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Error-Correction Capability of Column-Weight-Three LDPC Codes

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2 Author(s)
Chilappagari, S.K. ; Dept. of Electr. & Comput. Eng., Univ. of Arizona, Tucson, AZ ; Vasic, B.

In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ges 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any alpha > 0, exist N such that forall n > N, no code in the ensemble of column-weight-three codes can correct all alphan or fewer errors. The results are extended to the bit flipping algorithms.

Published in:

Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 5 )

Date of Publication:

May 2009

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