A4 Refereed article in a conference publication
Constructions a of lattices from number fields and division algebras
Authors: Roope Vehkalahti, Wittawat Kositwattanarerk, Frédérique Oggier
Conference name: IEEE International Symposium on Information Theory
Publisher: Institute of Electrical and Electronics Engineers Inc.
Publication year: 2014
Book title : Information Theory (ISIT), 2014 IEEE International Symposium on
Journal name in source: IEEE International Symposium on Information Theory - Proceedings
First page : 2326
Last page: 2330
Number of pages: 5
ISBN: 978-1-4799-5186-4
DOI: https://doi.org/10.1109/ISIT.2014.6875249
Web address : http://api.elsevier.com/content/abstract/scopus_id:84906536017
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. © 2014 IEEE.
