  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 from
sets of binary matrices with rank distance guarantees over the binary field by
mapping them onto QAM and PSK constellations. In this paper we demonstrate that
diversity embedded space-time codes for fading Inter-Symbol Interference (ISI)
channels can be designed with provable rank distance guarantees. As a corollary
we obtain an asymptotic characterization of the fixed transmit alphabet
rate-diversity trade-off for multiple antenna fading ISI channels. The key idea
is to construct and analyze properties of binary matrices with a particular
structure induced by ISI channels.
