On the Minimum-Weight Codewords of Array LDPC Codes with Column Weight 4

Abstract

In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and m ≤ q. Using some analytical approaches, the lower bound on the number of minimum-weight codewords of C(m,q) given by Kaji (IEEE Int. Symp. Inf. Theory, June/July 2009) is proven to be tight for m = 4 and q > 19. In other words, C(4,q) has 4q²(q-1) minimum-weight codewords for all q > 19. In addition, we show some interesting universal properties of the supports of generators of minimum-weight codewords of the code C(4,q)(q > 19).