On the Densest MIMO Lattices From Cyclic Division Algebras

Roope Vehkalahti*, Camilla Hollanti, Jyrki Lahtonen, Kalle Ranto

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

43 Citations (Scopus)

Abstract

It is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant. Using results from class field theory, a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas) is derived. Also numerous examples of division algebras achieving the bound are given. For example, a matrix lattice with quadrature amplitude modulation (QAM) coefficients that has 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant is constructed. Also, a general algorithm due to Ivanyos and Ronyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed. Also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed.

Original languageEnglish
Pages (from-to)3751-3780
Number of pages30
JournalIEEE Transactions on Information Theory
Volume55
Issue number8
DOIs
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed
EventIEEE International Symposium on Information Theory - Seattle, United States
Duration: 9 Jul 200614 Jul 2006

Keywords

  • Cyclic division algebras (CDAs)
  • dense lattices
  • discriminants
  • Hasse invariants
  • maximal orders
  • multiple-input multiple-output (MIMO) channels
  • multiplexing
  • space-time block codes (STBCs)
  • SPACE-TIME CODES
  • BLOCK-CODES
  • MAXIMAL-ORDERS
  • PERFECT SPACE
  • DIVERSITY
  • CONSTRUCTION
  • PERFORMANCE
  • TRADEOFF
  • ANTENNAS
  • NUMBER

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