Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

We present a novel decoding algorithm for q-ary low-density parity-check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature

Pivoting algorithms for maximum likelihood decoding of LDPC codes over erasure channels

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A decoding algorithm for LDPC codes over erasure channels with sporadic errors

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Generalized IRA erasure correcting codes for hybrid iterative/maximum likelihood decoding

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On the performance of moderate-length non-binary LDPC codes for space communications

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Short non-binary low-density parity-check codes for phase noise channels

This paper considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order $m$ , for channels with phase noise. In particular, $m$-ary differential phase-shift keying (DPSK)-modulated code symbols are transmitted over an additive white Gaussian noise (AWGN) channel with the Wiener phase noise. At the receiver side, non-coherent detection takes place, with the help of a multi-symbol detection algorithm, followed by a non-binary decoding step. Both the detector and the decoder operate on a joint factor graph. As a benchmark, finite length bounds and information rate expressions are computed and compared with the codeword error rate (CER) performance, as well as the iterative threshold of the obtained codes. As a result, performance within 1.2 dB from finite-length bounds is obtained, down to a CER of 10-3