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TELKOMNIKA Indonesian Journal of Electrical Engineering

Serial Min-max Decoding Algorithm Based on Variable Weighting for Nonbinary LDPC Codes

Zhongxun Wang, Xinglong Gao, Tiancheng Chen

Published Dec 2, 2013• 0 citations
Publisher

Abstract

In this paper, we perform an analysis on the min-max decoding algorithm for nonbinary LDPC (low-density parity-check) codes and propose serial min-max decoding algorithm. Combining with the weighted processing of the variable node message, we propose serial min-max decoding algorithm based on variable weighting for nonbinary LDPC codes in the end. The simulation indicates that when the bit error rate is 10^-3, compared with serial min-max decoding algorithm, traditional min-max decoding algorithm and traditional minsum algorithm, serial min-max decoding algorithm based on variable weighting can offer additional coding gain 0.2dB、0.8dB and 1.4dB respectively in additional white Gaussian noise channel and under binary phase shift keying modulation.

DOI
10.11591/telkomnika.v12i2.4176

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In this paper, we perform an analysis on the min-max decoding algorithm for nonbinary LDPC (low-density parity-check) codes and propose serial min-max decoding algorithm. Combining with the weighted processing of the variable node message, we propose serial min-max decoding algorithm based on variable weighting for nonbinary LDPC codes in the end. The simulation indicates that when the bit error rate is 10^-3, compared with serial min-max decoding algorithm, traditional min-max decoding algorithm and traditional minsum algorithm, serial min-max decoding algorithm based on variable weighting can offer additional coding gain 0.2dB、0.8dB and 1.4dB respectively in additional white Gaussian noise channel and under binary phase shift keying modulation.
Abstract: In this paper, we perform an analysis on the min-max decoding algorithm for nonbinary LDPC (lowdensity parity-check) codes and propose serial min-max decoding algorithm. After that, combining with the weighted processing of the variable node message, we propose serial min-max decoding algorithm based on variable weighting for nonbinary LDPC codes. In the end, we perform a detailed analysis on the features of optical communication and show the simulation model in optical communication system. The simulation indicates that when the bit error rate is 10-3 and used in optical communication, compared with serial min-max decoding algorithm, traditional min-max decoding algorithm and traditional min-sum algorithm, serial min-max decoding algorithm based on variable weighting can offer additional coding gain 0.2 dB, 0.3 dB and 0.4 dB respectively in (AWGN) additional white Gaussian noise channel and under (OOK) on-off keying modulation. Copyright © 2013 IFSA.
In this paper, we propose the min-max decoding algorithm of nonbinary LDPC codes based on early stopping by analyzing and combining traditional min-max decoding algorithm of nonbinary LDPC codes and the early stopping rule of binary LDPC codes. The simulation indicates that the proposed algorithm can greatly reduce the number of iterations in decoding process with almost no decoding performance loss compared with traditional minsum decoding algorithm of nonbinary LDPC codes and traditional min-max decoding algorithm of nonbinary LDPC codes in low signal-to-noise ratio region , which is in additive Gaussian white noise channel and under binary phase shift keying modulation. So the computational complexity can be effectively reduced and the real-time performance can be well improved.
When the code length is moderate, non-binary low-density parity-check (NB-LDPC) codes can achieve better error correcting performance than their binary counterparts at the expense of higher decoding complexity. The check node processing is a major bottleneck of NB-LDPC decoding. In this paper, Min-max decoding algorithm is proposed based on a new forward backward processing method of check nodes, select only a part of the most reliable information to the forward-backward calculation process, and change the variable nodes to check nodes (v-to-c) generation of information. Using this algorithm, a kind of code (768,1152) defined on GF(4) is simulated and compared with belief propagation in log domain (LOG-BP) decoding algorithm. Simulation results show Min-max decoding algorithm reduce information storage requirements and the computational complexity, conducive to engineering implementation.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
In this paper, we propose the modified minsum decoding algorithm of LDPC(Low-Density Parity-Check) code in the simplified difference-domain on the basis of detailed analysis of LDPC decoding algorithm in difference-domain. The simulation indicates that the proposed decoding algorithm offers almost no performance degradation compared with the BP(Belief Propagation) decoding algorithm in log-domain and the decoding algorithm in difference-domain and offers better performance than minsum decoding algorithm in log-domain and greatly reduces the computation complexity in AWGN(Additive White Gaussian Noise) channel and under BPSK(Binary Phase Shift Keying) modulation.