The nonassociative algebras used to build fast-decodable space-time block codes
S. Pumplün, Andrew Steele · Advances in Mathematics of Communications · 2015
Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,\sigma,c)$ a cyclic algebra. Given aninvertible element $d\in D$,we present three families of unital nonassociative algebras over $L\cap F$ definedon 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 codesin papersby 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 complexityat most $\mathcal{O}(M^{15})$.