Division algebra codes achieve MIMO block fading channel capacity within a constant gap

Laura Luzzi*, Roope Vehkalahti

*Corresponding author for this work

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

2 Citations (Scopus)


This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. In contrast to the standard approach in the literature which employs random lattice ensembles, the existence results in this paper are derived from number theory. It is shown that a multiblock construction based on division algebras achieves rates within a constant gap from block fading capacity both under maximum likelihood decoding and naive lattice decoding. First the gap to capacity is shown to depend on the discriminant of the chosen division algebra; then class field theory is applied to build families of algebras with small discriminants. The key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants.

Original languageEnglish
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
Number of pages5
ISBN (Electronic)978-146737704-1
Publication statusPublished - 2015
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Information Theory - Hong Kong, China
Duration: 14 Jun 201519 Jun 2015

Publication series

NameIEEE International Symposium on Information Theory
ISSN (Electronic)2157-8095


ConferenceIEEE International Symposium on Information Theory
Abbreviated titleISIT
CityHong Kong


  • MIMO
  • block fading
  • number theory
  • division algebras

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