  Rate and diversity impose a fundamental tradeoff in communications. This
tradeoff was investigated for Intersymbol Interference (ISI) channels in [4]. A
different point of view was explored in [1] where high-rate codes were designed
so that they have a high-diversity code embedded within them. Such diversity
embedded codes were investigated for flat fading channels and in this paper we
explore its application to ISI channels. In particular, we investigate the rate
tuples achievable for diversity embedded codes for scalar ISI channels through
particular coding strategies. The main result of this paper is that the
diversity multiplexing tradeoff for fading ISI channels is indeed successively
refinable. This implies that for fading single input single output (SISO) ISI
channels one can embed a high diversity code within a high rate code without
any performance loss (asymptotically). This is related to a deterministic
structural observation about the asymptotic behavior of frequency response of
channel with respect to fading strength of time domain taps.
