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

Volume

56

Issue

6

fYear

2010

fDate

6/1/2010 12:00:00 AM

Firstpage

2626

Lastpage

2639

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 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.

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;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2010.2046203

Filename

5466541