Title :
Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II
Author :
Chilappagari, Shashi Kiran ; Nguyen, Dung Viet ; Vasic, Bane ; Marcellin, Michael W.
Author_Institution :
Marvell Semicond., Inc., Santa Clara, CA, USA
fDate :
6/1/2010 12:00:00 AM
Abstract :
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.
Keywords :
error correction codes; graph theory; iterative methods; parity check codes; set theory; Gallager A algorithm; Tanner graph; column-weight-three LDPC codes; error correction capability; girth; iterations; trapping sets; Error analysis; Error correction; Error correction codes; Information theory; Maximum likelihood decoding; Message passing; Parity check codes; Semiconductor materials; Sufficient conditions; Tree graphs; Error floor; Gallager A algorithm; girth; low-density parity-check (LDPC) codes; trapping sets;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2046203
