Constructions A of Lattices from Number Fields and Division Algebras

Roope Vehkalahti*, Wittawat Kositwattanarerk, Frederique Oggier

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

3 Citations (Scopus)

Abstract

There is a rich theory of relations between lattices and linear codes over finite fields. However, this theory has been developed mostly with lattice codes for the Gaussian channel in mind. In particular, different versions of what is called Construction A have connected the Hamming distance of the linear code to the Euclidean structure of the lattice.

This paper concentrates on developing a similar theory, but for fading channel coding instead. First, two versions of Construction A from number fields are given. These are then extended to division algebra lattices. Instead of the Euclidean distance, the Hamming distance of the finite codes is connected to the product distance of the resulting lattices, that is the minimum product distance and the minimum determinant respectively.

Original languageEnglish
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
PublisherIEEE
Pages2326-2330
Number of pages5
ISBN (Electronic)978-147995186-4
DOIs
Publication statusPublished - 2014
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Information Theory - Honolulu, United States
Duration: 29 Jun 20144 Jul 2014

Publication series

NameIEEE International Symposium on Information Theory
PublisherIEEE
ISSN (Electronic)2157-8095

Conference

ConferenceIEEE International Symposium on Information Theory
Abbreviated titleISIT
CountryUnited States
CityHonolulu
Period29/06/201404/07/2014

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