On Successive Refinement of Diversity for Fading ISI Channels

Rate and diversity impose a fundamental trade-off in communications. This trade-off was investigated for flat-fading channels in as well as for Inter-symbol Interference (ISI) channels in . A different point of view was explored in where high-rate codes were designed so that they have a high-diversity code embedded within them. These diversity embedded codes were investigated for flat fading channels both from an information-theoretic viewpoint and from a coding theory viewpoint in . In this paper, we explore the use of diversity embedded codes for inter-symbol interference channels. In particular the main result of this paper is that the diversity multiplexing trade-off for fading MISO/SIMO/SISO ISI channels is indeed successively refinable. This implies that for fading ISI channels with a 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.