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Journal of Southwest Jiaotong University

A Family of Irregular LDPC Codes Based on Optical Orthogonal Codes

Wen Hong

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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).

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A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes
In this paper, we construct regular and irregular LDPC codes using (n, {k1,k2}, 1)block design. The problem of designing regular and irregular structured LDPC codes that have good overall error performance for wide range of code rates and block sizes with attractive storage requirements is attempted. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Further we analyze the constructed codes based on number of short cycles of the corresponding Tanner graph. The analysis shows that codes having small number of short cycles and a cycle structure which is not overly regular in their Tanner graph perform better. The presented codes are well structured and unlike random codes can lend themselves to a very low-complexity encoder and decoder implementation.
A novel and simple construction of regular LDPC codes was proposed, which used sparse binary sequences, through studying construction methods of LDPC codes. The distribution matrix of ones in parity-check matrix was introduced into the new construction. The cyclic cross correlation function and the cyclic auto correlation function were utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.