no errors. The general condition is re-formulated so as to model practical multi-carrier systems, such as OFDM. Consequently, a general resource-allocation framework is laid down for optimizing the transmitted power based on the characteristics of the LDPC code in use. The proposed optimization technique is utilized for power allocation in orthogonal frequency-division multiple access systems; and the transmitted power is minimized while guaranteeing reliable decoding. To validate the proposed approach, it is compared to information-theoretic-based methods that aim at optimizing the mutual information between the transmitter and the receiver. Both approaches are shown to provide almost identical performance for the scenarios addressed in this paper.

An innovative algorithm is introduced for cycle slip detection and correction in communication systems that employ APSK modulation. The algorithm is well suited for carrier phase synchronizers that are based on phase locked loops, and it achieves significant improvement in BER performance without compromising spectral efficiency. A systematic approach for the selection of all main algorithm parameters is detailed. In particular, the 16-APSK scheme, (recommended in the DVB-S2 standard) is analyzed by assuming an AWGN channel, and simulation results in the presence of various channel impairments are presented. The results establish the superiority of the proposed algorithm over other known cycle slip handling techniques for PLL synchronization. Integration with state-of-the-art iterative synchronization is also considered.

A Mixed Error Reduction (MER) scheme is presented for soft-decision decoding of binary product block codes. The MER scheme is realized by combining two algorithms having different performance objectives: bit-error-rate (BER) reduction followed by word-error-rate (WER) reduction. BER reduction is achieved by employing soft-in soft-out, possibly iterative, algorithm whose aim here is to improve the residual signal-to-noise ratio with each iteration. For WER reduction a two-step, soft-in hard-out, sub-optimal algorithm for decoding product codes is presented. This decoding algorithm guarantees correct decoding (at least) up to half the minimum Euclidean distance of the product code. The MER scheme exhibits good WER, as well as BER performance, with low computational burden.

Single Carrier FDMA (SC-FDMA) plays an important role in modern wireless communications as an alternative to OFDM mainly since it exhibits low peak-to-average power ratio. Accordingly, SC-FDMA is employed as the uplink scheme for the 3GPP long term evolution (LTE). In the presence of multipath, the SC-FDMA signal may arrive at the receiver perturbed by inter-symbol-interference, which renders the single-tap frequency-domain equalization suboptimal. Optimum maximum likelihood detection for SC-FDMA is often prohibitively complex, and hence useful mostly as a performance bound for suboptimal detection schemes. In this work, the optimum-detector performance is analyzed in detail; the analysis can be easily applied to any SC frequency-domain equalization scheme. Closed form bounds on the achievable bit error rate are provided for low and high SNR regimes in correlated and uncorrelated Rayleigh fading channels. The bounds reveal that the diversity order at high SNR is significantly smaller than in the low SNR regime. Moreover, error rate flaring behavior is demonstrated under optimum detection of SC-FDMA. The analytical results are verified by simulations.

Maximum likelihood sequence estimation (MLSE) in the shape of the Viterbi algorithm, although a strictly hard-output approach, is utilized for iterative decoding of turbo codes. It is a practical alternative when decoding complexity and speed may be traded for performance.

This paper studies the potential performance gain, referred to as scheduling gain, when decoding LDPC codes using scheduled belief-propagation. Introducing genie-aided scheduling, it is shown that the scheduling-gain can be quite impressive for moderate and short-length codes. Adaptive schedule based on edge ordering is presented. This approach compares favorably with serial scheduling schemes based on random node ordering. Density evolution-based analysis appropriately tailored for decoding finite-length LDPC codes is provided. For serial decoding and genie-aided decoding, it is shown that the performance in the first iteration can be accurately predicted analytically using the proposed technique.

This paper presents a method for constructing space-time block codes for multiple-input multiple-output (MIMO) Rayleigh fading channels. It employs orthogonal designs combined with the so-called diversity transform. Orthogonal designs provide the maximum diversity order for a given number of transmit and receive antennas. The diversity transform relies on unitary transforms that increase the channel alphabet; it does not alter the distance between input sequences, nor the bandwidth or information rate. A scheme of high diversity gain is tailored for any antenna array and signal constellation. Simulation results reveal that this scheme attains higher coding gains than other results known in the art.

The standard product construction is discussed with respect to nonlinear codes. Thus, so-called nonlinear product codes are obtained that are better than linear product codes of similar length and code rate, and at the same time, amenable for encoding/decoding. On the other hand, it is shown that certain notorious nonlinear codes have an augmented product construction, namely, they can be constructed by taking the union of a product code and certain of its cosets. The binary Hamming codes are shown to have similar construction. A simple two-stage decoder is proposed for nonlinear product (NLP) codes. The decoder is shown to be a bounded-distance (BD) information decoder that is the nonlinear equivalent of the BD decoder employed for linear codes. A list-based maximum-likelihood decoder is also discussed.

