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Error Correction Capability of Column-Weight-Three LDPC Codes (0710.3427v1)
Published 18 Oct 2007 in cs.IT and math.IT
Abstract: In 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 $\alpha>0, \exists N $ such that $\forall n>N$, no code in the ensemble of column-weight-three codes can correct all $\alpha n$ or fewer errors. We extend these results to the bit flipping algorithm.