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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 Â¿ 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 Â¿ 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.