The Necessary and Sufficient Condition of a Class of Quasi-Cyclic LDPC Codes without Girth Four

Ying ZHAO  Yang XIAO  

IEICE TRANSACTIONS on Communications   Vol.E92-B   No.1   pp.306-309
Publication Date: 2009/01/01
Online ISSN: 1745-1345
DOI: 10.1587/transcom.E92.B.306
Print ISSN: 0916-8516
Type of Manuscript: LETTER
Category: Fundamental Theories for Communications
low-density parity-check codes,  quasi-cyclic codes,  circulant matrices,  girth,  

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This letter presents a necessary and sufficient condition for a class of quasi-cyclic low-density parity-check (QC LDPC) codes without girth four. Girth-four property of a class of QC LDPC codes is investigated. Good QC LDPC codes without girth four can be constructed by selecting proper shifting factors according to the proposed theorems. Examples are provided to verify the theorems. The simulation results show that the QC LDPC codes without girth four achieve a better BER performance compared with that of randomly constructed LDPC codes.