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arXiv:cs/0508085 · IEEE International Symposium on Information Theory (ISIT)

On the asymptotic performance of iterative decoders for product codes

M. Schwartz, Paul H. Siegel, Alexander Vardy

Published Jan 1, 2005• 23 citations
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Abstract

We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function of the error-correction capabilities of the row and column codes, the number of decoding rounds, and the channel erasure probability. We examine both the case of codes capable of correcting a constant amount of errors, and the case of codes capable of correcting a constant fraction of their length

DOI
10.1109/isit.2005.1523647

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Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.
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