Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II

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 girth
g
¿ 10 can correct all error patterns with up to
(g
/2-1) errors in at most
g
/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth
g
¿ 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.