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This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n \times n$ array can experience deletions of rows and columns. These deletion errors are referred to as $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletions if ${t_{\mathrm {r}}}$ rows and ${t_{\mathrm {c}}}$ columns are deleted, while a code correcting these deletion patterns is called a $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletion correction code. The definitions for criss-cross insertions are similar. It is first shown that when $t_{r}=t_{c}$ the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. The focus of this paper lies on the case of (1, 1)-criss-cross deletions. A non-asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correction codes is shown which assures that the redundancy is at least $2n-3+2\log n$ bits. A code construction with an existential encoding and an explicit decoding algorithm is presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2 \log e$. A construction with explicit encoder and decoder is presented. The explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the construction. [ABSTRACT FROM AUTHOR]

The paper presents a novel efficient encoding and decoding method for self‐correction and anti‐interference used in big data product tracing system based on the cyclic code theory. The principle of constructing code set is first illustrated. Then the specific encoding and decoding methods suitable for the algebra rules are invented in sequence for efficiency. At last, to test the new coding system, the paper accelerates the decoding time by OpenMP more than 36 times. The error‐correcting code presents its perfect recovery property with a recovery rate of more than 95% under 60% damage rate. In analyzing its efficiency, the encoding process only costs 0.0045 second in average while the time of decoding method will increase with the damage rate's ascending, but it can be controlled within 16 seconds. In comparison to other coding patterns in the references, the newly error‐correcting and anti‐interference coding method achieves a balance in complexity, encoding rate, and decoding time with its priority in recovering rate under the damage rate of 60%. [ABSTRACT FROM AUTHOR]

For the recently developed quasi-reversible BCH codes with long lengths and high error-correcting capability, this paper is aimed at proposing a new and faster decoding procedure. It consists of four steps: 1) compute the consecutive syndromes; 2) calculate the syndrome functions by the forward and backward recursions; 3) solve a linear subsystem together with one matrix multiplication in order to find an error-locator polynomial; 4) determine the errors from the obtained polynomial by using the root-finding algorithm. This procedure, especially in Steps 2 and 3, differs greatly from the conventional procedures, which determine an error-locator polynomial directly from solving a linear system with the aid of the consecutive syndromes. The key idea behind this decoding technique is that the computational complexity of such a small subsystem instead of an originally large linear system can be significantly reduced, although there are additional forward and backward syndrome calculations with low complexity increasing. Finally, the illustrative examples and numerical simulations can be helpful to demonstrate the accuracy and efficacy of the presented decoding technique at different error-correcting capabilities. [ABSTRACT FROM AUTHOR]

Deletion errors are notoriously difficult to correct. The capacity of the binary deletion channel is not yet fully known, and there is no completely satisfactory solution even to the specific problem of correcting only two deletion errors. In this paper, we show that polarization theory, along with the powerful methods of polar coding and successive-cancellation decoding, can be extended to channels with deletion errors. Our results further generalize to channels corrupted by insertion errors and/or combinations of insertions and deletions. It was recently proposed to correct deletion errors using polar codes designed for the BEC, precoded with a sufficiently powerful CRC code. In this approach, in order to correct ${d}$ deletions in a codeword of length ${n}$ , successive-cancellation decoding is run separately for each of the $\binom {n}{d}$ possible deletion patterns, while treating the deleted symbols as erasures. The resulting complexity of decoding is ${O}\bigl ({n}^{d+1}\log {n}\bigr)$. In contrast, we develop herein a natural generalization of successive-cancellation decoding to channels with deletion errors. Our algorithm is based on the recursive structure of polar codes, processing the channel output in ${m} = \log _{2} {n}$ decoding layers, just like the conventional successive-cancellation decoder. Every node in each decoding layer propagates its uncertainty about the deletion pattern to the nodes in the next layer and, eventually, the correct deletion pattern becomes visible at the decoder output, with high probability. This makes it possible to consider at most $\binom {d+2}{2}$ scenarios at each node, and the overall decoding complexity is only ${O}\bigl ({d}^{3} {n} \log {n}\bigr)$ , which scales polynomially rather than exponentially with the number of deletions. Based on the proposed algorithm, we also investigate the channel polarization phenomenon. We are able to prove weak polarization where the number of deletions ${d}$ is small, i.e. ${d}={o}({n})$. We also conjecture the strong polarization for when ${d}={O}(1)$ and provide some evidence to support this conjecture. The strong polarization, if proven, implies that our coding scheme achieves the capacity of any binary-input symmetric channel which furthermore introduces a constant number of deletions. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k-tuple at most once (for predefined k). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length-n sequences for k = 2 + 2 log (n). This algorithm is then improved to support any value of k of the form k = a log (n), for 1 < a, while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes. [ABSTRACT FROM AUTHOR]

