Error Correction Capability of Column-Weight-Three LDPC Codes

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dc.creatorChilappagari, Shashi Kiran
dc.creatorVasic, Bane
dc.date2007-10-18
dc.date.accessioned2026-07-07T08:37:00Z
dc.date.available2026-07-07T08:37:00Z
dc.descriptionIn this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct $k \geq 5$ errors is to avoid cycles of length up to $2k$ in its Tanner graph. As a consequence of this result, we show that given any $α>0, \exists N $ such that $\forall n>N$, no code in the ensemble of column-weight-three codes can correct all $αn$ or fewer errors. We extend these results to the bit flipping algorithm.
dc.description16 pages, 3 figures. Submitted to IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/0710.3427
dc.identifierhttp://arxiv.org/abs/0710.3427
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140259
dc.subjectInformation Theory
dc.titleError Correction Capability of Column-Weight-Three LDPC Codes
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