Dense MIMO matrix lattices - A meeting point for class field theory and invariant theory

Jyrki Lahtonen*, Roope Vehkalahti

*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

The design of signal constellations for multi-antenna radio communications naturally leads to the problem of finding lattices of square complex matrices with a fixed minimum squared determinant. Since [5] cyclic division algebras, their orders and related structures have become standard material for researchers seeking to construct good MIMO-lattices. In recent submissions [3], [8] we studied the problem of identifying those cyclic division algebras that have the densest possible maximal orders. That approach was based on the machinery of Hasse invariants from class field theory for classifying the cyclic division algebras. Here we will recap the resulting lower bound from [3], preview the elementary upper bounds from [4] and compare these with some suggested constructions. As the lattices of the shape Es are known to be the densest (with respect to the usual Euclidean metric) in an 8-dimensional space it is natural to take a closer look at lattices of 2×2 complex matrices of that shape. We derive a much tighter upper bound to the minimum determinant of such lattices using the theory of invariants.

Original languageEnglish
Title of host publicationApplied Algebra, Algebraic Algorithms and Error-Correcting Codes - 17th International Symposium, AAECC- 17, Proceedings
Pages247-256
Number of pages10
DOIs
Publication statusPublished - 1 Dec 2007
MoE publication typeA4 Article in a conference publication
EventInternational Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - Bangalore, India
Duration: 16 Dec 200720 Dec 2007
Conference number: 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4851 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Abbreviated titleAAECC
CountryIndia
CityBangalore
Period16/12/200720/12/2007

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