Inverse Determinant Sums and Connections Between Fading Channel Information Theory and Algebra

R. Vehkalahti, Hsiao-Feng Lu, L. Luzzi
2013 IEEE Transactions on Information Theory  
This work concentrates on the study of 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 trade-off is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is
more » ... etely 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 trade-off and point counting in Lie groups.
doi:10.1109/tit.2013.2266396 fatcat:usnadpzeafewvekyc227qve4iy