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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]

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, 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]

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]

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 original design of standard digital fountain codes assumes that the coded information symbols are equally important. In many applications, some source symbols are more important than others, and they must be recovered prior to the rest. Unequal error protection (UEP) designs are attractive solutions for such source transmissions. In this paper, we introduce a more generalized design for the first universal fountain code design, Luby transform (LT) codes, that make it particularly suited for progressive bit stream transmissions. We apply the generalized LT codes to a progressive source and show that it has better UEP properties than other published results in the literature. For example, using the proposed generalization, we obtained up to 1.7-dB peak signal to noise ratio gain in a progressive image transmission scenario over the two major UEP fountain code designs. [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]

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]