This article is cited in 19 papers

Coding Theory

On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices

A. Sridharan^a, M. Lentmaier^b, D. V. Trukhachev^c, D. J. Costello^a, K. Sh. Zigangirov<sup>da

a</sup> University of Notre Dame
^b Institute of Communications and Navigation, German Aerospace Center
^c University of Alberta
^d Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: An ensemble of codes defined by parity-check matrices composed of $M\times M$ 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 $M\to\infty$, 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].

UDC: 621.391.15:519

Received: 20.07.2004
Revised: 28.10.2004

 English version: Problems of Information Transmission, 2005, 41:1, 33–44

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