Explicit Constructions of Multi-Block Space-Time Codes That Achieve The Diversity-Multiplexing Tradeoff

Constructions of multi-block space-time coding schemes that are optimal with respect to the diversity-multiplexing tradeoff when coding is applied over any number of independent fading blocks are presented in this paper. The constructions are based on the left-regular representation of elements of some cyclic division algebra. In particular, the main construction applies to the case when the quasi-static fading interval equals the number of transmit antennas, and the resultant scheme is termed minimal delay multi-block space-time coding scheme. Variations of this construction corresponding to the cases of non-minimal delay are also provided. As the number of coded blocks approaches infinity, coding schemes derived from the proposed constructions can be used to provide a reliable MIMO communication with vanishing error probability