We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with m > 2 strings (where a previous paper considered m = 2) in asymptotic terms, where code-words are taken from an error-correcting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both. [ABSTRACT FROM AUTHOR]

This paper proposes multilevel Reed–Solomon (MRS) codes and their iterative multistage soft decoding (IMSD) for visible light communication (VLC), realizing both high decoding performance and transmission spectrum efficiency. The proposed IMSD algorithm decodes the MRS codes level-by-level through iterating either hard decisions or extrinsic information of RS coded bits. Each level RS decoding is realized by cascading the adaptive belief propagation (ABP) algorithm that produces the extrinsic information and the Berlekamp–Massey (BM) algorithm that estimates the codeword. The earlier level decoding provides better a priori information for the later ones. A complexity reducing IMSD (CR-IMSD) algorithm is also proposed to facilitate the decoding. This paper further investigates a joint design of color-shift keying (CSK) constellation and the MRS code, optimizing the decoding performance. The CSK constellation is designed by considering both the set partitioning (SP) criterion and the harmonic mean of constellation’s minimum squared Euclidean distance (MSED). The MRS codes are further designed using the capacity and the equal error probability rules. Our simulation results show that the IMSD algorithm achieves significant iterative decoding gains. The performance of the designed MRS code is 0.3 dB away from the capacity limit at the bit error rate (BER) of 10−9. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In combinatorial group testing, the primary objective is to fully identify the set of at most d defective items from a pool of n items using as few tests as possible. The celebrated result for the combinatorial group testing problem is that the number of tests, denoted by $t$ , can be made logarithmic in n when ${d} = {O}(\text {poly}(\log {n}))$. However, state-of-the-art group testing codes require the items to be tested ${w} = \Omega \left ({\frac {{d} \log {n}}{\log {d} + \log \log {n}} }\right)$ times and tests to include $\rho = \Omega \left ({\frac {{n}}{{d} \log _{{d}} {n}}}\right)$ items. In many emerging applications, items can only participate in a limited number of tests and tests are constrained to include a limited number of items. In this paper, we study the “sparse” regime for the group testing problem where we restrict the number of tests each item can participate in by ${w}_{\max }$ or the number of items each test can include by $\rho _{\max }$ in both noiseless and noisy settings. These constraints lead to a largely unexplored regime where t is a fractional power of n, rather than logarithmic in n as in the classical setting. Our results characterize the number of tests t needed in this regime as a function of ${w}_{\max }$ or $\rho _{\max }$ and show, for example, that t decreases drastically when ${w}_{\max }$ is increased beyond a bare minimum. In particular, in the noiseless case it can be shown that if ${w}_{\max } \leq {d}$ , then we must have ${t}={n}$ , i.e., testing every item individually is optimal. We show that if ${w}_{\max }={d}+1$ , the number of tests decreases suddenly from ${t}={n}$ to ${t} = \Theta ({d} \sqrt {{n}})$. The order-optimal construction is obtained via a modification of the classical Kautz-Singleton construction, which is known to be suboptimal for the classical group testing problem. For the more general case, when ${w}_{\max }={{ ld}}+1$ for integer ${l}>1$ , the modified Kautz-Singleton construction requires ${t} = \Theta \left ({{d} {n}^{\frac {1}{{l}+1}}}\right)$ tests, which we prove to be near order-optimal. We also show that our constructions have a favorable encoding and decoding complexity, i.e. they can be decoded in $({poly}({d}) + {O}({t}))$ -time and each entry in any codeword can be computed in ${poly}(\log {n})$ memory space. We finally discuss an application of our results to the construction of energy-limited random access schemes for Internet of Things networks, which provided the initial motivation for our work. [ABSTRACT FROM AUTHOR]

