Improved low-density parity-check codes using irregular graphs

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Improved low-density parity-check codes using irregular graphs (2001)

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by Michael G. Luby , Michael Mitzenmacher , M. Amin Shokrollahi , Daniel A. Spielman

Venue:	IEEE Trans. Inform. Theory
Citations:	223 - 15 self

BibTeX

@ARTICLE{Luby01improvedlow-density,
    author = {Michael G. Luby and Michael Mitzenmacher and M. Amin Shokrollahi and Daniel A. Spielman},
    title = {Improved low-density parity-check codes using irregular graphs},
    journal = {IEEE Trans. Inform. Theory},
    year = {2001},
    volume = {47},
    pages = {585--598}
}

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Abstract

Abstract—We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes. We improve on Gallager’s results by introducing irregular parity-check matrices and a new rigorous analysis of hard-decision decoding of these codes. We also provide efficient methods for finding good irregular structures for such decoding algorithms. Our rigorous analysis based on martingales, our methodology for constructing good irregular codes, and the demonstration that irregular structure improves performance constitute key points of our contribution. We also consider irregular codes under belief propagation. We report the results of experiments testing the efficacy of irregular codes on both binary-symmetric and Gaussian channels. For example, using belief propagation, for rate I R codes on 16 000 bits over a binary-symmetric channel, previous low-density parity-check codes can correct up to approximately 16 % errors, while our codes correct over 17%. In some cases our results come very close to reported results for turbo codes, suggesting that variations of irregular low density parity-check codes may be able to match or beat turbo code performance. Index Terms—Belief propagation, concentration theorem, Gallager codes, irregular codes, low-density parity-check codes.

Keyphrases

low-density parity-check code irregular code irregular graph belief propagation decoding algorithm irregular low density parity-check code concentration theorem gaussian channel error-correcting code hard-decision decoding turbo code performance binary-symmetric channel irregular structure new family good irregular structure efficient method previous low-density parity-check code gallager low-density parity-check code rigorous analysis gallager result turbo code good irregular code index term belief propagation performance constitute key point new rigorous analysis irregular parity-check matrix

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