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Microelectronics & Computer

An Optimization Method of Degree Distributions for Irregular LDPC Codes

Yunfeng Guan

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The optimization method of degree distributions for irregular LDPC codes is key to get codes which exhibit a performance extremely close to Shannon capacity.The paper propose a practical method,which uses a simplification Gaussian Approximation (GA) algorithm to calculate the threshold quickly,then get the best degree distributions by adaptive particle swarm optimizer (APSO) with special restrictions.Simulation results shows that such a method has excellent optimization ability with low complexity,so it is of suggestive significance to the construction of excellent LDPC in both wireless and optical communication system.

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The optimization method of degree distributions for irregular LDPC codes is key to get codes which exhibit a performance extremely close to Shannon capacity.The paper propose a practical method,which uses a simplification Gaussian Approximation (GA) algorithm to calculate the threshold quickly,then get the best degree distributions by adaptive particle swarm optimizer (APSO) with special restrictions.Simulation results shows that such a method has excellent optimization ability with low complexity,so it is of suggestive significance to the construction of excellent LDPC in both wireless and optical communication system.
This paper presents a new design methodology/process for low-density parity-check codes (LDPC). To minimize the gap to Shannon limit, the particle swarm optimizer is applied to optimize the variable and check node degree distribution lambda and p respectively in case of irregular LDPC codes. discrete fast density evolution (FDE) is used (as the analysis technique) to compute the threshold value of LDPC code and the Shannon limit is evaluated based on Butman and McEliece formula. The results conducted show that, our proposed distributions with low degrees of (lambda, p) outperform other comparable distributions.
For irregular LDPC codes,the density evolution method can track the messages to find out the noise threshold, enabling optimization of the degree distribution. A new optimized scheme for irregular LDPC codes is proposed in this paper, which is combining Zhengya He's modified particle swarm optimization (PSO) algorithm with discrete density evolution (DDE) for the offset BP-based decoding algorithm. Several optimized degree distribution pairs and corresponding threshold of LDPC codes over Rician channel were given using the proposed scheme. The performance of the optimized LDPC codes was also analyzed. Simulation results shows that the proposed scheme is effective.
An efficient method of constructing irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes is proposed. In order to find the degree distribution with low convergence threshold, the extrinsic information transfer (EXIT) chart is utilized to optimize the degree distribution of LDPC codes. Then, a modified progressive edge growth (PEG) algorithm is used to get the mask matrix with the optimal degree distribution. Finally, the parity-check matrix of QC LDPC code is constructed based on the mask matrix, and the shift values are optimized to eliminate short cycles. Simulation results show that the constructed irregular QC LDPC codes with optimized degree distribution significantly outperform the regular QC LDPC codes in the additive white Gaussion noise (AWGN) channel.
The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.
Because the structure of check matrix of fast encodable irregular LDPC code is exceptional,normal design technique of optimization of degree distribution can not work well in this case.In this paper,a method of optimization of fast encodable irregular low-density parity-check codes' degree distribution is discussed based on differential evolution with particular restrictions.The principle of density evolution of irregular LDPC codes is explained.Gaussian approximation to program the evolution proceeding and differential evolution are analysed,and the particular restrictions on degree distribution are discussed.Simulation results show that some good distribution sequences are better than that reported before.