With technology scaling, burst errors or clustered errors are becoming increasingly common in different types of memories. Multiple bit upsets due to particle strikes, write disturbance errors, and magnetic field coupling are a few of the mechanisms which cause clustered errors. In this article, a new class of single burst error correcting codes are presented which correct a single burst of any size b within a codeword. A code construction methodology is presented which enables us to construct the proposed scheme from existing codes, e.g., Hamming codes. A new single step decoding methodology for the proposed class of codes is also presented which enables faster decoding. Different code constructions using Hamming codes, and BCH codes have been presented in this paper and a comparison is made with existing schemes in terms of decoding complexity and data redundancy. The proposed scheme in all cases reduces the decoder complexity for little to no increase in data redundancy, specifically for higher burst error sizes. [ABSTRACT FROM AUTHOR]

The rank-modulation scheme has been recently proposed to write and store data in flash memories efficiently. In this paper, a new construction of systematic error-correcting codes for permutations is presented under the Chebyshev distance. By constructing a subgroup code and using its coset codes to partition the set of information permutations, the proposed code construction can achieve much larger code cardinality and hence higher code rates. To facilitate the encoding and decoding of the constructed codes, we also investigate the concepts of ranking and unranking for permutations, and generalize them to $M$ -ranking and $M$ -unranking for multi-permutations. Examples are provided to demonstrate the relevant concepts and the encoding/decoding algorithms. [ABSTRACT FROM AUTHOR]

Gaussian thermal loss channels are of particular importance to quantum communication theory since they model realistic optical communication channels. Except for special cases, the quantum capacity of Gaussian thermal loss channels is not yet quantified completely. In this paper, we provide improved upper bounds of the Gaussian thermal loss channel capacity, both in energy-constrained and unconstrained scenarios. We briefly review Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energy-unconstrained case, that a family of GKP codes achieves the quantum capacity of Gaussian thermal loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize entanglement fidelity. Then, we solve the biconvex optimization heuristically by an alternating semi-definite programming method and report that, starting from Haar random initial codes, our numerical optimization yields a hexagonal GKP code as an optimal encoding in a practically relevant regime. [ABSTRACT FROM AUTHOR]

In this paper, we present linear systematic error-correcting codes Lk and L+k which are the results of our research on the sub-exceeding functions. Given an integer k such that k ≥ 3, these two codes are re-spectively [2k, k] and [3k, k] linear codes. The minimum distance of L3 is 3 and for k ≥ 4 the minimum distance of Lk is 4. The code L+k, the minimum distances are respectively 5 and 6 for k = 4 and k ≥ 5. By calculating the complexity of the algorithms, our codes have fast and efficient decoding. Then, for a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that the codes mentioned above present many advantages. [ABSTRACT FROM AUTHOR]

The interest in polar codes has been increasing significantly since their adoption for use in the 5th generation wireless systems standard. Successive cancellation (SC) decoding algorithm has low implementation complexity, but yields mediocre error-correction performance at the code lengths of interest. SC-Flip algorithm improves the error-correction performance of SC by identifying possibly erroneous decisions made by SC and re-iterates after flipping one bit. It was recently shown that only a portion of bit-channels are most likely to be in error. In this paper, we investigate the average log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, and develop the Thresholded SC-Flip (TSCF) decoding algorithm. We also replace the LLR selection and sorting of SC-Flip with a comparator to reduce the implementation complexity. Simulation results demonstrate that for practical code lengths and a wide range of rates, TSCF shows negligible loss compared with the error-correction performance obtained when all single-errors are corrected. At matching maximum iterations, TSCF has an error-correction performance gain of up to 0.45 dB compared with SC-Flip decoding. At matching error-correction performance, the computational complexity of TSCF is reduced by up to 40% on average and requires up to $5\times $ lower maximum number of iterations. [ABSTRACT FROM AUTHOR]

