Duality Bounds on the Cut-Off Rate with Applications to Ricean Fading

TL;DR

This paper derives upper bounds on the cut-off rate for Ricean fading channels, revealing how the gap between capacity and cut-off rate behaves at high SNR and the impact of side information on these bounds.

Contribution

It introduces a new technique for bounding the cut-off rate and applies it to Ricean fading channels, providing high SNR expansions and analyzing side information effects.

Findings

High SNR gap between capacity and cut-off rate approaches a finite limit.

The gap is approximately 0.26 nats for Rayleigh fading and 0.39 nats for large specular components.

Side information at the receiver is less efficiently utilized by the cut-off rate than by capacity.

Abstract

We propose a technique to derive upper bounds on Gallager's cost-constrained random coding exponent function. Applying this technique to the non-coherent peak-power or average-power limited discrete time memoryless Ricean fading channel, we obtain the high signal-to-noise ratio (SNR) expansion of this channel's cut-off rate. At high SNR the gap between channel capacity and the cut-off rate approaches a finite limit. This limit is approximately 0.26 nats per channel-use for zero specular component (Rayleigh) fading and approaches 0.39 nats per channel-use for very large specular components. We also compute the asymptotic cut-off rate of a Rayleigh fading channel when the receiver has access to some partial side information concerning the fading. It is demonstrated that the cut-off rate does not utilize the side information as efficiently as capacity, and that the high SNR gap between the two increases to infinity as the imperfect side information becomes more and more precise.