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We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge if and only if the Hamming distance between the corresponding codewords equals the minimum distance of the code. The algorithm uses a greedy local search to find a node optimizing a metric, e.g. the correlation between the received vector and the corresponding codeword. In addition, the cyclic redundancy check can be used to terminate the search as soon as a valid codeword is found, leading to an improvement in the average computational complexity of the algorithm. Simulation results for both binary symmetric channel and additive white Gaussian noise channel show that the presented decoder approaches the performance of maximum likelihood decoding for RM codes of length less than 1024 and for the second-order RM codes of length less than 4096. Moreover, it is demonstrated that the considered decoding approach outperforms state-of-the-art decoding algorithms of RM codes with similar computational complexity for a wide range of block lengths and rates. [ABSTRACT FROM AUTHOR]

A novel method to recursively construct a set of precoded polar codes of various rates and short-to-moderate lengths is presented. The proposed code design method minimizes the successive cancellation (SC) decoding error probability estimate under three constraints. The first constraint is the minimum distance requirement to improve the maximum-likelihood (ML) performance of the resulting code and therefore the performance under the SC list (SCL) decoding. The other two constraints introduce preselected supercode and subcode, where the supercode ensures fast computation of the minimum distance and the subcode ensures reduction of the search space size. The supercode is given by the Plotkin sum of shorter codes, which are nested to simplify computation of low-weight codewords. These low-weight codewords are needed to satisfy the minimum distance constraint. The simulation results indicate that the proposed precoded polar codes of lengths 128 and 256 provide a better frame error rate (FER) than polar codes with CRC and e-BCH polar subcodes under the SCL decoding algorithm with the list size $8-128$. [ABSTRACT FROM AUTHOR]

In coded caching system we prefer to design a coded caching scheme with low subpacketization and small transmission rate (i.e., the low implementation complexity and the efficient transmission during the peak traffic times). Placement delivery arrays (PDA) can be used to design code caching schemes. In this article we propose a framework of constructing PDAs via Hamming distance. As an application, two classes of coded caching schemes with linear subpacketizations and small transmission rates are obtained. [ABSTRACT FROM AUTHOR]

In his pioneering work on LDPC codes, Gallager dismissed codes with parity-check matrices of weight two after proving that their minimum Hamming distances grow at most logarithmically with their code lengths. In spite of their poor minimum Hamming distances, it is shown that quasi-cyclic LDPC codes with parity-check matrices of column weight two have good capability to correct phased bursts of erasures which may not be surpassed by using quasi-cyclic LDPC codes with parity-check matrices of column weight three or more. By modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. Quasi-cyclic LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel are also considered. Examples of such codes based on Reed-Solomon and Gabidulin codes are presented. [ABSTRACT FROM AUTHOR]

In this article, we propose a limited feedback-based space-shift keying (SSK) modulation scheme where transmitter (Tx) obtains partial channel state information (CSI) via a feedback link from receiver (Rx). More specifically, the Tx does not receive perfect information of channel gain, but is aware only of channel gain ordering. Based on the received partial CSI, the Tx adapts the spatial constellation and allocates different transmit weights to each transmit antenna representing spatial constellation points. Furthermore, the power adapted spatial constellation points are encoded by using gray coding scheme, which results in unit hamming distance between adjacent spatial constellation points. Next, a multiple-input single-output (MISO) system with maximum–likelihood detection is investigated. Accurate expressions for the average bit error rate (ABER) for ${2}\times {1}$ and ${4}\times {1}$ MISO systems over Rayleigh fading channel are derived. Further, an approximate expression for the ABER of a generalized MISO system is also obtained. It is shown analytically that the ABER performance of the proposed SSK scheme can be improved by applying a non-uniform power allocation to make transmit links more distinguishable at the Rx. Moreover, we demonstrate analytically that the proposed scheme attains a diversity order which is twice of the conventional SSK scheme. Numerical results, corroborated by Monte Carlo simulations, verify the proposed analysis and clearly highlight that, the proposed scheme significantly outperforms existing closed-loop spatial constellation-based schemes relying on full CSI in Tx and conventional open-loop SSK scheme. [ABSTRACT FROM AUTHOR]

Irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes with the block dual-diagonal (BDD) parity structure are widely adopted in many communication standards because the BDD structure supports an efficient encoding and many degree-2 variable nodes inside are adequate for the construction of mid- to high-rate codes. However, we observe that low-rate irregular QC LDPC codes with the BDD parity structure inherently contain too many degree-2 variable nodes and suffer from error floors in high signal-to-noise ratio (SNR) region. In this paper, a generalized BDD structure including double-weight circulants as well as circulant permutation matrices is proposed for low-rate irregular QC LDPC codes with low error floors which is achieved with a little bit giving up error performance in the waterfall region. When constructing the parity part of a code with the generalized BDD structure, the portion of double-weight circulants is variable so that the resulting LDPC code can achieve a desired degree distribution including degrees 2 and 3 while supporting the efficient encoding. We show that low-rate QC LDPC codes constructed with the proposed BDD structure have better theoretical properties and lower error floor than those with the conventional BDD structure. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an artificial-intelligence (AI) driven approach to design error correction codes (ECC). Classic error-correction code design based upon coding-theoretic principles typically strives to optimize some performance-related code property such as minimum Hamming distance, decoding threshold, or subchannel reliability ordering. In contrast, AI-driven approaches, such as reinforcement learning (RL) and genetic algorithms, rely primarily on optimization methods to learn the parameters of an optimal code within a certain code family. We employ a constructor-evaluator framework, in which the code constructor can be realized by various AI algorithms and the code evaluator provides code performance metric measurements. The code constructor keeps improving the code construction to maximize code performance that is evaluated by the code evaluator. As examples, we focus on RL and genetic algorithms to construct linear block codes and polar codes. The results show that comparable code performance can be achieved with respect to the existing codes. It is noteworthy that our method can provide superior performances to classic constructions in certain cases (e.g., list decoding for polar codes). [ABSTRACT FROM AUTHOR]

Multilevel flash memories enable multiple bits to be stored in a single memory cell and hence a significant increase of the storage capacity. The multiple bits that are used for labeling the threshold voltage level of a memory cell belong to different pages. A multilevel flash memory channel resembles a multi-user channel with asymmetric noise, while the data of different pages, which are encoded independently, resembles data of multiple users. In this paper, performance analyses are proposed for this channel by using the union bound technique. In particular, we investigated two different binary labeling schemes of a cell level, the Gray labeling and non-Gray labeling with three maximum-likelihood (ML)-based decoding schemes, which are the joint multi-page ML decoding, page-separate ML decoding, and default setting ML decoding. Our analysis reveals an asymptotic diminishing rate of decoding errors as the channel noise approaches zero, based on which the code design criteria are proposed. It is shown theoretically that the Gray mapping has no joint (i.e., multi-page) decoding gain. The corresponding diminishing decoding error rate is dominated by the weakest code in each page and hence a separate decoding scheme is adequate. On the other hand, the non-Gray mapping has a joint decoding gain which means the weak code can exploit the decoding of the strong code and the diminishing rate of its decoding errors is not subject to the cask effect. Therefore, for Gray mapping, a symmetric coding scheme using equal-strength code for each page achieves better error performance, while for non-Gray mapping with joint decoding, the symmetric coding is not necessary. Moreover, by using the asymmetric coding scheme through assigning different code rates to different pages, the non-Gray mapping can achieve higher overall sum rate than Gray mapping with a similar decoding error rate performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance metric. Upper and lower bounds are derived on the minimum amount of information exchange. Furthermore, explicit encoding and decoding algorithms are provided for many cases. [ABSTRACT FROM AUTHOR]

Locally decodable codes and locally correctable codes (LCCs) have several important applications, such as private information retrieval, secure multiparty computation, and circuit lower bounds. Three major parameters are considered in LCCs: query complexity, message length, and codeword length. The most familiar LCCs in the regime of low query complexity are the generalized Reed–Muller (GRM) codes. However, it has not previously been determined whether there exist codes that have shorter codeword lengths than GRM codes with the same query complexity and message length. In this paper, we show that the projective Reed–Muller (PRM) codes are such LCCs for some parameters. The GRM code is specified by the alphabet size $q$ , the number of variables $m$ , and the degree $d$ , where $d\le q-2$. When $d= q-2$ and $q-1$ is a power of a prime, we prove that there exists a PRM code with shorter codeword length than the GRM code with the same query complexity and message length. We also present for these PRM codes a perfectly smooth local decoder to recover a symbol in a codeword by accessing not more than $q$ symbols at the coordinates of the codeword. [ABSTRACT FROM AUTHOR]

