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Graph-based convolutional and block LDPC codes

  • Coding Theory
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Abstract

We consider regular block and convolutional LDPC codes determined by paritycheck matrices with rows of a fixed weight and columns of weight 2. Such codes can be described by graphs, and the minimum distance of a code coincides with the girth of the corresponding graph. We consider a description of such codes in the form of tail-biting convolutional codes. Long codes are constructed from short ones using the “voltage graph” method. On this way we construct new codes, find a compact description for many known optimal codes, and thus simplify the coding for such codes. We obtain an asymptotic lower bound on the girth of the corresponding graphs. We also present tables of codes.

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Authors and Affiliations

  1. St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

    I. E. Bocharova, B. D. Kudryashov & R. V. Satyukov

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  1. I. E. Bocharova
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  2. B. D. Kudryashov
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  3. R. V. Satyukov
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Correspondence to I. E. Bocharova.

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Original Russian Text © I.E. Bocharova, B.D. Kudryashov, R.V. Satyukov, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 4, pp. 69–90.

Supported in part by the Royal Swedish Academy of Sciences and the Russian Academy of Sciences, grant no. 621-2007-6281.

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Bocharova, I.E., Kudryashov, B.D. & Satyukov, R.V. Graph-based convolutional and block LDPC codes. Probl Inf Transm 45, 357–377 (2009). https://doi.org/10.1134/S0032946009040061

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