Fast–decodable MIDO codes from non–associative algebras

By defining a multiplication on a direct sum of n copies of a given cyclic division algebra, we obtain new unital non–associative algebras. We employ their left multiplication to construct rate–n and rate–2 fully diverse fast ML–decodable space–time block codes for a Multiple–Input–Double–Output (MIDO) system. We give examples of fully diverse rate–2 4 × 2, 6 × 2, 8 × 2 and 12 × 2 space–time block codes and of a rate–3 6 × 2 code. All are fast ML–decodable. Our approach generalises the iterated codes in Markin and Oggier.