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

Susanne Pumplün; Andrew  Steele

doi:10.3934/amc.2015.9.449

Article Contents

2015, Volume 9, Issue 4: 449-469. Doi: 10.3934/amc.2015.9.449

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

Susanne Pumplün^1, and
Andrew Steele^2,

1.
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD
2.
Flat 203, Wilson Tower, 16 Christian Street, London E1 1AW

Received: March 2014

Revised: November 2014

Published: November 2015

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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 $\mathcal{O}(M^{15})$.

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Mathematics Subject Classification: Primary: 17A35, 94B05.

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