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Journal of Hangzhou Dianzi University

Construction of Quasi-cyclic LDPC Codes Based on Optical Orthogonal Codes

Zhao Ze-mao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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Pacific-Asia Conference on Circuits, Communications and Systems•Jul 1, 2011•4 citations
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.
Combining the perfect cyclic difference sets with the quasi-cyclic codes,a new algorithm for constructing QC-LDPC codes based on cyclic difference sets is proposed.First,the author obtains a small initial matrix that meet the requirements of the weights based on cyclic difference sets,and then the zeros elements,non-zero elements of the initial matrix are replaced by all-zero matrices and cyclic shift matrices.For the purpose of determining the shift coefficient,the cycle length of six is eliminated by computer searching.Simulations show that,under the AWGN channel and the BP decoding algorithm,our QC-LDPC codes are better than the random LDPC codes in the bit error rate and they are more proper for hardware implementation.
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.
A method to construct a flexible length or rate of quasi-cyclic Low Density Parity Check(LDPC) codes based on Balanced Incomplete Block Design(BIBD) and cycle permutation matrix is proposed.Based on actual demand,the corresponding template matrix is constructed by BIBD method.The template matrix is extended by the appropriate cycle permutation matrix.The quasi-cyclic LDPC codes constructed by the proposed method have a good structure and flexibility.This method improves the efficiency of construction good codes which meet the needs of a practical application.Simulations show that quasi-cyclic LDPC codes constructed by the proposed method perform well over AWGN channels with iterative decoding and have a lower error floor.
Based on the optical orthogonal codes, a method for constructing irregular LDPC (low-density parity check) codes was presented. These LDPC codes are quasi-cyclic codes and can be encoded with low complexity with a linear relationship to code length. These codes have Tanner graphs free of 4-cycles. They perform well with the sum-product iterative decoding. Compared with random codes and regular LDPC codes based on the optical orthogonal codes with similar parameters, they have decoding performance gains respectively about 0.3 and 0.15 dB when bit error rate is 10~(-5).
This paper presents a construction method of quasi-cyclic non-binary low density parity-check(NB-LDPC)code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional extension.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared with the GF(29)-based RS(511,305)and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain(NCG)at the bit error rate(BER)of 10-7.Compared with the binary QC-LDPC codes constructed by the traditional way,the binary LDPC codes randomly constructed,the32-ary QC-LDPC codes constructed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB,0.03dB and 0.83dB NCGrespectively at the BERof 10-7.Through performance simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feature,conducive to hardware implementation,but also shows better error correction performance in the short code length.
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.