Successive refinement of ISI channels with single degree of freedom

Rate and diversity impose a fundamental trade-off in communications. This tradeoff was investigated for Intersymbol Interference (ISI) channels in [7]. A different point of view was explored in [4] 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 the application to single input single output (SISO) and single input multiple output (SIMO) channels was explored in [2]. In this paper we extend the results in [2] for channels with single degree of freedom. We characterize the rate tuples achievable for these channels through particular coding strategies. The main result of this paper is that the diversity multiplexing tradeoff for fading MISO/SIMO ISI channels is indeed successively refinable. This implies that for fading ISI channels with single degree of freedom 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 as well as a coding scheme to take advantage of this observation.