Journal ArticleDOI
FFT-Based BP Decoding of General LDPC Codes Over Abelian Groups
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A wide class of low-density parity-check codes is introduced, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes.Abstract:
We introduce a wide class of low-density parity-check (LDPC) codes, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes. A belief-propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is also presented. Moreover, an encoding procedure is developedread more
Citations
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Journal ArticleDOI
Decoding Algorithms for Nonbinary LDPC Codes Over GF $(q)$
TL;DR: This letter addresses the problem of decoding nonbinary low-density parity-check (LDPC) codes over finite fields GF(q), with reasonable complexity and good performance, and introduces a simplified decoder which is inspired by the min-sum decoder for binary LDPC codes.
Journal ArticleDOI
Density Evolution for Nonbinary LDPC Codes Under Gaussian Approximation
TL;DR: This paper generalizes the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying channels for prime q and binary-modulated channels for q that is a power of 2 and proves that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities.
Proceedings ArticleDOI
A Polar Code Based Unsourced Random Access for the Gaussian MAC
TL;DR: This work proposes a polar code based scheme for the unsourced random access Gaussian channel based on T-fold irregular repetition slotted ALOHA (IRSA), which concludes that replacing of LDPC codes with polar codes in IRSA scheme leads to a significant performance gain.
Journal ArticleDOI
Short Turbo Codes over High Order Fields
TL;DR: Two classes of turbo codes constructed on high-order finite fields are introduced and provide remarkable coding gains over binary LDPC and turbo codes in the moderate-short block length regime.
Journal ArticleDOI
Nonbinary Hybrid LDPC Codes
Lucile Sassatelli,David Declercq +1 more
TL;DR: It is shown in particular that the class of hybrid LDPC codes can be asymptotically characterized and optimized using density evolution (DE) framework, and a technique to maximize the minimum distance of the code is presented.
References
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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.
Journal ArticleDOI
Factor graphs and the sum-product algorithm
TL;DR: A generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph, that computes-either exactly or approximately-various marginal functions derived from the global function.
Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Journal ArticleDOI
The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
TL;DR: Certain notorious nonlinear binary codes contain more codewords than any known linear code and can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes).