Constructions of multi-block space-time coding schemes that are optimal with respect to the diversitymultiplexing 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.