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Journal of Air Force Engineering University

An Updating Decoding Algorithm of Non-binary LDPC Codes

Xiaoyu Wang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

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.

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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.
An improved decoding algorithm is presented in order to solve the problem of inconvenient for hardware implementation in decoding algorithm for non-binary LDPC codes based on the FFT-BP algorithm. The innovation of the new algorithm is the importing of the logarithmic operations, which will transform multiplication operations to addition operations in the logarithmic domains. Thus the presented algorithm has the advantages of the reduced complexity and the more convenient hardware implementation. A simulation is made using regular non binary LDPC codes under White Gaussian Noise channel based on GF(4). The result shows that the decoding complexity is much more reduced with the performance decrease by about 0.07 dB when BER( Bit Error Rate )is 10-4.
This paper investigates the decoding of rate 1/2 Non-Binary LDPC codes using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The iterative decoding approach based on the well known Extended-Min-Sum (EMS) algorithm, considered as the most efficient decoding algorithm to decode NB-LDPC codes, executes the decoding process iteratively. The main operations of this algorithm are the variable and check node updates which are performed at least eight times requiring a long decoding time to achieve good performance in terms of Frame Error Rate (FER). The proposed decoding near ML approach is based on ML search where the number of candidates is highly reduced using a technique privileging the most reliable and nearest codewords. Simulation results show that the proposed algorithm achieves, at a reduced list of 5 searched candidates in average at 3 dB, the performance offered by the EMS algorithm. We also show that by slightly increasing the list of candidates, the proposed algorithm outperforms the EMS algorithm.
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).
This paper reduces the complexity of decoding non-binary low-density parity-check (LDPC) codes by set partition. In the check node update, the input vectors are partitioned into several sets such that different elements in the virtual matrix enjoy various computational strategies. As a result, the proposed algorithm achieves high computational efficiency by setting strategies according to the correct probability of these elements. Simulation results indicate that it significantly decreases the complexity of check node update with negligible performance loss.
Recently low-density parity check (LDPC) codes have been applied in more areas, and the research of non-binary LDPC codes has become more significant. In this paper, we establish a dynamic scheduling strategy to reduce complexity of non-binary LDPC codes decoding, and choose extended min-sum algorithm as the model. The dynamic scheduling strategy is based on the idea of nodes reliability. When decoding, we select a part of check nodes to update messages in real time according to the reliability rules, and only the variable nodes getting new messages can participate in the message propagation. Compared with usual standard flooding scheduling, this dynamic scheduling strategy can reduce decoding complexity effectively. We also optimize the message of variable nodes according to reliability, which ensure that the error correction performance of decoding algorithm is not affected. Our simulations over a BPSK-AWGN channel show that this dynamic scheduling strategy can reduce complexity in non-binary LDPC codes belief propagation decoding without affecting error correction performance.
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.