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Lecture notes in electrical engineering

A Stopping Criterion Based on Check-Sum Variations for Decoding Nonbinary LDPC Codes

Wen Fan, Haiyang Liu, Wei Yang, Junfeng Zhao, Aaron Z. Jia

Published Oct 28, 2015• 0 citations
Publisher
DOI
10.1007/978-81-322-2580-5_38

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In order to detect uncorrectable error frames and early terminate their iterative belief-propagation (BP) decoding for binary or nonbinary LDPC codes, a unified early stopping criterion using check-sum variation patterns is proposed. In addition to low computational overhead and easy choice of threshold parameters, it can be adapted to different channels. Simulation results show that the proposed criterion greatly reduces the average number of iterations (ANI) at low to medium signal-to-noise ratio (SNR) while keeping the error performance degradation negligible over a wide SNR region.
A two-stage hybrid iterative decoding algorithm with an efficient stopping criterion for nonbinary low-density parity-check (LDPC) codes is proposed, which combines weighted symbol-flipping (WSF) algorithm and fast Fourier transform q-ary sum-product algorithm (FFT-QSPA). The first WSF decoding would be stopped in advance by analyzing the trend of the number of unsatisfied checks. If the first stage decoding is stopped or failed, the second powerful FFT-QSPA is activated. The proposed decoding with the efficient stopping achieves error performance as good as that of FFT-QSPA with a low complexity, and converges faster than hybrid WSF (HWSF) algorithm.
Nonbinary low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, a new stopping criterion is proposed. Based on the changes of the variance of variable node¿s extrinsic information, the criterion can predict a decoding failure and decide whether the iteration of the decoder should be stopped. The simulation results show that the stopping criterion can greatly reduces the average number of required iterations of GF(q)-LDPC decoder with negligible performance loss.