Ensembles of codes over Abelian groups
(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:
https://lup.lub.lu.se/record/b9c10962-dcc6-481d-affe-41d535e44d7e
- author
- Como, Giacomo LU and Fagnani, Fabio
- organization
- publishing date
- 2005-12-01
- 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}}, }