AffiliationUniv Arizona, Dept Elect & Comp Engn
Gallager A algorithm
low-density parity-check (LDPC) codes
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CitationS. K. Chilappagari and B. Vasic, "Error-Correction Capability of Column-Weight-Three LDPC Codes," in IEEE Transactions on Information Theory, vol. 55, no. 5, pp. 2055-2061, May 2009, doi: 10.1109/TIT.2009.2015990.
RightsCopyright © 2009 IEEE
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AbstractIn 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.
VersionFinal accepted manuscript