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a connection between locally repairable codes with multiple disjoint repair sets and packings is derived under the condition that each repair set contains exactly one check symbol. Particularly, conditions under which an optimal locally repairable code corresponds to a packing are also characterized. As an application of this connection, some optimal locally repairable codes can be obtained by packings. Specifically, two constructions of locally repairable codes are proposed which not only generalize some known explicit constructions but also give optimal locally repairable codes with flexible new parameters. [ABSTRACT FROM AUTHOR]

Enabled by new storage mediums, Computation-in-Memory is a novel architecture that has shown great potential in reducing the burden of massive data processing by bypassing the communication and memory access bottleneck. Suggested by Cassuto and Crammer, allowing for ultra-fast Hamming distance computations to be performed in resistive memory with low-level conductance measurements has the potential to drastically speed up many modern machine learning algorithms. Meanwhile, Hamming distance Computation-in-Memory remains a challenging task as a result of the non-negligible device variability in practical resistive memory. In this paper, build upon the work of Cassuto and Crammer, we study memristor variability due to two distinct sources: resistance variation, and the non-deterministic write process. First, we introduce a technique for estimating the Hamming distance under resistance variation alone. Then, we propose error-detection and error-correction schemes to deal with non-ideal write process. We then combine these results to concurrently address both sources of memristor variabilities. In order to preserve the low latency property of Computation-in-Memory, all of our approaches rely on only a single vector-level conductance measurement. We use so-called inversion coding as a key ingredient in our solutions and we prove the optimality of this code given the restrictions on bit-accessible information. Finally, we demonstrate the efficacy of our approaches on the k-nearest neighbors classifier. [ABSTRACT FROM AUTHOR]

In this paper, time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs) are considered, and the connections existing between their low-weight codewords and cycles in their Tanner graphs are studied. Using the polynomial representation of these codes, we show that parity-check matrices having columns with weight ≥2 can be analyzed considering a certain number of parity-check sub-matrices having regular columns with weight 2. These sub-matrices are associated to cycles in the code Tanner graph and define as many codes we denote as component codes. Based on this observation, we find that codewords of the main code can be expressed as combinations of codewords of the component codes. The design of codes free of codewords up to a certain weight is also addressed. We show that low-weight codewords in the main code can be avoided by removing some types of cycles in its Tanner graph. Our design approach is applied to some well-known ensembles of SC-LDPC-CCs to prove its effectiveness. [ABSTRACT FROM AUTHOR]

In conventional multiple description coding (MDC), two descriptions of a source are generated and sent over ON/OFF channels. In this paper, we are interested in exploiting the redundancy built in MDC to additionally confer robustness against other channel errors. In particular, we consider a multiple description lattice vector quantizer (MDLVQ) whose output (a pair of side lattice points) is mapped to a pair of binary indexes and each index is sent over a binary channel. One channel is noiseless, while the other is noisy. Thus, at the decoder, one description is received error-free, while the other may carry bit errors. Then the decoder uses the error-free description as side information to improve the reconstruction. The effectiveness of the decoder in alleviating the impact of bit errors depends on the mapping $\gamma $ of side lattice points to binary indexes. We propose the design of a structured bit-error resilient mapping $\gamma $. For this, the set of side lattice points is first partitioned using Voronoi regions of an appropriate coarse lattice. Next a good linear channel code is selected, each Voronoi region is assigned a coset of this channel code, and the side lattice points within each Voronoi region are mapped to binary sequences in the corresponding coset. In addition, we argue that the performance of $\gamma $ is improved by assigning cosets close in Hamming distance to neighboring Voronoi regions, and propose a technique to achieve this goal. We derive a lower bound on the error correction performance of the proposed mapping $\gamma $ in terms of the performance of the channel code $C$ used in its construction. Interestingly, we prove that, as the rate of the MDLVQ grows to infinity, the mapping $\gamma $ becomes as good as the code $C$ in correcting bit errors. Simulation results show the significant superiority of the proposed index mapping versus random mappings. [ABSTRACT FROM AUTHOR]

A method to design efficient puncture-constrained interleavers for turbo codes (TCs) is introduced. Resulting TCs profit from a joint optimization of puncturing pattern and interleaver to achieve an improved error rate performance. First, the puncturing pattern is selected based on the constituent code Hamming distance spectrum and on the TC extrinsic information exchange under uniform interleaving. Then, the interleaver function is defined via a layered design process taking account of several design criteria, such as minimum span, correlation girth, and puncturing constraints. We show that applying interleaving with a periodic cross connection pattern that can be assimilated to a protograph improves error-correction performance when compared to the state-of-the-art TCs. An application example is elaborated and compared with the long-term evolution standard: a significant gain in performance can be observed. An additional benefit of the proposed technique resides in the important reduction of the search space for the different interleaver parameters. [ABSTRACT FROM PUBLISHER]

