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Ensembles of codes over Abelian groups

Como, Giacomo LU and Fagnani, Fabio (2005) 2005 IEEE International Symposium on Information Theory, ISIT 05 2005. p.1788-1792
Abstract

In this paper we study ensembles of Abelian group codes on symmetric channels. Our main example is the AWGN channel where the inputs are restricted to a GU constellation admitting ℤm as a generating group. For codes which are ℤm-free modules, we prove a sort of Shannon theorem which exactly characterizes which are the rates for which reliable transmission is possible. In particular we prove that for the 2r- PSK constellation, group codes over ℤ2r do achieve Shannon capacity. Finally, we study the performance of low density ℤm- codes and we prove average convergence rate of their word error probability.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Group codes, Low density parity check codes, M-PSK, Non-binary modulation
host publication
Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05
volume
2005
pages
5 pages
conference name
2005 IEEE International Symposium on Information Theory, ISIT 05
conference location
Adelaide, Australia
conference dates
2005-09-04 - 2005-09-09
external identifiers
  • scopus:33749441788
ISBN
0780391519
9780780391512
DOI
10.1109/ISIT.2005.1523653
language
English
LU publication?
yes
id
b9c10962-dcc6-481d-affe-41d535e44d7e
date added to LUP
2019-06-29 15:56:47
date last changed
2019-08-16 14:00:17
@inproceedings{b9c10962-dcc6-481d-affe-41d535e44d7e,
  abstract     = {<p>In this paper we study ensembles of Abelian group codes on symmetric channels. Our main example is the AWGN channel where the inputs are restricted to a GU constellation admitting ℤ<sub>m</sub> as a generating group. For codes which are ℤ<sub>m</sub>-free modules, we prove a sort of Shannon theorem which exactly characterizes which are the rates for which reliable transmission is possible. In particular we prove that for the 2<sup>r</sup>- PSK constellation, group codes over ℤ<sub>2r</sub> do achieve Shannon capacity. Finally, we study the performance of low density ℤ<sub>m</sub>- codes and we prove average convergence rate of their word error probability.</p>},
  author       = {Como, Giacomo and Fagnani, Fabio},
  isbn         = {0780391519},
  keyword      = {Group codes,Low density parity check codes,M-PSK,Non-binary modulation},
  language     = {eng},
  location     = {Adelaide, Australia},
  month        = {12},
  pages        = {1788--1792},
  title        = {Ensembles of codes over Abelian groups},
  url          = {http://dx.doi.org/10.1109/ISIT.2005.1523653},
  volume       = {2005},
  year         = {2005},
}