A Noncommutative Analogue of the Odlyzko Bounds and Bounds on Performance for Space-Time Lattice Codes

Benjamin Linowitz, Matthew Satriano, Roope Vehkalahti

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

This paper considers space-time coding over several independently Rayleigh faded blocks. In particular, we will concentrate on giving upper bounds for the coding gain of lattice space-time codes as the number of blocks grow. This problem was previously considered in the single antenna case by Bayer-Fluckiger et al. in 2006. Crucial to their work was Odlyzko's bound on the discriminant of an algebraic number field, as this provides an upper bound for the normalized coding gain of number field codes. In the MIMO context natural codes are constructed from division algebras defined over number fields and the coding gain is measured by the discriminant of the corresponding (noncommutative) algebra. In this paper, we will develop analogues of the Odlyzko bounds in this context and show how these bounds limit the normalized coding gain of a very general family of division algebra based space-time codes. These bounds can also be used as benchmarks in practical code design and as tools to analyze asymptotic bounds of performance as the number of independently faded blocks increases.

Original languageEnglish
Article number7047898
Pages (from-to)1971-1984
Number of pages14
JournalIEEE Transactions on Information Theory
Volume61
Issue number4
DOIs
Publication statusPublished - 1 Apr 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • algebra
  • fading
  • MIMO
  • Space-time codes

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