On the Gilbert-Varshamov distance of abelian group codes

Giacomo Como; Fabio Fagnani

doi:10.1109/ISIT.2007.4557182

On the Gilbert-Varshamov distance of abelian group codes

Giacomo Como, Fabio Fagnani

Department of Automatic Control

Polytechnic University of Turin

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

Abstract

The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of ℤ_m-linear codes are introduced and their typical minimum distance characterized in terms of the Gilbert-Varshamov distances associated to the subgroups of ℤ_m. For the AWGN channel with 8-PSK as input it is shown that the typical ℤ₈ -linear code achieves the Gilbert-Varshamov bound.

Original language	English
Title of host publication	Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007
Pages	2651-2655
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2007.4557182
Publication status	Published - 2007 Dec 1
Event	2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: 2007 Jun 24 → 2007 Jun 29

Conference

Conference	2007 IEEE International Symposium on Information Theory, ISIT 2007
Country/Territory	France
City	Nice
Period	2007/06/24 → 2007/06/29

Subject classification (UKÄ)

Control Engineering

Access to Document

10.1109/ISIT.2007.4557182

Cite this

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title = "On the Gilbert-Varshamov distance of abelian group codes",

abstract = "The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of ℤm-linear codes are introduced and their typical minimum distance characterized in terms of the Gilbert-Varshamov distances associated to the subgroups of ℤm. For the AWGN channel with 8-PSK as input it is shown that the typical ℤ8 -linear code achieves the Gilbert-Varshamov bound.",

author = "Giacomo Como and Fabio Fagnani",

year = "2007",

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doi = "10.1109/ISIT.2007.4557182",

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AU - Fagnani, Fabio

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N2 - The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of ℤm-linear codes are introduced and their typical minimum distance characterized in terms of the Gilbert-Varshamov distances associated to the subgroups of ℤm. For the AWGN channel with 8-PSK as input it is shown that the typical ℤ8 -linear code achieves the Gilbert-Varshamov bound.

AB - The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of ℤm-linear codes are introduced and their typical minimum distance characterized in terms of the Gilbert-Varshamov distances associated to the subgroups of ℤm. For the AWGN channel with 8-PSK as input it is shown that the typical ℤ8 -linear code achieves the Gilbert-Varshamov bound.

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U2 - 10.1109/ISIT.2007.4557182

DO - 10.1109/ISIT.2007.4557182

M3 - Paper in conference proceeding

AN - SCOPUS:51649099247

SN - 1424414296

SN - 9781424414291

SP - 2651

EP - 2655

BT - Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007

T2 - 2007 IEEE International Symposium on Information Theory, ISIT 2007

Y2 - 24 June 2007 through 29 June 2007

ER -

On the Gilbert-Varshamov distance of abelian group codes

Abstract

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