This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs

Coded modulation scheme of high-coding gain is presented for flat fading channels. The scheme introduces a product construction that employs two types of codes: "standard" good codes and codes that are more suitable for the fading environment. Short-blocklength codes of unique features are, thus, obtained for the bandwidth-limited regime. Using this approach, codes of bandwidth efficiencies 1, 2, and 3 bits/s/Hz are detailed. An iterative decoding algorithm for this product construction is devised. It relies on separate columns/rows decoding linked by (reliability) information transfer. Simulation results reveal that these codes compare favorably with known codes of short block-length when perfect channel state information is available to the receiver. The proposed approach is easily extended for the frequency-selective fading channel with multicarrier signaling

Generalized multilevel constructions for binary Reed-Muller R(r,m) codes using projections onto GF(2q) are presented. These constructions exploit component codes over GF(2),GF(4),...,GF(2q) that are based on shorter Reed-Muller codes, and set partitioning using partition chains of length-2lcodes. This is then used for deriving multilevel constructions for the Barnes-Wall A(r, m) family of lattices. Similarly, the latter construction involves component codes over GF(2),GF(4),...,GF(2q) and set partitioning based on partition chains of length-2llattices. These constructions of Reed-Muller codes and Barnes-Wall lattices are readily applicable for their efficient decoding

Adaptive bit loading algorithms are proposed for MIMO and MIMO-OFDM systems, thus better exploiting space and frequency diversity. Constant power allocation is assumed over all subchannels while the bit error rate is unconstrained. An efficient bit loading algorithm, which maximizes system bit rate under target mean BER restriction is formulated for a multiple antenna system. A bound on the maximum gap from capacity is introduced as a combination of the constant-power gap and the so-called rate quantization gap

A binary product lattice is generated from two binary component lattices of lower dimensions by employing the Kronecker product. This work focuses on codes carved from binary product lattices. Defined as such, an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points. A novel approach is disclosed yielding an explicit connection between source bits and lattice points. Decoding methods typically used for binary product codes do not apply for product lattices. Several alternative decoding approaches are discussed. In particular, a provably bounded-distance decoder is presented. It relies on the fact that a product lattice code point may be regarded as a two-dimensional array whose rows and columns are points in the component lattices. The obtained results are compared with classical lattices known in the art

A non-iterative soft decision decoding for direct product codes is discussed. The proposed decoder initially "distorts" the received matrix in a non-linear fashion - matching it to the geometrical properties of a certain, more basic, decoder. Thus, a low complexity decoding algorithm is obtained. On top of providing an efficient stopping criterion within the framework of iterative decoding, the proposed decoder also boosts overall performance for bounded decoding complexity

This paper concerns the construction of the so-called augmented product codes and augmented product lattices. These are obtained by augmenting product codes or product lattices from certain classes thus obtaining a higher dimensional code or a lattice from the same class. Certain properties of the augmented product construction are derived, and a few examples are given for code/lattice constructions. In particular, it is shown that the Reed-Muller codes, the Golay code, the Barnes-Wall lattices as well as the Leech lattice all have an augmented product construction

This work addresses the problem of decoding turbo convolutional codes. In particular, it is concerned with the question of how maximum likelihood sequence estimation (MLSE), in the shape of the Viterbi algorithm (VA), can be utilized in the framework of turbo decoding. It is shown that the conventional VA, which is a soft-input hard-output decoder, can be used for iterative decoding of turbo codes. Moreover, it is demonstrated how the VA can be used for obtaining accurate BER estimation as well as an effective stopping criterion.

A product lattice is a high-dimensional lattice constructed using two lower dimensional lattices, in equivalence to binary product block codes constructed from two lower dimensional binary block codes. However, decoding methods typically used for binary product codes do not necessarily apply to product lattices. In this work several approaches for decoding product lattices are presented. In particular, bounded-distance decoding, which relies on the fact that all the rows and columns of the product lattice are points in the component lattices, is detailed. This property of product lattices enables one to efficiently decode the product lattice by employing separate decoders for the (much smaller dimensional) component lattices. Measures for the efficiency of these decoding methods are derived, and it is shown, also by means of computer simulation, that they are comparable to known decoding methods of lattices both in terms of effective coding gain and complexity.

This paper concerns the construction of the so-called augmented product codes and augmented product lattices. These are obtained by augmenting product codes or product lattices from certain classes thus obtaining higher dimensional codes or lattices from the same class, respectively. Certain properties of the augmented product construction are derived, and specific construction examples are given. In particular, it is shown that the Reed-Muller codes, the Golay code, the Barnes-Wall lattices, as well as the Leech lattice all have various augmented product constructions.

Adaptive bit loading algorithms are proposed for multicarrier transmission systems. Constant power allocation is assumed over all subchannels while the (subchannel) bit error rate is unconstrained. The algorithms are computationally efficient and their performance compare favorably with the prior art

Lattice-based construction of codes is of theoretical as well as practical importance in particular for communications over bandwidth-limited channels. We investigate the so called product lattice construction. Certain fundamental properties of product lattices are derived, and it is demonstrated that their performance are comparable to those of known good lattices. Practical issues concerning encoding and decoding of product lattices are discussed.

