Ensembles of codes over Abelian groups

Giacomo Como, Fabio Fagnani

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

4 Citations (SciVal)

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.

Original languageEnglish
Title of host publicationProceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05
Pages1788-1792
Number of pages5
Volume2005
DOIs
Publication statusPublished - 2005 Dec 1
Event2005 IEEE International Symposium on Information Theory, ISIT 05 - Adelaide, Australia
Duration: 2005 Sep 42005 Sep 9

Conference

Conference2005 IEEE International Symposium on Information Theory, ISIT 05
Country/TerritoryAustralia
CityAdelaide
Period2005/09/042005/09/09

Subject classification (UKÄ)

  • Control Engineering

Keywords

  • Group codes
  • Low density parity check codes
  • M-PSK
  • Non-binary modulation

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