On successive refinement of diversity for fading ISI channels

TL;DR

This paper demonstrates that the diversity multiplexing trade-off in fading ISI channels can be successively refined, allowing high-diversity codes to be embedded within high-rate codes without performance loss.

Contribution

It proves the successively refinable nature of the diversity multiplexing trade-off for fading ISI channels and introduces a coding scheme leveraging this property.

Findings

Successive refinement of diversity multiplexing trade-off in ISI channels

Embedding high-diversity codes within high-rate codes is asymptotically lossless

Structural analysis of frequency response behavior under fading

Abstract

Rate and diversity impose a fundamental trade-off in communications. This trade-off was investigated for flat-fading channels in [15] as well as for Inter-symbol Interference (ISI) channels in [1]. A different point of view was explored in [12] 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 [5] and from a coding theory viewpoint in [2]. 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.