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International Symposium on Turbo Codes and Iterative Information Processing

Symbol Message Passing Decoding of LDPC Codes for Orthogonal Modulations

Emna Ben Yacoub, Balázs Matuz

Published Aug 30, 2021• 1 citation
Publisher

Abstract

A simple decoder for q-ary low-density parity-check codes is studied, termed symbol message passing. The decoder passes hard decisions from a q-ary alphabet. For orthogonal modulations over the additive white Gaussian channel for which the modulation order and the field order q are equal, it is shown that the extrinsic messages can be modelled as observations of a q-ary symmetric channel, allowing to work out density evolution equations. A stability analysis is provided which emphasizes the influence of degree-3 variable nodes. Simulation results show performance gains for increasing q w.r.t. binary low-density parity-check codes with bit-interleaved coded modulation, and potential savings in decoding complexity.

DOI
10.1109/istc49272.2021.9594277

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A simple decoder for q-ary low-density parity-check codes is studied, termed symbol message passing. The decoder passes hard decisions from a q-ary alphabet. For orthogonal modulations over the additive white Gaussian channel for which the modulation order and the field order q are equal, it is shown that the extrinsic messages can be modelled as observations of a q-ary symmetric channel, allowing to work out density evolution equations. A stability analysis is provided which emphasizes the influence of degree-3 variable nodes. Simulation results show performance gains for increasing q w.r.t. binary low-density parity-check codes with bit-interleaved coded modulation, and potential savings in decoding complexity.
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.
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A new low-complexity message passing algorithm is described for decoding low-density parity-check (LDPC) codes by exchanging binary messages. The algorithm computes the local maximum-likelihood binary message (LMLBM) at each symbol node, given the combination of local channel information and partial syndrome components from adjacent parity check nodes. When channel information is quantized, the locally ML messages are pre-computed and stored in a dynamic global lookup table. The proposed algorithm uses memoryless extrinsic messages so that density evolution thresholds can be directly computed. Thresholds are obtained for regular ensembles, predicting good performance on quantized binary-input additive white Gaussian noise (biAWGN) channels.
A simple decoding algorithm, dubbed symbol message passing decoder, is studied for q-ary low-density parity-check codes over the q-ary Poisson pulse-position modulation channel. The messages in the decoder are symbols from the finite field Fq{\mathbb{F}_q}Fq​. To improve performance, a second decoder with an extended message set {E∪Fq}\left\{ {{\text{E}} \cup {\mathbb{F}_q}} \right\}{E∪Fq​} is also investigated, where E denotes an erasure. Thresholds within 1.3 dB from the Shannon limit are obtained for low field orders.
Low complexity decoding algorithms are necessary to meet data rate requirements in excess of 1 Tbps. In this paper, we study one and two bit message passing algorithms for belief propagation decoding of low-density parity-check (LDPC) codes and analyze them by density evolution. The variable nodes (VNs) exploit soft information from the channel output. To decrease the data flow, the messages exchanged between check nodes (CNs) and VNs are represented by one or two bits. The newly proposed quaternary message passing (QMP) algorithm is compared asymptotically and in finite length simulations to binary message passing (BMP) and ternary message passing (TMP) for spectrally efficient communication with higher-order modulation and probabilistic amplitude shaping (PAS). To showcase the potential for high throughput forward error correction, spatially coupled LDPC codes and a target spectral efficiency (SE) of 3 bits/QAM symbol are considered. Gains of about 0.7 dB and 0.1 dB are observed compared to BMP and TMP, respectively. The gap to unquantized belief propagation (BP) decoding is reduced to about 0.75 dB. For smaller code rates, the gain of QMP compared to TMP is more pronounced and amounts to 0.24 dB in the considered example.