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Pseudocodeword-free criterion for codes with cycle-free Tanner graph

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Abstract

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.

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Acknowledgements

The author wishes to thank Gretchen L. Matthews for her support while the author is at Clemson University, Patanee Udomkavanich for her advice, and the anonymous reviewers for their helpful suggestions and comments. This work is supported by the Thailand Research Fund under Grant TRG5880116 and the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, 10400, Thailand

    Wittawat Kositwattanarerk

  2. Centre of Excellence in Mathematics, The Commission on Higher Education, Si Ayutthaya RD., Bangkok, 10400, Thailand

    Wittawat Kositwattanarerk

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  1. Wittawat Kositwattanarerk
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Correspondence to Wittawat Kositwattanarerk.

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Communicated by T. Etzion.

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Kositwattanarerk, W. Pseudocodeword-free criterion for codes with cycle-free Tanner graph. Des. Codes Cryptogr. 86, 2791–2805 (2018). https://doi.org/10.1007/s10623-018-0476-3

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  • DOI: https://doi.org/10.1007/s10623-018-0476-3

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