This paper considers an uplink multiuser multiple-input-multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs), in which K users equipped with a single-antenna communicate with one base station (BS) with N_{\mathrm{ r}} antennas. In this system, we present a novel multiuser MIMO detection framework inspired by coding theory. The key idea of the proposed framework is to create a code {\mathcal C} of length 2N\mathrm{ r} over a spatial domain. This code is constructed by an auto-encoding function that is completely described by a channel transformation followed by a quantization function of the ADCs for a fixed input constellation set. Using the proposed framework, we present a novel weighted minimum distance decoding (wMDD) that achieves the optimal detection performance by appropriately exploiting unequal channel reliabilities. In addition, we show that bit error rate exponentially decreases with the minimum distance of the code {\mathcal C} , which plays a similar role with a condition number in conventional MIMO systems. Furthermore, we develop the communication method that uses the wMDD when the explicit channel state information is not available at the BS. Finally, numerical results are provided to verify the superiority of the proposed method. [ABSTRACT FROM PUBLISHER]

Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing $\eta $ unreliable symbols and realizing them with the two most likely decisions, $2^\eta $ decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve’s corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals’ low-complexity feature. [ABSTRACT FROM PUBLISHER]

Many studies were carried out for the construction of low density parity-check (LDPC) codes. They usually focused on introducing the construction methods for good LDPC codes instead of a general method for code optimization. This paper proposes a method with high versatility, called the parallel vector message passing-based edge exchange (PMPE), for optimizing a type of graph-based LDPC codes, without changing the code parameters of mother codes, such as the code length, code rate, and degree distribution. With the approximately nearest codewords searching approach, we find the optimization method can increase the Hamming distance of the LDPC codes. For the quasi-cyclic (QC) LDPC codes, an optimization method, called the parallel vector message passing oriented-to the QC-LDPC codes (QC-PMP), is further suggested, with which the quasi-cyclic characteristics of QC-LDPC codes can remain unchanged in the optimization. To evaluate the performance of the parity-check matrix corresponding to a Tanner graph, a very simple metric, the cycles metric, is introduced to work with the proposed PMPE and QC-PMP algorithms. The experimental results show that the performance of the LDPC codes optimized with the proposed PMPE can be improved significantly at low BER range compared with the mother codes of the random codes, including the regular MacKay code of rate 0.5 and the regular PEG code of rate 0.9. For the case of the regular and irregular QC-LDPC codes with different code lengths and code rates, the optimized LDPC codes with the proposed QC-PMP algorithm significantly outperform the mother codes. [ABSTRACT FROM AUTHOR]

Motivated by applications involving hot data, the notion of (r, t) -availability was introduced, where a symbol is said to have (r, t) -availability if it can be reconstructed, respectively, from t disjoint repair alternatives of other symbols, each of size at most r . The key to constructing a family of locally repairable codes with (r, t) -availability is the design of a membership matrix for dividing global parities into local ones such that each repair group contains only one parity symbol. Although explicit designs of membership matrices are available, it remains unclear whether membership matrices with significantly better parameters can be constructed, which was a question left open. To tackle the open problem, this paper first provides a connection between the design of membership matrices and the design of a combinatorial object in the well-known combinatorial design theory, called resolvable configurations. This paper then proposes several direct designs of membership matrices based on Euclidean geometry, finite fields, circulant permutation matrices, affine permutation matrices, and Reed–Solomon codes. By leveraging the notion of resolvable configurations and the Kronecker product, this paper further proposes a two-step design of membership matrices. The proposed direct and two-step designs of membership matrices are shown to have significantly better parameters than those recently available. [ABSTRACT FROM AUTHOR]

This paper constructs an objective function for symbol flipping decoding algorithms, considering not only soft reliability, but also hard reliability. The maximization of this objective function indicates that the flipping metric should involve both the information before and after symbol flipping, while the existing algorithms consider the information before symbol flipping. Theoretical analysis shows that such prediction mechanism, together with hard reliability, can significantly improve the error performance of symbol flipping algorithms. Simulation results show that the proposed algorithms provide effective tradeoff between error performance and complexity for decoding non-binary LDPC codes. [ABSTRACT FROM PUBLISHER]

