Natural orders for asymmetric space–time coding: minimizing the discriminant

Amaro Barreal*, Capi Corrales Rodrigáñez, Camilla Hollanti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Algebraic space–time coding—a powerful technique developed in the context of multiple-input multiple-output (MIMO) wireless communications—has profited tremendously from tools from Class Field Theory and, more concretely, the theory of central simple algebras and their orders. During the last decade, the study of space–time codes for practical applications, and more recently for future generation (5G(Formula presented.)) wireless systems, has provided a practical motivation for the consideration of many interesting mathematical problems. One such problem is the explicit computation of orders of central simple algebras with small discriminants. In this article, we consider the most interesting asymmetric MIMO channel setups and, for each treated case, we provide explicit pairs of fields and a corresponding non-norm element giving rise to a cyclic division algebra whose natural order has the minimum possible discriminant.

Original languageEnglish
Pages (from-to)371–391
JournalAPPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
Volume29
Issue number5
DOIs
Publication statusPublished - Nov 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Central simple algebras
  • Discriminant
  • Division algebras
  • MIMO
  • Natural orders
  • Space–time coding

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