In this paper, new index coding problems are studied, where each receiver has erroneous side information. Although side information is a crucial part of index coding, the existence of erroneous side information has not been considered yet. We study an index code with receivers that have erroneous side information symbols in the error-free broadcast channel, which is called an index code with side information errors (ICSIE). The encoding and decoding procedures of the ICSIE are proposed, based on the syndrome decoding. Then, we derive the bounds on the optimal codelength of the proposed index code with erroneous side information. Furthermore, we introduce a special graph for the proposed index coding problem, called a \delta s -cycle whose properties are similar to those of the cycle in the conventional index coding problem. Properties of the ICSIE are also discussed in the \delta s -cycle and clique. Finally, the proposed ICSIE is generalized to an index code for the scenario having both additive channel errors and side information errors, called a generalized error correcting index code. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior on the binary erasure channel. We also consider the construction of families of rate-compatible SC-TC ensembles. Our numerical results show that the threshold saturation of the BP decoding threshold to the maximum a posteriori threshold of the underlying uncoupled ensembles occurs for large enough coupling memory. The improvement of the BP threshold is especially significant for SCCs and BCCs, whose uncoupled ensembles suffer from a poor BP threshold. For a wide range of code rates, SC-TCs show close-to-capacity performance as the coupling memory increases. We further give a proof of threshold saturation for SC-TC ensembles with identical component encoders. In particular, we show that the DE of SC-TC ensembles with identical component encoders can be properly rewritten as a scalar recursion. This allows us to define potential functions and prove threshold saturation using the proof technique recently introduced by Yedla et al. [ABSTRACT FROM PUBLISHER]

Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and r=n-k$ parity nodes is used to encode data in a distributed storage system. It is known that if h$ out of the n$ nodes are inaccessible and d$ surviving (helper) nodes are used to recover the lost data, then we need to download at least h/(d+h-k)$ fraction of the data stored in each of the helper nodes (Dimakis et al., 2010 and Cadambe et al., 2013). If this lower bound is achieved for the repair of any h$ erased nodes from any d$ helper nodes, we say that the MDS code has the (h,d)$ -optimal repair property. We study high-rate MDS array codes with the optimal repair property (also known as minimum storage regenerating codes, or MSR codes). Explicit constructions of such codes in the literature are only available for the cases where there are at most three parity nodes, and these existing constructions can only optimally repair a single node failure by accessing all the surviving nodes. In this paper, given any r$ and n$ , we present two explicit constructions of MDS array codes with the (h,d) . The encoding, decoding, repair of failed nodes, and update procedures of these codes all have low complexity. Codes in the second family have the optimal access property and can be constructed over any base field $F$ as long as $|F|\ge n+1$ . Moreover, both code families have the optimal error resilience capability when repairing failed nodes. We also construct several other related families of MDS codes with the optimal repair property. [ABSTRACT FROM PUBLISHER]

Generalized integrated interleaved codes refer to two-level Reed-Solomon codes, such that each code of the nested layer belongs to different subcode of the first-layer code. In this paper, we first devise an efficient decoding algorithm by ignoring first-layer miscorrection and by intelligently reusing preceding results during each iteration of a decoding attempt. Neglecting first-layer miscorrection also enables to explicitly and neatly formulate the decoding failure probability. We next derive an erasure correcting algorithm for redundant arrays of independent disks systems. We further construct an algebraic systematic encoding algorithm, which had been open. Analogously, we propose a novel generalized integrated interleaving scheme over binary Bose-Chaudhuri–Hocquenghem codes, reveal a lower bound on the minimum distance, and derive a similar encoding and decoding algorithm as those of Reed-Solomon codes. [ABSTRACT FROM AUTHOR]

Error-correcting output coding (ECOC) is one of the most widely used strategies for dealing with multi-class problems by decomposing the original multi-class problem into a series of binary sub-problems. In traditional ECOC-based methods, binary classifiers corresponding to those sub-problems are usually trained separately without considering the relationships among these classifiers. However, as these classifiers are established on the same training data, there may be some inherent relationships among them. Exploiting such relationships can potentially improve the generalization performances of individual classifiers, and, thus, boost ECOC learning algorithms. In this paper, we explore to mine and utilize such relationship through a joint classifier learning method, by integrating the training of binary classifiers and the learning of the relationship among them into a unified objective function. We also develop an efficient alternating optimization algorithm to solve the objective function. To evaluate the proposed method, we perform a series of experiments on eleven datasets from the UCI machine learning repository as well as two datasets from real-world image recognition tasks. The experimental results demonstrate the efficacy of the proposed method, compared with state-of-the-art methods for ECOC-based multi-class classification. [ABSTRACT FROM PUBLISHER]

