Smallest Size of Circulant Matrix for Regular (3, L) and (4, L) Quasi-Cyclic LDPC Codes with Girth 6

Manabu HAGIWARA  Marc P.C. FOSSORIER  Takashi KITAGAWA  Hideki IMAI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.11   pp.2891-2894
Publication Date: 2009/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.2891
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
LDPC codes,  difference matrix,  quasi-cyclic codes,  regular LDPC codes,  circulant matrix,  lower bounds,  

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Summary: 
In this paper, we investigate the smallest value of p for which a (J,L,p)-QC LDPC code with girth 6 exists for J=3 and J=4. For J=3, we determine the smallest value of p for any L. For J=4, we determine the smallest value of p for L ≤ 301. Furthermore we provide examples of specific constructions meeting these smallest values of p.