A projection of binary Reed-Muller codes R(r,m) onto GF(4)/sup m-2/ is presented. For an R(r,m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r,m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r-2, m-2) and R(r, m-2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.

The overall number of nearest neighbors in bounded distance decoding (BDD) algorithms is given by N/sub 0,eff/=N/sub 0/+N/sub BDD/. Where NBDD denotes the number of additional, non-codeword, neighbors that are generated during the (suboptimal) decoding process. We identify and enumerate the nearest neighbors associated with the original generalized minimum distance (GMD) and Chase (1972) decoding algorithms. After careful examination of the decision regions of these algorithms, we derive an approximated probability ratio between the error contribution of a noncodeword neighbor (one of N/sub BDD/ points) and a codeword nearest neighbor. For Chase algorithm 1 it is shown that the contribution to the error probability of a noncodeword nearest neighbor is a factor of 2/sup d-1/ less than the contribution of a codeword, while for Chase algorithm 2 the factor is 2/sup [d/2]-1/, d being the minimum Hamming distance of the code. For Chase algorithm 3 and GMD, a recursive procedure for calculating this ratio, which turns out to be nonexponential in d, is presented. This procedure can also be used for specifically identifying the error patterns associated with Chase algorithm 3 and GMD. Utilizing the probability ratio, we propose an improved approximated upper bound on the probability of error based on the union bound approach. Simulation results are given to demonstrate and support the analytical derivations.

For a code C, bounded distance decoding algorithms perform as optimal algorithms within the balls B(c), centered at the codewords c/spl isin/C, with radius equal to half the minimum Euclidean distance of the code. Thus distinct bounded-distance algorithms vary in performance due to their different behavior outside the balls B(c). We investigate this issue by analyzing the decision regions of some known (e.g., GMD) and some new bounded-distance algorithms presented in this work. In particular, we show that there are three distinct types of nearest neighbors and classify them according to their influence on the decision region. Simulation results and computer-generated images of the decision regions are provided to illustrate the analytical results for block and lattice codes on additive white Gaussian noise (AWGN) channels.

We present a novel scheme that combines decision feedback equalization (DFE) with high-rate error-detection coding in an efficient manner. The proposed scheme is shown to considerably outperform the conventional practice on channels with high SNR, such as those encountered in twisted-pair telephony systems. In order to analyze the performance of our method, we introduce an approximate mathematical model taking into account the error propagation phenomenon. Based on this model, upper and lower bounds on the overall probability of error are developed. These show that a simple low-redundancy error-detecting code, when properly integrated with the equalizer, can make the overall probability of error several orders of magnitude lower than that obtained with the conventional DFE, or with a DFE followed by an error-correcting code. Computer simulations of the proposed method have been performed for several channels, including the so-called high-bit-rate digital subscriber line (HDSL) test-loop 4, which is known to have a considerable amount of intersymbol interference. For all these channels, our results show that a reduction in the probability of error by more than three orders of magnitude can be obtained using codes of rate 0.96 and above. This, in turn, translates into power savings (coding gain) of 2.5 to 3 dB.

Two soft-decision decoding algorithms for the (6, 3, 4) quaternary code hexacode are presented. Both algorithms realize half the minimum Euclidean distance of the code. The proposed algorithms are most practical. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed with at most 187 and 519 real-number operations respectively. Compare this to 651, respectively 3595, operations required by the best known maximum likelihood decoders (Vardy and Be'ery, 1991, 1993), and 431, respectively 1007, operations required by the bounded-distance decoders (Amrani et al., 1994). We present some simulation results for the proposed Leech lattice decoders revealing near-optimal performance. A comparison to known trellis codes is also provided.

Multilevel constructions of the binary Golay code and the Leech lattice are described. Both constructions are based upon the projection of the Golay code and the Leech lattice onto the (6,3,4) hexacode over GF(4). However, unlike the previously reported constructions, the new multilevel constructions make the three levels independent by way of using a different set of coset representatives for one of the quaternary coordinates. Based upon the multilevel structure of the Golay code and the Leech lattice, efficient bounded-distance decoding algorithms are devised. The bounded-distance decoder for the binary Golay code requires at most 431 operations. As compared to 651 operations for the best known maximum-likelihood decoder. Efficient bounded-distance decoding of the Leech lattice is achieved by means of partitioning it into four cosets of Q/sub 24/, beyond the conventional partition into two H/sub 24/ cosets. The complexity of the resulting decoder is only 953 real operations on the average and 1007 operations in the worst case, as compared to about 3600 operations for the best known in maximum-likelihood decoder. It is shown that the proposed algorithms decode correctly at least up to the guaranteed error-correction radius of the maximum-likelihood decoder. Thus, the loss in coding-gain is due primarily to an increase in the effective error-coefficient, which is calculated exactly for both algorithms. Furthermore, the performance of the Leech lattice decoder on the AWGN channel is evaluated experimentally by means of a comprehensive computer simulation. The results show a loss in coding-gain of less than 0.1 dB relative to the maximum-likelihood decoder for BER ranging from 10/sup -1/ to 10/sup -7/.>