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Journal of Sichuan University

Analysis for Gaussian Approximation and Structure Optimization of IRA Codes

Wen Lei

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Code structure is an important factor which affects performance of IRA codes.THe structure of IRA codes was optimized based on Gaussian approximation.The graph model theory of IRA codes was introduced,and the Tanner graph was presented.The impact of 2 degree to the structure of codes was analysed.Based on given noise variance,the Gaussian approximation of IRA codes was researched on AWGN channel,and the degree sequences was designed.IRA codes were designed based on Gaussian approximation and simulated by computer.Simulation results showed that the IRA codes have better performance than MacKay LDPC codes,and the convergence of message are well.

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Analysis for Gaussian Approximation and Structure Optimization of IRA Codes

Abstract:Code structure is an important factor which affects performance of IRA codes. THe structure of IRA codes was optimized based on Gaussian approximation. The graph model theory of IRA codes was introduced, and the Tanner graph was presented. The impact of 2 degree to the structure of codes was analysed. Based on given noise variance, the Gaussian approximation of IRA codes was researched on AWGN channel, and the degree sequences was designed. IRA codes were designed based on Gaussian approximation and simulated by computer. Simulation results showed that the IRA codes have better performance than MacKay LDPC codes, and the convergence of message are well.

•Jan 1, 2007•0 citations

Gaussian Approximation of Irregular Repeat-Accumulate Codes over Mixed Gaussian/Erasure Channels

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Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.

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Performance analysis of finite-length LDPC codes

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In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.

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In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.

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Design of masking matrix for QC-LDPC codes

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The masking matrix plays an important role in constructing new classes of regular and irregular quasi-cyclic low density parity check (QC-LDPC) codes. By coupling two identical graphs in a special way, we present a new structure of the masking matrix, whose Tanner graph can be seen as a protograph. From this perspective, we propose a Gaussian Approximation algorithm for protograph-based LDPC codes to analyze the asymptotic performance of this class of codes. It is shown that, although the proposed structure of the masking matrix has almost the same convergence threshold as the conventional one produced randomly by progressive edge growth (PEG) algorithm, the former converges faster than the latter. Simulation results illustrate that the QC-LDPC code constructed by the proposed structure of the masking matrix has about 0.2dB coding gains compared with the conventional one.

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Design of q-ary Irregular Repeat-Accumulate Codes

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This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.

International Conference on Advanced Information Networking and Applications (AINA)•Jan 1, 2009•8 citations
Code structure is an important factor which affects performance of IRA codes.THe structure of IRA codes was optimized based on Gaussian approximation.The graph model theory of IRA codes was introduced,and the Tanner graph was presented.The impact of 2 degree to the structure of codes was analysed.Based on given noise variance,the Gaussian approximation of IRA codes was researched on AWGN channel,and the degree sequences was designed.IRA codes were designed based on Gaussian approximation and simulated by computer.Simulation results showed that the IRA codes have better performance than MacKay LDPC codes,and the convergence of message are well.
Abstract:Code structure is an important factor which affects performance of IRA codes. THe structure of IRA codes was optimized based on Gaussian approximation. The graph model theory of IRA codes was introduced, and the Tanner graph was presented. The impact of 2 degree to the structure of codes was analysed. Based on given noise variance, the Gaussian approximation of IRA codes was researched on AWGN channel, and the degree sequences was designed. IRA codes were designed based on Gaussian approximation and simulated by computer. Simulation results showed that the IRA codes have better performance than MacKay LDPC codes, and the convergence of message are well.
Gaussian approximation models the message density in message passing decoders as Gaussian distribution.In this paper,irregular repeat accumulate(IRA) codes over the mixed white Gaussian noise/erasure channels are designed using Gaussian approximation.Recursive equations of density evolution and analytic expressions of bit error rate are derived.The analytic results not only provide a way to predict asymptotic performance of IRA codes but also help us design good IRA codes over the mixed channel.Comparison between simulation results and thresholds computed from analytic results shows that predication from the theoretical results is accurate enough.The optimized IRA codes designed for the mixed channels have better performance than that of IRA codes designed for AWGN channels when the designed erasure probability is close to the actual probability.
In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.
In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.
The masking matrix plays an important role in constructing new classes of regular and irregular quasi-cyclic low density parity check (QC-LDPC) codes. By coupling two identical graphs in a special way, we present a new structure of the masking matrix, whose Tanner graph can be seen as a protograph. From this perspective, we propose a Gaussian Approximation algorithm for protograph-based LDPC codes to analyze the asymptotic performance of this class of codes. It is shown that, although the proposed structure of the masking matrix has almost the same convergence threshold as the conventional one produced randomly by progressive edge growth (PEG) algorithm, the former converges faster than the latter. Simulation results illustrate that the QC-LDPC code constructed by the proposed structure of the masking matrix has about 0.2dB coding gains compared with the conventional one.
This paper is concerned with the construction of a class of nonbinary irregular repeat accumulate (IRA) codes. Since they are defined on the finite field GF(q) (q>2), we will refer to the constructed codes as q-ary IRA (QIRA) codes. While preserving the excellent error correcting capability of q-ary LDPC codes, QIRA codes can be efficiently encoded like conventional binary IRA codes. By adopting the progressive edge growth (PEG) algorithm to construct the parity check matrices, we can achieve the increased girth of their factor graphs and improved decoding performance. Simulation results show that, using the sum-product algorithm on GF(q), QIRA codes outperform binary LDPC codes and turbo codes in terms of bit error ratio and frame error ratio on AWGN channels. Especially, they could achieve excellent error performance when combined with high order modulations. Feasibility study indicates, with the use of the extended min-sum (EMS) decoding algorithm, QIRA codes are competitive candidates for practical applications.