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

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.