Towards a complete DMT classification of division algebra codes

Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

1 Citation (Scopus)
221 Downloads (Pure)

Abstract

This work aims at providing new lower bounds for the diversity-multiplexing gain trade-off of a general class of lattice codes based on division algebras. In the low multiplexing gain regime, some bounds were previously obtained from the high signal-to-noise ratio estimate of the union bound for the pairwise error probabilities. Here these results are extended to cover a larger range of multiplexing gains. The improvement is achieved by using ergodic theory in Lie groups to estimate the behavior of the sum arising from the union bound. In particular, the new bounds for lattice codes derived from Q-central division algebras suggest that these codes can be divided into two classes based on their Hasse invariants at the infinite places. Algebras with ramification at the infinite place seem to provide a better diversity-multiplexing gain trade-off.
Original languageEnglish
Title of host publication2016 IEEE International Symposium on Information Theory (ISIT 2016)
Subtitle of host publicationProceedings of a meeting held 10-15 July 2016, Barcelona, Spain
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages2993-2997
Number of pages5
ISBN (Electronic)9781509018062
ISBN (Print)9781509018079
DOIs
Publication statusPublished - Sep 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: 10 Jul 201615 Jul 2016

Publication series

NameProceedings of the IEEE International Symposium on Information Theory (ISIT)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
ISSN (Print)2157-8117

Conference

Conference2016 IEEE International Symposium on Information Theory, ISIT 2016
CountrySpain
CityBarcelona
Period10/07/1615/07/16

Keywords

  • cs.IT
  • math.IT
  • math.NT

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