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

Article, Preprint English OPEN
Pumpluen, Susanne ; Steele, Andrew (2015)
  • Publisher: American Institute of Mathematical Sciences
  • Related identifiers: doi: 10.3934/amc.2015.9.449
  • Subject: Computer Science - Information Theory | 17A35, 94B05
    arxiv: Computer Science::Information Theory

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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