The nonassociative algebras used to build fast-decodable space-time block codes

Abstract

Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,\sigma ,c)$ a cyclic algebra. Given an invertible element $d\in D$, we present three families of unital nonassociative algebras over $L\cap F$ 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 $\mathcal{O}(M^{15})$.

Final version, to appear in Advances in Mathematics of Communications. Contains updated contact details for second author

References in corpus (1)

• Tensor products of nonassociative cyclic algebras

Cited by in corpus (6)

• Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma ,\delta )$-codes
• Nonassociative cyclic extensions of fields and central simple algebras
• Tensor products of nonassociative cyclic algebras
• How to obtain lattices from (f,sigma,delta)-codes via a generalization of Construction A
• The automorphisms of Petit's algebras
• Quotients of orders in algebras obtained from skew polynomials with applications to coding theory