CYCLIC DIVISION ALGEBRAS IN SPACE-TIME CODING: A BRIEF OVERVIEW

This paper aims at giving an introduction on space-time (ST) coding and on how cyclic division algebras (CDAs) fit into the picture. First, we describe the typical radio transmission model and then proceed to the notion of space-time coding and further on to multiple-input multiple-output (MIMO) channels. Cyclic division algebras provide us with a useful tool for,designing codes for MIMO channels. The theory of their noncommutative orders allows us to build denser lattices, i.e. to pack more codewords in a given signal space. Finally, we establish a congenial connection between the density and the discriminant of an order. The theory is supported by illuminating examples. The material presented here is mainly reviewed from our (Vehkalahti-Hollanti-Lahtonen-Ranto) recent submission "On the densest MIMO lattices from cyclic division algebras" [1].