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

Sridharan, A. and Lentmaier, M. and Truhachev, D. and Costello Jr., D. and Zigangirov, K. Sh. (2005) On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices. Problems of Information Transmission, Vol. 41 (No. 1), pp. 33-44.

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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 [Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963]. 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.

Item URL in elib:https://elib.dlr.de/19168/
Document Type:Article
Additional Information: LIDO-Berichtsjahr=2005,
Title:On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Sridharan, A.UNSPECIFIEDUNSPECIFIED
Lentmaier, M.UNSPECIFIEDUNSPECIFIED
Truhachev, D.UNSPECIFIEDUNSPECIFIED
Costello Jr., D.UNSPECIFIEDUNSPECIFIED
Zigangirov, K. Sh.UNSPECIFIEDUNSPECIFIED
Date:2005
Journal or Publication Title:Problems of Information Transmission
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:Yes
Volume:Vol. 41
Page Range:pp. 33-44
Status:Published
Keywords:Channel Coding, Parity-Check, Low-Density
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W KN - Kommunikation/Navigation
DLR - Research area:Space
DLR - Program:W KN - Kommunikation/Navigation
DLR - Research theme (Project):UNSPECIFIED
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation
Deposited By: DLR-Beauftragter, elib
Deposited On:09 Oct 2005
Last Modified:14 Jan 2010 20:01

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