We present an in-depth analysis of the problem of lossy compression of binary sources in the presence of correlated side information, where the correlation is given by a generic binary asymmetric channel and the Hamming distance is the distortion metric. Our analysis is motivated by systematic rate-distortion gains observed when applying asymmetric correlation models in Wyner-Ziv video coding. First, we derive for the first time the rate-distortion function for conventional predictive coding in the binary-asymmetric-correlation-channel scenario. Second, we propose a new bound for the case where the side information is only available at the decoder—Wyner-Ziv coding. We conjecture this bound to be tight. We show that the maximum rate needed to encode as well as the maximum rate-loss of Wyner-Ziv coding relative to predictive coding corresponds to uniform sources and symmetric correlations. Importantly, we show that the upper bound on the rate-loss established by Zamir is not tight and that the maximum value is actually significantly lower. Moreover, we prove that the only binary correlation channel that incurs no rate-loss for Wyner-Ziv coding compared with predictive coding is the Z-channel. Finally, we complement our analysis with new compression performance results obtained with our state-of-the-art Wyner-Ziv video coding system. [ABSTRACT FROM AUTHOR]

Distributed arithmetic coding (DAC) is a variant of AC that can realize Slepian-Wolf coding in a nonlinear way. In our previous work, we defined codebook cardinality spectrum (CCS) and Hamming distance spectrum (HDS) for DAC. In this paper, we make use of CCS and HDS to analyze tailed DAC, which is a form of DAC that, as traditional AC, maps the last few symbols of each source block onto non-overlapped intervals. First, we derive the exact HDS formula for tailless DAC, a form of DAC that maps all the symbols of each source block onto overlapped intervals, and show that the HDS formula previously given is in fact approximation. Then, the HDS formula is extended to tailed DAC. Using CCS, we also deduce the average codebook cardinality, which is closely related to decoding complexity, and rate loss of tailed DAC. The effects of tail length are extensively analyzed. It is revealed that by increasing tail length to a value not close to the bitstream length, closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss. Finally, theoretical analyses are verified by experiments. [ABSTRACT FROM PUBLISHER]

Distributed arithmetic coding (DAC) is an effective technique for implementing Slepian–Wolf coding (SWC). It has been shown that a DAC code partitions source space into unequal-size codebooks, so that the overall performance of DAC codes depends on the cardinality and structure of these codebooks. The problem of DAC codebook cardinality has been solved by the so-called codebook cardinality spectrum (CCS). This paper extends the previous work on CCS by studying the problem of DAC codebook structure. We define Hamming distance spectrum (HDS) to describe DAC codebook structure and propose a mathematical method to calculate the HDS of DAC codes. The theoretical analyses are verified by experimental results. [ABSTRACT FROM AUTHOR]

The weighted bit-reliability-based (wBRB) algorithm for nonbinary LDPC codes suffers certain loss of symbol-reliability. Thus, this paper enhances its soft-decision version by passing multiple symbol-reliability instead of bit-reliability. Furthermore, it demonstrates that plurality robustly indicates symbol-reliability of extrinsic information-sums. Thus, this paper enhances the hard-decision version by introducing symbol-reliability from plurality. Analysis results show that these two enhanced decoding algorithms significantly outperform the wBRB algorithm with reasonable overhead. [ABSTRACT FROM PUBLISHER]

We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion and queue-based channel models, which were recently shown to approximate well binary modulated correlated fading channels used with hard-decision demodulation. We establish conditions on the codes and channels parameters under which ML and minimum Hamming distance decoding are equivalent. We also present results on the optimality of classical perfect and quasi-perfect codes when used over the channels under ML decoding. Finally, we briefly apply these results to the dual problem of syndrome source coding with and without side information. [ABSTRACT FROM AUTHOR]

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary LDPC codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary LDPC code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary LDPC codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary LDPC codes. [ABSTRACT FROM AUTHOR]

The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance, where one example is in the design of transport format combination indicators (TFCIs) in CDMA. Considering convenience for encoding, we focus on the distance profiles with respect to cyclic subcode chains (DPCs) of cyclic codes over $GF(q)$ with length n$ such that \gcd(n, q)=1$. In this paper, the optimum DPCs and the corresponding optimum cyclic subcode chains are investigated on the punctured second-order Reed–Muller code for increasing message length, where two standards on the optimums are studied according to the rhythm of increase. Ignoring the dimension profile, the device will coincide with that of TFCI. [ABSTRACT FROM AUTHOR]

