Rank Distance Codes for ISI channels

Designs for transmit alphabet constrained space-time codes naturally lead to questions about the design of rank distance codes. Recently, diversity embedded multi-level space-time codes for flat fading channels have been designed by using sets of binary matrices with rank distance guarantees over the binary field and mapping them onto QAM and PSK constellations. In this paper we give the design of diversity embedded space-time codes for fading Inter-Symbol Interference (ISI) channels with provable rank distance guarantees. In the process of doing so we also get a (asymptotic) characterization of the rate-diversity trade-off for multiple antenna fading ISI channels when there is a fixed transmit alphabet constraint. The key idea is to construct and analyze properties of binary matrices with the particular structure induced by ISI channels.