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Journal of Computers

The Min-max Decoding Algorithm of Nonbinary

Zhongxun Wang, Xinglong Gao

Published Oct 30, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.4304/jcp.9.10.2488-2492

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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.
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.
This paper presents an improved decoding algorithm of non-binary LDPC codes based on the Expanded Min-Sum algorithm,analyzes the complexity of the algorithm in decoding efficiency.According to the fact that the reliability of variable note is increased with the increase of the iterative number,the reliability of the variable notes is estimated by the maximum post probability of variable notes and illegal parity-check values.By the estimation rule,the iterative calculations or some variable notes are stopped,the number of calculation for updating variable and parity-check notes is reduced,thus the decoding complexity is decreased and the decoding efficiency is improved.A simulation is made using regular non-binary LDPC codes under White Gaussian Noise channel based on GF(4),the result shows that the performance decreases by about 0.05 dB when BER(Bit Error Rate) is,but the decoding complexity is reduced and the decoding efficiency is improved significantly.
Non-binary low density parity check codes can achieve better err-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. Min-Max decoding algorithm is one of the low-complexity quasi-optimal iterative algorithms. However, a problem of the Min-Max decoding algorithm is iteration inefficient in the case of low SNR. In this paper, an adaptive method is proposed based on the Min-Max decoding algorithm. By comparing the correlation among each iteration output, setting an appropriate threshold to determine whether ahead of the end of iteration, which makes the adaptive Min-Max decoding algorithm very attractive for practical purposes
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.
To speed up the convergence rate of non-binary low-density parity check codes and reduce decoding computational complexity of decoding algorithm, a weighted symbol flipping decoding algorithm based on iterative stopping criteria is proposed. The algorithm determines the position and amplitude of the flipped symbol according to the weight of the information node and the flipping function in the check equation, and selects the optimal value of the weighting factor through simulation. At the same time, the iteration stop criterion is introduced, and the iteration is stopped by setting the number of parity equations without satisfying the different signal-to-noise ratio. The simulation results show that the channel additive white Gauss noise, the algorithm ensures the invariant properties of weighted symbol flipping decoding algorithm under the condition that can accelerate the convergence speed, reduce the average number of iterations, so the decoding performance and complexity trad-off between effective.