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International Conference on Mechanic Automation and Control Engineering

Research and Simulation of Low Density Parity Check Codes

Xiaohua Zhang, Shoufeng Peng, Feifei Fan

Published Jul 27, 2012• 0 citations
Publisher

Abstract

Low density parity check (LDPC) codes has obtained widely appreciated, because of its superior performance. In this paper, expounded the principle of the low density parity check code construction, and studied its encoding and decoding algorithm. Then we carried out LDPC codes' simulation under additive white Gaussian noise channel, verified the superior error correction capability of LDPC codes.

DOI
10.1109/mace.2012.609

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Low density parity check (LDPC) codes has obtained widely appreciated, because of its superior performance. In this paper, expounded the principle of the low density parity check code construction, and studied its encoding and decoding algorithm. Then we carried out LDPC codes' simulation under additive white Gaussian noise channel, verified the superior error correction capability of LDPC codes.
Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding.
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.
Based on the structure of parity-check matrix of RU algorithm,a class of Quasi-cycle Low-density Parity-check(QC-LDPC) codes with complexity is constructed by selecting sub-matrices reasonably to restrict and consisting of lower dual diagonal matrices.Simulation results show that not only the proposed codes have lower complexity,but also the error-correcting performance is better than QC-LDPC codes randomly constructed and practical Block-LDPC codes in the additive white Gaussion noise channel.It can get 0.3 dB Signal to Noise Ratio(SNR) gain at a Bit Error Rate(BRE) of 10-6.
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.
Low-Density Parity-Check code (LDPC) is a kind of linear block error-correcting codes.Sum-product algorithm is an iterative decoding algorithms commonly used in LDPC code decoding.This paper studies into the LDPC code message passing iterative decoding algorithm under the binary symmetric channel (BSC) and simulates the bit error probability,then simulates the convergence of check nodes' and variable nodes' probability density in the iterative process using the method of density evolution.The result show that under a given channel threshold,LDPC code has a good correction performance.