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Dianzi qijian

Research on Construction of Quasi-Cyclic LDPC Codes Based on PEG Algorithm

Zhang Jian-bin

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In order to take into account the requirements of high error correction performance and simple hardware implementation of LDPC codes,this paper presents a new algorithm for constructing check matrix of LDPC codes based on PEG algorithm.After constructing a basic matrix with PEG algorithm,we can get cyclic shift matrix under the proposed formula of shift parameter,and then,using the cyclic shift matrix and all-zero matrix to extend the basic matrix optimally,we can get the quasi-cyclic LDPC matrix in which the girth is 8 at least.The algorithm ' s error correction performance is very close to that of PEG algorithm,and is particularly better than that of PEG algorithm when S/N is higher than 1.2 dB.It ' s hardware implementation is more simple than that of PEG algorithm,and the algorithm is flexibly to set the parameters of the LDPC codes.

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In order to take into account the requirements of high error correction performance and simple hardware implementation of LDPC codes,this paper presents a new algorithm for constructing check matrix of LDPC codes based on PEG algorithm.After constructing a basic matrix with PEG algorithm,we can get cyclic shift matrix under the proposed formula of shift parameter,and then,using the cyclic shift matrix and all-zero matrix to extend the basic matrix optimally,we can get the quasi-cyclic LDPC matrix in which the girth is 8 at least.The algorithm ' s error correction performance is very close to that of PEG algorithm,and is particularly better than that of PEG algorithm when S/N is higher than 1.2 dB.It ' s hardware implementation is more simple than that of PEG algorithm,and the algorithm is flexibly to set the parameters of the LDPC 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.
Progressive Edge-Growth(PEG) algorithm is a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.
The construction of low-density parity codes(LDPC) is one of the hottest fields in the research of LDPC codes. In this paper, we propose a quasi-cyclic(QC) construction method of parity-check matrix of LDPC codes, named block-PEG method. In this method, a basic matrix is constructed firstly, then the none-zero elements in the matrix are extended by circulant permutation matrices, and the parity-check matrix is obtained at last. The simulation results indicate that the performances of LDPC codes constructed by block-PEG method are similar with that of PEG algorithm. In linear-time, block-PEG can generate LDPC codes with similar performance of the PEG-generated codes.
Based on the characteristics of optical orthogonal codes,a new algorithm for constructing quasi-cyclic LDPC codes is proposed.Firstly,based on optical orthogonal codes,we can get an initial matrix which meets the parameter request,then under the proposed formula and the characteristics of quasi-cyclic LDPC codes to determine the shift parameter matrix.Finally,using all-zero matrix and the circlet permutation matrix to fill the shift parameter matrix,we can get a check matrix without cycles with length of 4 and 6.Simulations show that,under the AWGN channel and the BP decoding algorithm,the new quasi-cyclic LDPC codes are better than Mackay's codes in the bit error rate and they are more proper for hardware implementation.
We propose a new algorithm based on PEG algorithm to construct high-girth quasi-cyclic low-density parity check (QC-LDPC) codes. Before our improved algorithm in introduction, we depict the general algorithm based on PEG algorithm to construct QC - LDPC code, if necessary to eliminate the short cycles, that would bring in cycles-search. When code length of basic matrix is not too long, the algorithm is feasible, but with the code length growth, cycles-search will bring large of calculation and time-consuming sharply. Therefore we put forward an improved method by using the specific relation of basic matrix rows to replace traditional cycles-search, effectively eliminates short cycles, and largely reduces the time complexity at the same time. Through the simulation analysis, the performance can also be comparable with random constructed LDPC codes.
We propose a general method for constructing regular and irregular quasi-cyclic LDPC codes based on the modified PEG (progressive edge growth) graph. The idea of permutation vector is introduced. Through permutation vectors, the QC-LDPC codes based on arbitrary circulant permutation matrices, which are not limited to identity matrix, Q-matrix or D-matrix, can be generated with flexible parameters such as block length, code rate, degree distribution. Simulation results demonstrate that QC-LDPC codes using the new PEG algorithm show an error correction performance comparable to the random LDPC codes based on the traditional PEG algorithm. In addition, the PEG QC-LDPC codes have more hardware-friendly parity check matrices than the random PEG LDPC codes and can fulfill linear-time encoding. The QC-LDPC codes based on D-matrix and Q-matrix are more suitable to be used in QC-LDPC codes than identity matrix because they outperform that of identity matrix by 0.1-0.2 dB in the new PEG algorithm.