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A Modified Extended Min-Sum Algorithm based on Posterior Probability Thresholding for Non-binary LDPC Codes

Yatong Zhao, Liqian Wang, Miao Zhu, Weiming Wang, Kai Tao, Yinlong Shi, Xue Chen

Published May 7, 2022• 0 citations
Publisher

Abstract

This letter focuses on the improvement in the error correction performance of the extended min-sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, we propose a novel threshold-based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the method’s complexity.

DOI
10.22541/au.165193202.22527475/v1

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This letter focuses on the improvement in the error correction performance of the extended min-sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, we propose a novel threshold-based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the method’s complexity.
Abstract This letter focuses on improving the error correction performance of the extended min‐sum (EMS) decoding algorithm. Introducing factor/offset modifications in the check node update process of the EMS algorithm can improve the performance. Based on this, the authors propose a novel threshold‐based modified EMS algorithm that introduces the factor/offset in a targeted manner by setting a threshold for the posterior probability. Simulation results show that an additional performance gain of the order of 0.08 dB is obtained with the proposed method without significantly increasing the complexity of the method.
Low Density Parity Check (LDPC) codes have been widely applied in recent years, and Extended Min-Sum (EMS) decoding algorithm is the most practical algorithm, which has a fairly low computational cost. Due to the great loss in error correction performance of EMS algorithm, in this paper, we establish constraints to obtain reliable nodes while decoding and evaluate the reliability of the nodes. The nodes and information transferred between nodes are processed and optimized according to the reliability of the nodes. High reliability nodes will not be updated in the decoding process while the information of the sub-reliability nodes will be optimized in different situations, thereby improving the decoding accuracy. This algorithm can accelerate the convergence of the algorithm, while the reduced number of update nodes can control the increase of the computation to a certain extent, and maintain the advantage of the low computation quantity of EMS algorithm. Through simulation results and computational analysis, we prove that the improved algorithm has significantly improved error correction performance compared with the traditional EMS algorithm. Under the same conditions, it has completely entered the waterfall area at 3.6dB, and the EMS algorithm has not entered the waterfall area. By comparing the average iteration times of decoding of the two algorithms, the convergence speed of the algorithm can be reflected. Compared with EMS algorithm, the improved algorithm has significantly improved the convergence speed in most areas, which indicates that the processing of sub-reliable nodes accelerates the convergence of the algorithm. Finally, the average update times of the check nodes and variable nodes of the two algorithms are compared respectively. Although the improved algorithm introduces extra processing flow, it speeds up the convergence of the algorithm, and the computational cost of decoding is less expensive.
In this paper the combined normalized and offset extended min sum (EMS) is proposed for efficient decoding of non-binary low density parity check (LDPC) codes. EMS is the approximation of the sum product algorithm for reducing the computation complexity. However there is a performance gap between EMS and SP algorithm due to this approximation. The approximate check node messages of the extended min sum are compensated by both normalized and offset factor. The normalized factor and offset factor is determined for one iteration and is kept constant for all SNRs and iterations. It will shown in bit error rate simulation of (1008, 504) LDPC code over GF (4) that combined normalized offset extended min sum has superior performance than normalized and offset extended min sum. However, it requires only extra one multiplication for each cycle.
In comparison to the binary LDPC codes, the nonbinary low-density parity-check (NB-LDPC) codes have the advantage of solving burst errors. In order to improve the accuracy of the decoding results, an improved extended min-sum (EMS) algorithm is proposed in this paper. By adopting the feedback idea of joint iterative detection algorithm and introducing the reliability and stability parameters, the new algorithm can mitigate the influence of Log-likelihood ratio (LLR) oscillation on the decoding result and adjust the update information of the check node properly, thereby improving the decoding accuracy. This method can effectively restrain the LLR oscillation and speed up the convergence rate, thus the final decision result can be amended. Simulation results show that, the proposed improved EMS decoding algorithm heightens the bit error rate performance and reduces average number of iterations, meanwhile the additional computations are within acceptable range.
In this paper, we propose a new improved algorithm to reduce the decoding complexity of NB-LDPC codes especially when the number of iteration is large. The proposed algorithm is based on the extended min-sum (EMS) which truncates the message vectors and trellis-based EMS (T-EMS) which employs the trellis representation. Our modification of EMS introduces the thresholds to further truncate the incoming messages to the check node. The performance of our improved new algorithm is only 0.05dB (resp 0.2dB) to BP in the waterfall region over GF(8) (resp GF(128)), but the complexity will reduce to lower than half of the EMS when the threshold is chosen reasonable.
The decoding algorithms of Nonbinary low-density parity-check (NB-LDPC) codes mainly include Belief Propagation (BP), Fast Fourier Transforms (FFT) and Extended Min-Sum (EMS). Among these decoding algorithms, although EMS has the lowest decoding complexity, there is still room for improvement. Therefore, this paper proposes a new algorithm based on the EMS algorithm to further improve the decoding complexity and performance. In order to reduce complexity, an adaptive truncation rule is added to the decoding process. The adaptive truncation rule chooses the length of automatic truncation to reduce the average number of iterations. Thus, the complexity of decoding algorithm is reduced. Besides the weighting factors is added to the variable update iteration process, which effectively improves the decoding performance. The results show that the proposed algorithm has about 0.9 dB gain compared with the EMS decoding algorithm when the bit error rate (BER) is 10--4and the Galois field GF(q) (q16).