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Jisuanji fangzhen

Optimization of Degree Distribution of Fast Encodable Irregular Low-density Parity-check Code

Zengping Chen

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

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.

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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.
A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check(LDPC)codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation results show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.
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.
To design low-density parity-check (LDPC) codes with asymmetric channels and analyze their performance, an achievable asymmetric discrete density evolution method is proposed, which is based on offset min-sum decoding. First, the iterative formula of low-complexity asymmetric channel discrete density evolution is derived by means of combinatorics, difference method and the binomial theorem. The iterative formula is applied to further optimize the design of the LDPC codes using the offset min-sum decoding, and the optimal degree distributions and performance of the LDPC codes under different quantization ranges and step sizes are obtained under the asymmetric channel. Finally, the optimal offset values under high-precision quantization are obtained. The results show that under the asymmetric channel, the complexity of the proposed asymmetric density evolution method based on the offset min-sum decoding is reduced by an order of magnitude than that using the original method. For a fixed code rate, the smaller the variable node degree of the regular codes, the better the performance and the smaller the optimal offset value. For irregular LDPC codes, the optimal degree distributions and offset values are determined according to the differential evolution algorithm. For a fixed code rate, the larger the maximum variable node degree, the better the performance of irregular codes.
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.
A statistical-based density evolution algorithm is proposed for nonbinary low-density parity-check (LDPC) codes. It is applicable to both regular and irregular codes under study. The algorithm proposed serves as a tool to analyze the performance limit for iterative decoding of nonbinary LDPC codes, which in turn guides code design. Specifically, it provides approximated evaluations of convergence thresholds for codes given specific degree distributions. It is shown that, for a class of quasi-cyclic (QC) structured extended irregular repeat-accumulate (SeIRA) nonbinary LDPC codes, degree distributions can be optimized via the algorithm proposed. Simulation results exhibit that the nonbinary LDPC codes designed outperform the optimized binary LDPC codes on the AWGN channel with similar code length and rate in terms of bits. Performance gap between the binary and nonbinary LDPC codes is larger in the scenario of higher order modulation.