To avoid data corruption, error correction codes (ECCs) are widely used to protect memories. ECCs introduce a delay penalty in accessing the data as encoding or decoding has to be performed. This limits the use of ECCs in high-speed memories. This has led to the use of simple codes such as single error correction double error detection (SEC-DED) codes. However, as technology scales multiple cell upsets (MCUs) become more common and limit the use of SEC-DED codes unless they are combined with interleaving. A similar issue occurs in some types of memories like DRAM that are typically grouped in modules composed of several devices. In those modules, the protection against a device failure rather than isolated bit errors is also desirable. In those cases, one option is to use more advanced ECCs that can correct multiple bit errors. The main challenge is that those codes should minimize the delay and area penalty. Among the codes that have been considered for memory protection are Reed-Solomon (RS) codes. These codes are based on non-binary symbols and therefore can correct multiple bit errors. In this paper, single symbol error correction codes based on Reed-Solomon codes that can be implemented with low delay are proposed and evaluated. The results show that they can be implemented with a substantially lower delay than traditional single error correction RS codes. [ABSTRACT FROM PUBLISHER]

We consider the task of communicating a data stream—a long, possibly infinite message not known in advance to the sender—over a channel with adversarial noise. For any given noise rate $c<1$ , we show an efficient, constant-rate scheme that correctly decodes a $(1-c)$ fraction of the stream sent so far with high probability, or aborts if the noise rate exceeds $c$ . In addition, we prove that no constant-rate scheme can recover more than a $(1-c)$ fraction of the stream sent so far with non-negligible probability, which makes our scheme optimal in that aspect. The parties are assumed to preshare a random string unknown to the channel. Our techniques can also be applied to the task of interactive communication (two-way communication) over a noisy channel. In a recent paper (Braverman and Rao, STOC11), the possibility of two-party interactive communication as long as the noise level is $< 1/4$ was shown. By allowing the parties to preshare some private random string, we extend this result and construct a (nonefficient) constant-rate interactive protocol that succeeds with overwhelming probability against noise rates up to $1/2$ . We complete this result by proving that no constant-rate protocol can withstand noise rates $> 1/2$ . [ABSTRACT FROM PUBLISHER]

This paper proposes for single carrier signaling a simple structure that combines turbo equalization and decoding of correlated sources in multipath-rich multiuser Rayleigh fading multiple access channels (MAC), where the correlation between the sources is exploited by vertical iterations (VI) between the decoders. The bit-flipping model with a flipping probability pe is used to express the correlation ρ between the sources as ρ = 1-2pe. The proposed simple structure, spatially concatenated codes (SpCC), can achieve turbo-like performance over MAC channels suffering from severe inter-symbol interference (ISI), even though it uses short memory convolutional codes. First of all, to achieve turbo-like performance we introduce VIs to exploit the knowledge about the source correlation by exchanging extrinsic log-likelihood ratio (LLR) between the two decoders. We then add a rate-1 doped accumulator (D-ACC) to flexibly adapt for the variation of correlations between the sources. The results of computer simulations and extrinsic information transfer (EXIT) analysis confirm that in multipath-rich environments the proposed structure can achieve excellent performances, 1.02-1.28 dB away from the Slepian-Wolf-Shannon limit, at 1% outage probability for 0 <; ρ ≤ 1. [ABSTRACT FROM PUBLISHER]

The corruption of compressed video bitstreams during their transmission over error-prone communication channels leads to degradation in the visual quality at the decoder. In order to effectively conceal the corrupted video data an exact error detection scheme is of utmost importance. In this paper, we present a new error detection scheme for the H.264/AVC using the RD optimized motion vector constraints to improve the error detection rate. The simulation results show that the detection rate of the proposed algorithm is about 86%, although the proposed scheme brings about a small amount of bitrate increment and causes a slight decrement in the PSNR during the encoding. [ABSTRACT FROM PUBLISHER]

In this paper, the second moment of the ripple size during the Luby transform (LT) decoding process is analyzed. Combined with a result by Karp et al. (2004) stating that the expectation of the ripple size is of the order of k, our study gives bounds on the error probability of the LT decoder. Furthermore, an analytic expression for the variance of the ripple size up to terms of constant order is given, and the expression of Karp et al. for the expectation of the ripple size is refined up to terms of the order of 1/k. This provides a first step toward an analytic finite-length analysis of LT decoding. [ABSTRACT FROM PUBLISHER]

