Two Generalizations of the Rank-Distance Space-Time Code

Recently Lu and Kumar made use of binary, maximal rank-distance codes to construct space-time codes, which we shall term rank-distance space-time (RDST) codes, over PAM, QAM, and 2-PSK constellations which are optimal under the rate-diversity tradeoff. The RDST code can be regarded as being composed of layers with each layer or component, associated to a maximal-rank binary code. Two generalizations of the RDST code are presented here. In the first, the ranks of the binary codes in the different layers of the RDST code are allowed to vary and this is shown to improve the diversity-multiplexing gain tradeoff of the overall space-time code. In the second, we provide a construction for spacetime codes based on power-series expansion with respect to a prime ideal in a number field. An advantage of this approach is that it relates to a broad class of constellations. Special instances of this construction are shown to yield the RDST code as well as subsequent generalizations of the RDST code by Hammons and by Lu respectively.