Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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

Sridharan, Arvind ; Lentmaier, Michael LU ; Truhachev, Dmitri ; Costello Jr., Daniel J. and Zigangirov, Kamil LU (2005) In Problems of Information Transmission 41(1). p.33-44
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].
Please use this url to cite or link to this publication:
author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
LDPC codes
in
Problems of Information Transmission
volume
41
issue
1
pages
33 - 44
publisher
Pleiades Publishing
external identifiers
  • scopus:24944536959
ISSN
0032-9460
DOI
10.1007/s11122-005-0008-4
language
English
LU publication?
yes
id
28d49fd9-73c7-4223-9856-c3a5be06df30 (old id 3731714)
date added to LUP
2016-04-04 09:24:40
date last changed
2025-10-14 11:27:48
@article{28d49fd9-73c7-4223-9856-c3a5be06df30,
  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].}},
  author       = {{Sridharan, Arvind and Lentmaier, Michael and Truhachev, Dmitri and Costello Jr., Daniel J. and Zigangirov, Kamil}},
  issn         = {{0032-9460}},
  keywords     = {{LDPC codes}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{33--44}},
  publisher    = {{Pleiades Publishing}},
  series       = {{Problems of Information Transmission}},
  title        = {{On the minimum distance of codes with parity-check matrices constructed from permutation matrices}},
  url          = {{http://dx.doi.org/10.1007/s11122-005-0008-4}},
  doi          = {{10.1007/s11122-005-0008-4}},
  volume       = {{41}},
  year         = {{2005}},
}