A1 Refereed original research article in a scientific journal
Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra
Authors: Vehkalahti R, Lu HF, Luzzi L
Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication year: 2013
Journal: IEEE Transactions on Information Theory
Journal name in source: IEEE TRANSACTIONS ON INFORMATION THEORY
Journal acronym: IEEE T INFORM THEORY
Number in series: 9
Volume: 59
Issue: 9
First page : 6060
Last page: 6082
Number of pages: 23
ISSN: 0018-9448
DOI: https://doi.org/10.1109/TIT.2013.2266396
Abstract
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.
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.
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