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现代传播：中国传媒大学学报

A Method on Construction of LDPC Parity-Check Matrix

Lizhi Zhao

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

A method on construction of LDPC Parity-check matrix was proposed,by removing loops with girth 4 in a semi-random parity-check matrix.Simulation results show that the proposed method can effectively avoid the influence on the performance of LDPC codes exerted by short loops,so the decoding performance is distinctively improved.Furthermore,the better performance can be obtained as the increasing of code lengths.

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A method on construction of LDPC Parity-check matrix was proposed,by removing loops with girth 4 in a semi-random parity-check matrix.Simulation results show that the proposed method can effectively avoid the influence on the performance of LDPC codes exerted by short loops,so the decoding performance is distinctively improved.Furthermore,the better performance can be obtained as the increasing of code lengths.
Low-density Parity-check (LDPC) coding is a class of advanced channel coding techniques. To improve the performance of LDPC codes, a simple and effective method to construct QC-LDPC codes without short cycles (cycles of length four and six) is proposed. The approach is especially effective when the parity-check matrix of QC-LDPC codes is composed of circulant permutation matrices. Firstly, we analyze the shapes of the cycles in the exponent matrix, to get the required conditions of no four-cycles and six-cycles. Then we show how to construct the parity-check matrix without four-cycles and six-cycles by filling rows of the exponent matrix with arithmetic sequences. Simulation results show that the proposed codes have better performance than array codes. Though the performance of the proposed codes is not as well as random codes at higher Eb/N0, they can be applied to practical communications because of being encoded in linear time with shift registers.
The presence of circles would lay a great impact on the quasi-cyclic LDPC decoding.Therefore,the parity check matrix with good girth distribution is beneficial to the performance of code.This paper first makes a analysis on girth distribution of the check matrix.Then a reasonable constraint is set between the mother matrix and shift matrix,thus,by this way,the check matrix could maximize the minimum cycle length of the check matrix and the average length of the cycle.Finally,a method to construct QC-LDPC code with high girth is given.Simulation results show that this method for minimizing the short code cycle could construct good practical codes.
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
A design of low-density parity-check (LDPC) code via the masking technology and progressive optimization is proposed. The code generated by this method has lower computational complexity, and their parity-check matrices can effectively refrain from the girth -4 phenomenon. The proposed method has the superiorities such as better girth-length characteristic and more flexible trim in the length and rate of the code. Experiment results indicate that the error-correction performance of the new code should be better than or as good as the capability of the code which is constructed without been masking. Futhermore, under the condition of short code length, the performance is better than that of LDPC codes via the randomized construction methods.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
The high encoding complexity of LDPC codes can be solved by designing structured parity-check matrix. If the parity-check matrix of LDPC codes is composed of same type of blocks, decoder implementation can be simple, this structure allow structured decoding and required memory for storing the parity-check matrix can be reduced largely. In this paper, we propose a construction algorithm for short block length structured LDPC codes based on girth condition, PEG algorithm and variable node connectivity. The code designed by this algorithm shows similar performance to other codes without structured constraint in low SNR and better performance in high SNR than those by simulation