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Girth of the Tanner graph and error correction capability of LDPC codes

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4 Author(s)
Chilappagari, S.K. ; Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ ; Nguyen, D.V. ; Vasić, B. ; Marcellin, M.W.

We investigate the relation between the girth and the guaranteed error correction capability of gamma-left regular LDPC codes. For column-weight-three codes, we give upper and lower bounds on the number of errors correctable by the Gallager A algorithm. For higher column weight codes, we find the number of variable nodes which are guaranteed to expand by a factor of at least 3gamma/4, hence giving a lower bound on the guaranteed correction capability under the bit flipping (serial and parallel) algorithms. We also establish upper bounds by studying the sizes of smallest possible trapping sets.

Published in:

Communication, Control, and Computing, 2008 46th Annual Allerton Conference on

Date of Conference:

23-26 Sept. 2008

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