On the minimum distance of low-density parity-check codes with parity-check matrices constructed from permutation matrices
A Sridharan, M Lentmaier, DV Truhachev… - Problems of Information …, 2005 - Springer
A Sridharan, M Lentmaier, DV Truhachev, DJ Costello Jr, KS Zigangirov
Problems of Information Transmission, 2005•SpringerAn 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].
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].
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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