Optimal rate-diversity tradeoff STBCs from codes over arbitrary finite fields

A linear rank-distance code is a set of matrices over a finite field F_q, with the rank over Fq as a distance metric. A space-time block code (STBC) is a finite set of complex matrices with the rank over the complex field as a metric. Rank-distance codes over prime fields F_p have found applications as space-time codes. In this paper, we extend this result to arbitrary finite fields by providing an isomorphism from F_q (q = p^m) to a subset of the ring of integers of an appropriate number field. Using this map and a maximal rank-distance code over F_q, we construct STBC that achieve optimal rate-diversity tradeoff for any given diversity order. Simulation results confirm the diversity gain obtained using these codes.