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

Abstract

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.

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

“…In this section, we describe the proposed SMP algorithm [15] in detail, assuming transmission over the q-SC. SMP decoding is an iterative algorithm, where CNs and VNs exchange q-ary messages.…”

“…The submatrices B i in (3) of B q dv,dc are given by The results are summarized in Tables II, IV, VI and VIII. For the sake of comparison, the iterative decoding thresholds of uncoupled regular LDPC ensembles, which can be computed from the analysis in [15] , are provided in Tables I, III, V and VII. As expected, a (d v , d c ) SC-LDPC code ensemble attains a remarkably larger threshold than the corresponing uncoupled ensemble. For example, for q = 512 and R = 1/2, the (3, 6) SC-LDPC code ensemble has threshold = 0.139, while the (3,6) uncoupled code ensemble has threshold = 0.11.…”

“…In [8], a lookup table-based decoding algorithm that is practical for small values of q was presented. In [15], a novel decoding algorithm for q-ary LDPC codes, dubbed symbol message passing (SMP), was introduced, with better performance and similar complexity than the algorithm in [14] for list size 1.…”

“…In this paper, we extend the analysis of the SMP algorithm of [15] to SC-LDPC codes. We derive the density evolution for protograph-based SC-LDPC codes for transmission over the q-SC.…”

Symbol Message Passing Decoding of LDPC Codes for Orthogonal Modulations

“…Recently, a symbol message passing (SMP) decoder for non-binary LDPC codes over the q-ary symmetric channel (qSC) was proposed [7]. Messages in the decoder consist of the most reliable symbol only.…”