On Successive Refinement of Diversity for Fading ISI Channels

TL;DR

This paper demonstrates that the diversity multiplexing tradeoff 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 that the diversity multiplexing tradeoff for fading ISI channels is successively refinable, enabling embedded high-diversity codes within high-rate codes.

Findings

Diversity multiplexing tradeoff in fading ISI channels is successively refinable.

High-diversity codes can be embedded within high-rate codes without asymptotic performance loss.

Structural analysis of frequency response relates to fading strength of channel taps.

Abstract

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.