The Coding Gain of Real Matrix Lattices: Bounds and Existence Results

Roope Vehkalahti*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

The paper considers the question of the normalized minimum determinant (or asymptotic coding gain) of real matrix lattices. The coding theoretic motivation for such study arises, for example, from the questions considering multiple-input multiple-output (MIMO) ultra-wideband (UWB) transmission. At the beginning, totally general coding gain bounds for real MIMO lattice codes is given by translating the problem into geometric language. Then code lattices that are produced from division algebras are considered. By applying methods from the theory of central simple algebras, coding gain bounds for code lattices coming from orders of division algebras are given. Finally, it is proven that these bounds can be reached by using maximal orders. In the case of 2 x 2 matrix lattices, this existence result proves that the general geometric bound derived earlier can be reached.

Original languageEnglish
Pages (from-to)4359-4366
Number of pages8
JournalIEEE Transactions on Information Theory
Volume56
Issue number9
DOIs
Publication statusPublished - Sep 2010
MoE publication typeA1 Journal article-refereed

Keywords

  • Cyclic division algebras
  • mathematics
  • multiple-input multiple-output (MIMO) systems
  • space-time (ST) coding
  • ultra-wideband (UWB)
  • SPACE-TIME CODES
  • DIVISION-ALGEBRAS
  • DIVERSITY
  • CONSTRUCTION
  • TRADEOFF

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