On the Minimum Weight of Simple Full-Length Array LDPC Codes

Kenji SUGIYAMA  Yuichi KAJI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.6   pp.1502-1508
Publication Date: 2008/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.6.1502
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
LDPC code,  simple full-length array LDPC code,  minimum weight,  minimum distance,  

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Summary: 
We investigate the minimum weights of simple full-length array LDPC codes (SFA-LDPC codes). The SFA-LDPC codes are a subclass of LDPC codes, and constructed algebraically according to two integer parameters p and j. Mittelholzer and Yang et al. have studied the minimum weights of SFA-LDPC codes, but the exact minimum weights of the codes are not known except for some small p and j. In this paper, we show that the minimum weights of the SFA-LDPC codes with j=4 and j=5 are upper-bounded by 10 and 12, respectively, independent from the prime number p. By combining the results with Yang's lower-bound limits, we can conclude that the minimum weights of the SFA-LDPC codes with j=4 and p>7 are exactly 10 and those of the SFA-LDPC codes with j=5 are 10 or 12.