Advanced

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
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
Springer
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
2013-05-02 09:54:45
date last changed
2016-10-13 04:30:00
@misc{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},
  keyword      = {LDPC codes},
  language     = {eng},
  number       = {1},
  pages        = {33--44},
  publisher    = {ARRAY(0xb7ed528)},
  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},
  volume       = {41},
  year         = {2005},
}