The nonassociative algebras used to build fast-decodable space-time block codes - Pumpluen, Susanne; Steele, Andrew (American Institute of Mathematical Sciences, 2015)
Let K/F and K/L be two cyclic Galois field extensions and D a cyclic algebra. Given an invertible element d in D, we present three families of unital nonassociative algebras defined on the direct sum of n copies of D. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors. We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-m for nm transmit and m receive antennas. We present a DMT-optimal rate-3 code for 6 transmit and 3 receive antennas which is fast-decodable, with ML-decoding complexity at most O(M^15).