Inverse determinant sums and connections between fading channel information theory and algebra

Roope Vehkalahti, Hsiao-Feng Lu, Laura Luzzi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This work considers inverse determinant sums, which arise from the union bound on the error probability, as a tool for designing and analyzing algebraic space-time block codes. A general framework to study these sums is established, and the connection between asymptotic growth of inverse determinant sums and the diversity-multiplexing gain tradeoff is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growth of the unit group. This reduces the inverse determinant sum analysis to studying certain asymptotic integrals in Lie groups. Using recent methods from ergodic theory, a complete classification of the inverse determinant sums of the most well-known algebraic space-time codes is provided. The approach reveals an interesting and tight relation between diversity-multiplexing gain tradeoff and point counting in Lie groups.

Original languageEnglish
Article number6523963
Pages (from-to)6060-6082
Number of pages23
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 5 Sep 2013


  • Algebra
  • Lie groups
  • Zeta functions
  • diversity-multiplexing gain tradeoff (DMT)
  • division algebra
  • multiple-input multiple-output (MIMO)
  • number theory
  • space-time block codes (STBCs)
  • unit group


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