Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II
Shashi Kiran Chilappagari, Dung Viet Nguyen, Bane V. Vasic, Michael W. Marcellin · IEEE Transactions on Information Theory · 2010
The relation between the girth and the error correction capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girthg¿ 10 can correct all error patterns with up to(g/2-1) errors in at mostg/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girthg¿ 8, it is shown that girth alone cannot guarantee correction of all error patterns with up to(g/2-1) errors under the Gallager A algorithm. Sufficient conditions to correct(g/2-1) errors are then established by studying trapping sets.