Spatially Coupled LDPC Codes Constructed From Protographs
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This paper constructs protograph-based spatially coupled low-density parity-check codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain, and obtains sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit.Abstract:
In this paper, we construct protograph-based spatially coupled low-density parity-check (LDPC) codes by coupling together a series of $L$ disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying $L$ , we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary $L$ . We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large $L$ , the BP thresholds on both the binary erasure channel and the binary-input additive white Gaussian noise channel saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a posteriori decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output channels with low-complexity BP decoding.read more
Citations
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Journal ArticleDOI
Design Guidelines of Low-Density Parity-Check Codes for Magnetic Recording Systems
TL;DR: A comprehensive survey of the latest research advancements in LDPC-code design for MR systems from the perspectives of code construction, decoder design, as well as asymptotic performance-evaluation methodology is presented.
Convergence analysis for a class of LDPC convolutional codes on the erasure channel
TL;DR: An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices with structured irregularity in the Tanner graph of the codes leads to significantly better thresholds when compared to the corresponding LDPC block codes.
Journal ArticleDOI
Randomly Punctured LDPC Codes
TL;DR: An efficient way to accurately predict BP thresholds of randomly punctured LDPC code ensembles on the binary-input additive white Gaussian noise channel (BI-AWGNC), given only the BP threshold of the mother code ensemble on the BEC and the design rate is provided.
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Spatially Coupled Turbo-Like Codes
TL;DR: This paper proposes 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 gives a proof of threshold saturation for SC-TC ensembles with identical component encoders.
References
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Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
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Error control coding : fundamentals and applications
Shu Lin,Daniel J. Costello +1 more
TL;DR: This book explains coding for Reliable Digital Transmission and Storage using Trellis-Based Soft-Decision Decoding Algorithms for Linear Block Codes and Convolutional Codes, and some of the techniques used in this work.
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The capacity of low-density parity-check codes under message-passing decoding
TL;DR: The results are based on the observation that the concentration of the performance of the decoder around its average performance, as observed by Luby et al. in the case of a binary-symmetric channel and a binary message-passing algorithm, is a general phenomenon.
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A recursive approach to low complexity codes
TL;DR: It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities.
MonographDOI
Modern Coding Theory
TL;DR: This summary of the state-of-the-art in iterative coding makes this decision more straightforward, with emphasis on the underlying theory, techniques to analyse and design practical iterative codes systems.