Quasi-cyclic LDPC codes: Construction and rank analysis of their parity-check matrices

Author

Liu, Keke ; Huang, Qin ; Lin, Shu ; Abdel-Ghaffar, Khaled

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA

fYear

2012

Firstpage

227

Lastpage

233

Abstract

A construction of binary and non-binary quasi-cyclic (QC)-LDPC codes based on partitions of finite fields of characteristic 2 is proposed. The construction is carried out in the Fourier transform domain. The parity-check matrices of these QC-LDPC codes are arrays of circulant permutation matrices. The ranks of these arrays are analyzed and combinatorial expressions are derived. Example codes are given and simulations show that they perform well over the AWGN channel decoded with message-passing decoding algorithms.

Keywords

AWGN channels; Fourier transforms; Galois fields; binary codes; channel coding; combinatorial mathematics; cyclic codes; decoding; matrix algebra; parity check codes; AWGN channel; Fourier transform domain; binary QC-LDPC code; circulant permutation matrix arrays; combinatorial expressions; finite fields; message passing decoding algorithm; nonbinary quasicyclic LDPC code; parity check matrices; rank analysis; Channel coding; Decoding; Fourier transforms; Iterative decoding; Null space;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory and Applications Workshop (ITA), 2012

Conference_Location

San Diego, CA

Print_ISBN

978-1-4673-1473-2

Type

conf

DOI

10.1109/ITA.2012.6181797

Filename

6181797