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Journal of Electronics (China)

SPARSE SEQUENCE CONSTRUCTION OF LDPC CODES

He, Shanbao, Zhao Zhao, Chunming, Shi, Zhihua

Published Jan 1, 2005• 0 citations
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Abstract

This letter proposes a novel and simple construction of regular Low-Density Parity-Check (LDPC) codes using sparse binary sequences. It utilizes the cyclic cross correlation function of sparse sequences to generate codes with girth8. The new codes perform well using the sumproduct decoding. Low encodingcomplexity can also be achieved due to the inherent quasi-cyclic structure of the codes.

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This letter proposes a novel and simple construction of regular Low-Density Parity-Check (LDPC) codes using sparse binary sequences. It utilizes the cyclic cross correlation function of sparse sequences to generate codes with girth8. The new codes perform well using the sumproduct decoding. Low encodingcomplexity can also be achieved due to the inherent quasi-cyclic structure of the codes.
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.
In this paper, we propose a novel and simple construction of regular LDPC codes using sparse binary sequences. The distribution matrix of ones in a parity-check matrix is introduced into this new construction. The cyclic cross correlation function and the cyclic auto correlation function are employed to ensure that the girth of Tanner graph is at least 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.
theconstruction ofLDPCcodes andtheconstruction isbasedonthelines andpoints ofafinite geometry. Inthispaper, wepropose anovel andsimple con- Itcangetquasi-cyclic LDPCcodes withlowencoding struction ofregular LDPCcodes using sparse binary complexity. sequences. Thedistribution matrix ofonesinaparity- Inthis paper wepresent aneffective algorithm which check matrix isintroduced into this newconstruction. cangenerate LDPC codeswithperformance slightly Thecyclic cross correlation function andthecyclic better thanthatofthePEGcodes, while maintaining autocorrelation function areemployed toensure that fairly lowencoding complexity. Inthenextsection, we thegirth ofTanner graphisatleast eight. Thenew describe LDPC codesfromsparse binary sequences, codes perform wellusing thesum-product algorithmtheir structures andtheir girth distribution. Section foriterative decoding. Lowencoding complexity can 3lists thedetailed construction ofLDPCcodes based also beachieved duetotheinherent quasi-cyclic struc- onsparse sequences. Performance comparisons ofdiftureoftheLDPCcodes. ferent classes ofLDPC codes aregiveninSection 4. Section 5concludes this paper.