Multiuser cooperative schemes usually rely on relay selection or channel selection to avoid deep fading and achieve diversity while maintaining acceptable spectral efficiency. In some applications such as underwater acoustic communications, the low speed of the acoustic wave results in a very long delay between the channel state information (CSI) measurement time and the relay assignment time, which leads to a severely outdated CSI. To remedy this, we propose distributed coding schemes that aim at achieving good diversity-multiplexing trade-off (DMT) for multiuser scenarios where CSI is not available for resource allocation. We consider a network with multiple source nodes, multiple relay nodes, and a single destination. We first introduce a distributed linear block coding scheme, including Reed-Solomon codes, where each relay implements a column of the generator matrix of the code, and soft decision decoding is employed to retrieve the information at the destination side. We derive the end-to-end error performance of this scheme and show that the achievable diversity equals the minimum Hamming distance of the underlying code, while its DMT outperforms that of existing schemes. We extend the proposed scheme to distributed convolutional codes, and show that achieving higher diversity orders is also possible. [ABSTRACT FROM PUBLISHER]

Slepian-Wolf coding (SWC) can be effectively implemented by distributed arithmetic coding (DAC) codes. A theoretical tool named spectrum has been developed to analyze the complexity of the full-search binary DAC (BDAC) decoder for equiprobable sources. Following this work, this paper aims at improving the coding efficiency of BDAC codes. To achieve this goal, this paper analyzes how BDAC codes partition source space into codebooks and links codebook cardinalities with the initial spectrum. Further, by exploiting the final spectrum, this paper proves that the decoding error probability of BDAC codes will not tend to zero as code length goes to infinity, even at rates greater than the Slepian-Wolf limit. On the basis of theoretical analyses, two techniques are proposed to reduce the decoding error probability of BDAC codes, i.e., the permutation technique, which removes "near" (in the sense of Hamming distance) codewords in each codebook, and the weighted branching technique, which reduces the mis-pruning risk of proper paths during the decoding. The effectiveness of both techniques is well verified by experimental results. [ABSTRACT FROM PUBLISHER]

Energy-efficient communication using a class of spatial modulation (SM) that encodes the source information entirely in the antenna indices is considered in this paper. The energy-efficient modulation design is formulated as a convex optimization problem, where minimum achievable average symbol power consumption is derived with rate, performance, and hardware constraints. The theoretical result bounds any modulation scheme of this class, and encompasses the existing space shift keying (SSK), generalized SSK (GSSK), and Hamming code-aided SSK (HSSK) schemes as special cases. The theoretical optimum is achieved by the proposed practical energy-efficient HSSK (EE-HSSK) scheme that incorporates a novel use of the Hamming code and Huffman code techniques in the alphabet and bit-mapping designs. Experimental studies demonstrate that EE-HSSK significantly outperforms existing schemes in achieving near-optimal energy efficiency. An analytical exposition of key properties of the existing GSSK (including SSK) modulation that motivates a fundamental consideration for the proposed energy-efficient modulation design is also provided. [ABSTRACT FROM PUBLISHER]

This paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes. [ABSTRACT FROM PUBLISHER]

Previous interleavers designed for Serially Concatenated Codes (SCCs) have achieved a limited Minimum Hamming Distance (MHD) between the legitimate permutations of the encoded bit sequence. Hence, we propose a novel Evolutionary Algorithm (EA) capable of designing improved interleavers for SCCs, without artificially limiting the achievable MHD. As a result, increased MHDs and therefore reduced error floors are achieved, even if only a modest EA complexity can be afforded. [ABSTRACT FROM PUBLISHER]

This paper considers the optimization of a class of joint source-channel codes described by finite-state encoders (FSEs) generating variable-length codes. It focuses on FSEs associated to joint source-channel integer arithmetic codes, which are uniquely decodable codes by design. An efficient method for computing the free distance of such codes using Dijkstra's algorithm is proposed. To facilitate the search for codes with good distance properties, FSEs are organized within a tree structure, which allows the use of efficient branch-and-prune techniques avoiding a search of the whole tree. [ABSTRACT FROM PUBLISHER]

In this paper, diversity analysis of bit-interleaved coded multiple beamforming (BICMB) is extended to the case of general spatial interleavers, removing a condition on their previously known design criteria. We provide a method to get diversity order, simplifying the calculation of pairwise error probability (PEP). By using the Singleton bound, we also show the maximum achievable diversity for given code rate and the number of subchannels. [ABSTRACT FROM PUBLISHER]