A Write Once Memory (WOM) is a storage medium with binary memory elements, called cells, that can change from the zero state to the one state only once. Examples of WOMs include punch cards and optical disks. WOM-codes, introduced by Rivest and Shamir, permit the reuse of a WOM by taking into account the location of cells that have already been changed to the one state. The objective in designing WOM-codes is to use the fewest number of cells to store a specified number of information bits in each of several reuses of the memory. An [n,k,t] WOM-code \cal C is a coding scheme for storing k information bits in n cells t times. At each write, the state of each cell can be changed, provided that the cell is changed from the zero state to the one state. The rate of \cal C, defined by \cal R(\cal C)=kt/n, indicates the total amount of information that is possible to store in a cell in t writes. Two WOM-code constructions correcting a single cell-error were presented by Zémor and Cohen. In this paper, we present another construction of a single-error-correcting WOM-code with a better rate. Our construction can be adapted also for single-error-detection, double-error-correction, and triple-error-correction. For the last case, we use triple-error-correcting BCH-like codes, which were presented by Kasami and more recently described again by Bracken and Helleseth. Finally, we show two constructions that can be combined for the correction of an arbitrary number of errors. [ABSTRACT FROM AUTHOR]

A new coding framework is established for channels whose outputs are overlapping pairs of symbols. Such channels are motivated by storage applications in which the spatial resolution of the reader may be insufficient to isolate adjacent symbols. Reading symbols as pairs changes the coding-theoretic error model from the standard bounded number of symbol errors to a bounded number of pair errors. Starting from the most basic coding-theoretic questions, the paper studies codes that protect against pair-errors. It provides answers on pair-error correctability conditions, code construction and decoding, and lower and upper bounds on code sizes. Asymptotic analysis of pair-error correction shows that there exist pair-error codes with rates that are strictly higher than the best known codes in the Hamming metric. [ABSTRACT FROM AUTHOR]

Digital Video Broadcasting - Handheld (DVB-H) is a new digital terrestrial broadcasting standard customized for the multimedia service on the mobile devices and the handheld terminals. It introduces a technique known as multi-protocol encapsulation forward error correction (MPE-FEC) for the IP-datagrams in the data link layer to improve the mobile performance. Every MPE-FEC frame is constructed independently in the DVB-H standard. In this paper, a frame-related coding approach for MPE-FEC frames is proposed. When a MPE-FEC frame is built during the data link layer encoding process, the rightmost n columns in the MPE part of the current MPE-FEC frame are filled with the data populated from the leftmost n columns of its previous MPE-FEC frame. After the encoding process, a correlation is set up between the adjacent frames. This correlation can be utilized by the proposed decoding algorithm to enhance the error correction capability. The theoretical analysis and simulations results show that the proposed approach can provide better error correction capability than the DVB-H standard as well as the conventional zero-padding method in random noise channels. As a more efficient decoding strategy, the proposed approach is a good candidate for the decoding of MPE-FEC frame. [ABSTRACT FROM AUTHOR]

The use of open-loop coding can be easily extended to a closed-loop concatenated code if the transmitter has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio (SNR). From this optimization, a linear feedback scheme is produced that is asymptotically optimal in the sense of blocklength-normalized SNR; it is then compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit error rate (BER) and frame error rate (FER). It is also shown that if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O\left(C\over R\right), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low-density parity-check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits. [ABSTRACT FROM AUTHOR]

Raptor codes are a class of concatenated codes composed of a fixed-rate precode and a Luby-transform (LT) code that can be used as rateless error-correcting codes over communication channels. These codes have the atypical features of dynamic code-rate, highly irregular Tanner graph check-degree distribution, random LT-code structure, and LT-precode concatenation, which render a hardware-efficient decoder implementation achieving good error-correcting performance a challenging task. In this paper, the design of hardware-efficient Raptor decoders with good performance is addressed through joint optimizations targeting 1) the code construction, 2) decoding schedule, and 3) decoder architecture. First, random encoding is decoupled by developing a two-stage LT-code construction scheme that embeds structural features in the LT-graph that are amenable to efficient implementation while guaranteeing good performance. An LT-aware LDPC precode construction methodology that ensures architectural-compatibility with the structured LT code is also proposed. Second, a decoding schedule is optimized to reduce memory cost and account for processing workload-variability caused by the varying code rate. Third, to address the problems of check-degree irregularity and hardware underutilization, a novel reconfigurable check unit that attains a constant throughput while processing a varying number of LT and LDPC nodes is presented. These design steps collectively are employed to generate serial and partially-parallel decoder architectures. A Raptor code instance constructed using the proposed method having LT data-block length of 1210 is shown to outperform or closely match the performance of conventional LDPC codes over the code-rate range [0.4,2\over 3]. The corresponding hardware serial decoder is synthesized using 65-nm CMOS technology and achieves a throughput of 22 Mb/s at rate 0.4 for a BER of 10^-6, dissipates an average power of 222 mW at 1.2 V, and occupies an area of \ 1.77~mm^2. [ABSTRACT FROM AUTHOR]

