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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.

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author
and
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
article number
1523653
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
2022-01-31 22:50:28
@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}},
  booktitle    = {{Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05}},
  isbn         = {{0780391519}},
  keywords     = {{Group codes; Low density parity check codes; M-PSK; Non-binary modulation}},
  language     = {{eng}},
  month        = {{12}},
  pages        = {{1788--1792}},
  title        = {{Ensembles of codes over Abelian groups}},
  url          = {{http://dx.doi.org/10.1109/ISIT.2005.1523653}},
  doi          = {{10.1109/ISIT.2005.1523653}},
  volume       = {{2005}},
  year         = {{2005}},
}