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

doi:10.1587/transfun.E92.A.2891

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Online ISSN : 1745-1337
Print ISSN : 0916-8508

Regular Section

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

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Keywords: LDPC codes, difference matrix, quasi-cyclic codes, regular LDPC codes, circulant matrix, lower bounds

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2009 Volume E92.A Issue 11 Pages 2891-2894

DOI https://doi.org/10.1587/transfun.E92.A.2891

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Abstract

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.

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