The Forward Link Only (FLO) merit of fountain codes is utilized to avoid excessive retransmission requests for multicast communications. Two important and basic classes of fountain codes, Random Linear (RL) codes and Luby Transform (LT) codes, are considered in this paper as application layer Forward Error Correction (FEC) codes. High Peak-to-Average Power Ratio (PAPR) is a notorious physical layer problem in OFDM systems. We take the PAPR constraint into account in the encoding of fountain codes for OFDM multicast communications. We propose a selective mapping (SLM) technique that selects the best P candidates among the QP candidates. This SLM technique performs significant better than the conventional SLM technique that selects the best candidate among the Q candidates. Mathematical analysis and computer simulation verify the excellence of our designs. [ABSTRACT FROM AUTHOR]

Multipulse pulse position modulation (MPPM) has been widely proposed to improve data rate over traditional pulse position modulation (PPM) in free-space optical communication systems. Encoders for MPPM are typically lookup-table-based, thus restricting the practical size of MPPM codebooks. Power-of-two-sized MPPM codebooks typically do not have an efficient soft-in soft-out decoder, making them poorly suited for concatenation with an outer code under iterative decoding. In this paper, a new coding technique based on constrained coding is introduced that allows construction of codes which have an efficient encoding algorithm. More importantly, these new codes are suitable for iterative soft-decision decoding in concatenation with an outer error-correcting code. Simulation results for both the Gaussian and Poisson channels show that a serial concatenation with an outer low-density parity-check code (LDPC) can achieve between 2 to 3 dB coding gain over comparable Reed-Solomon and LDPC-coded MPPM systems. [ABSTRACT FROM PUBLISHER]

This paper introduces a new approach to cooperative communications. Consider two partner nodes that cooperate to convey their data to a common destination, each transmitting not only its own "local" data but also acting as a relay for its partner, thereby effecting spatial diversity. In the proposed scheme, each partner multiplexes local data with relayed data and convolutionally encodes the resulting bitstream prior to transmission; the other partner then uses its knowledge of the relayed data to prune edges from the code trellis, thereby decoding at a lower (and more robust) rate. The destination observes two copies of each source's data — one transmitted as local information, the other transmitted as relayed information — and employs iterative decoding to recover the same. The resulting performance is superior to that of cooperation schemes based on time sharing — for example, a gain of 4.1 dB is observed at a frame-error rate of 10^-3 with memory M = 3 codes — as well as schemes employing the newer algebraic superposition approach of Xiao et al., with trellis pruning enjoying an advantage of 0.55 dB to 1.04 dB over algebraic superposition, depending on M. The new approach requires some additional decoding complexity at each partner node, but the decoding complexity at the destination node is kept constant. [ABSTRACT FROM AUTHOR]

A novel number theoretic transform called Inverse Gray Robust Symmetrical Number System (IGRSNS) is proposed for error control coding in this paper. IGRSNS is obtained by modifying Robust Symmetrical Number System (RSNS) that was proposed earlier, using Inverse Gray code property. Due to ambiguities present in each residue, RSNS has a short dynamic range (DR) compared to that in other number systems. The short DR of RSNS enables it to be effectively used for error detection without the addition of any redundant modulus as in Redundant Residue Number System. Although RSNS has a large redundant range, its detection ability is not optimal due to the Gray code property associated with it. In an attempt to overcome this limitation, we have proposed Inverse Gray coding to be combined with RSNS in increasing its effectiveness in error detection. The resulting IGRSNS thus inherits properties of both RSNS and Gray code. Analysis and simulations show that IGRSNS has a near-optimal error detection ability. The potential of IGRSNS for error correction is also investigated. Further, a novel error correction algorithm using one redundant modulus is proposed. Simulations show that the proposed algorithm performs well under all cases of single bit errors. [ABSTRACT FROM PUBLISHER]