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Low-density parity-check codes based on steiner systems and permutation matrices

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Abstract

An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    F. I. Ivanov & V. V. Zyablov

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  1. F. I. Ivanov
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  2. V. V. Zyablov
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Correspondence to F. I. Ivanov.

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Original Russian Text © F.I. Ivanov, V.V. Zyablov, 2013, published in Problemy Peredachi Informatsii, 2013, Vol. 49, No. 4, pp. 41–56.

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Ivanov, F.I., Zyablov, V.V. Low-density parity-check codes based on steiner systems and permutation matrices. Probl Inf Transm 49, 333–347 (2013). https://doi.org/10.1134/S0032946013040042

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