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On the minimum distance of low-density parity-check codes with parity-check matrices constructed from permutation matrices

  • Coding Theory
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Abstract

An ensemble of codes defined by parity-check matrices composed of M × M permutation matrices is considered. This ensemble is a subensemble of the ensemble of low-density parity-check (LDPC) codes considered by Gallager [1]. We prove that, as M → ∞, the minimum distance of almost all codes in the ensemble grows linearly with M. We also show that in several cases the asymptotic minimum-distance-to-block-length ratio for almost all codes in the ensemble satisfies Gallager’s bound [1].

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REFERENCES

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Authors and Affiliations

  1. University of Notre Dame, Indiana, USA

    A. Sridharan, D. J. Costello Jr. & K. Sh. Zigangirov

  2. German Aerospace Center (DLR), Institute of Communications and Navigation, Wessling

    M. Lentmaier & K. Sh. Zigangirov

  3. University of Alberta, Edmonton, Canada

    D. V. Truhachev

Authors
  1. A. Sridharan
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  2. M. Lentmaier
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  3. D. V. Truhachev
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  4. D. J. Costello Jr.
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  5. K. Sh. Zigangirov
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Additional information

Translated from Problemy Peredachi Informatsii, No. 1, 2005, pp. 39–52.

Original Russian Text Copyright © 2005 by Sridharan, Lentmaier, Truhachev, Costello, Zigangirov.

Supported in part by the NSF, Grant CCR02-05310; NASA, Grant NAG5-12792; and the Indiana 21st Century Research and Technology Fund.

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Sridharan, A., Lentmaier, M., Truhachev, D.V. et al. On the minimum distance of low-density parity-check codes with parity-check matrices constructed from permutation matrices. Probl Inf Transm 41, 33–44 (2005). https://doi.org/10.1007/s11122-005-0008-4

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  • DOI: https://doi.org/10.1007/s11122-005-0008-4

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