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International Symposium on Turbo Codes and Iterative Information Processing

A symbol-reliability based message-passing decoding algorithm for nonbinary LDPC codes over finite fields

Chao Chen, Baoming Bai, Xiao Ma, Xinmei Wang

Published Sep 1, 2010• 9 citations
Publisher

Abstract

Based on the idea of plurality voting, we develop a low-complexity symbol-reliability based message-passing decoding algorithm for nonbinary low-density parity-check (LDPC) codes over finite fields. A key feature of the algorithm is that the message passed in the Tanner graph is the field element with the highest reliability. This leads to a very simple check node update. The algorithm requires only finite and integer operations. Moreover, the estimation of the signal-to-noise ratio (SNR) is not needed. Compared to the Fast Fourier Transform based q-ary sum-product algorithm (FFT-QSPA), the proposed decoding algorithm provides an excellent trade-off between performance and complexity for the nonbinary LDPC codes constructed based on finite geometries, finite fields and cyclotomic cosets.

DOI
10.1109/istc.2010.5613849

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A modified bit-reliability based decoding algorithm is presented based on a recent work by Huang et al. For the presented algorithm, only one Galois field element is passed and exchanged along the edges of the Tanner graph. At variable nodes, full messages rather than extrinsic messages are processed to further reduce the computational complexity. At check nodes, only hard reliability is considered and the main operation is to compute the check-sum and send one extrinsic symbol back to variable nodes. Simulation results show that, even with lower complexity and less memory consumption, the presented algorithm still can perform very closely to the original wBRB algorithm with low quantization bits (3 ~ 4 bits) when decoding the majority-logic decodable nonbinary LDPC codes. For codes constructed in high order fields, the presented algorithm can even outperform the original wBRB algorithm.
In this paper, we propose a binary message-passing algorithm for decoding low-density parity-check (LDPC) codes. The algorithm substantially improves the performance of purely hard-decision iterative algorithms with a small increase in the memory requirements and the computational complexity. We associate a reliability value to each nonzero element of the code's parity-check matrix, and differentially modify this value in each iteration based on the sum of the extrinsic binary messages from the check nodes. For the tested random and finite-geometry LDPC codes, the proposed algorithm can achieve performance as close as 1.3 dB and 0.7 dB to that of belief propagation (BP) at the error rates of interest, respectively. This is while, unlike BP, the algorithm does not require the estimation of channel signal to noise ratio. Low memory and computational requirements and binary message-passing make the proposed algorithm attractive for high-speed low-power applications.