Error correction capability of column-weight-three LDPC codes under the Gallager A algorithm-Part II

Authors:
Shashi Kiran Chilappagari;Dung Viet Nguyen;Bane Vasic;Michael W. Marcellin
Affiliations:
Marvell Semiconductor, Inc., Santa Clara, CA;Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ;Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ;Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ
Venue:
IEEE Transactions on Information Theory
Year:
2010

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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.