Quasi-Cyclic LDPC Codes on Cyclic Subgroups of Finite Fields

Author

Li Zhang ; Shu Lin ; Abdel-Ghaffar, Khaled ; Zhi Ding ; Bo Zhou

Author_Institution

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

Volume

59

Issue

9

fYear

2011

fDate

9/1/2011 12:00:00 AM

Firstpage

2330

Lastpage

2336

Abstract

A new class of quasi-cyclic LDPC codes whose parity-check matrices are arrays of circulant permutation matrices constructed based on cyclic subgroups of finite fields is presented. This class of codes contains several known classes of algebraic quasi-cyclic LDPC codes as subclasses. Experimental results show that the codes constructed perform very well over the AWGN channel when decoded with iterative decoding based on belief propagation. This class of new QC-LDPC codes contains a subclass of codes which have large minimum distances. Combinatorial expressions for the ranks of the parity-check matrices of a subclass of codes constructed based on fields of characteristic two are given.

Keywords

AWGN channels; cyclic codes; iterative decoding; parity check codes; AWGN channel; belief propagation; circulantpermutation matrices; cyclic subgroups; finite fields; iterative decoding; parity-check matrices; quasi-cyclic LDPC codes; AWGN channels; Bit error rate; Decoding; Dispersion; Iterative decoding; Null space; Quasi-cyclic LDPC code; array; circulant permutation matrix; cyclic subgroups; finite field; rank; row-column constrained matrix;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2011.060911.100208

Filename

5910110