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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
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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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