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

Haiyang LIU  Gang DENG  Jie CHEN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.11   pp.2236-2246
Publication Date: 2014/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.2236
Type of Manuscript: PAPER
Category: Coding Theory
low-density parity-check (LDPC) code,  array code,  minimum-weight codeword,  cyclic shift closure,  

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In this paper, we investigate the minimum-weight codewords of array LDPC codes C(m,q), where q is an odd prime and mq. 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).