Construction of quasi-cyclic LDPC codes based on a two-dimensional MDS code

Authors:
Chao Chen;Baoming Bai;Xinmei Wang
Affiliations:
State Key Lab. of ISN, Xidian University, Xi'an, China;State Key Lab. of ISN, Xidian University, Xi'an, China;State Key Lab. of ISN, Xidian University, Xi'an, China
Venue:
IEEE Communications Letters
Year:
2010

Citing 2
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Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

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Abstract

In this letter, we first propose a general framework for constructing quasi-cyclic low-density parity-check (QCLDPC) codes based on a two-dimensional (2-D) maximum distance separable (MDS) code. Two classes of QC-LDPC codes are defined, whose parity-check matrices are transposes of each other. We then use a 2-D generalized Reed-Solomon (GRS) code to give a concrete construction. The decoding parity-check matrices have a large number of redundant parity-check equations while their Tanner graphs have a girth of at least 6. The minimum distances of the codes are very respectable. Experimental studies show that the constructed QC-LDPC codes perform well with the sum-product algorithm (SPA).