A Strengthened Cutset Upper Bound on the Capacity of the Relay Channel and Applications

TL;DR

This paper introduces a new, tighter upper bound on the relay channel capacity using mutual information inequalities, resolving several open conjectures and improving existing bounds for various relay channel models.

Contribution

It develops a novel upper bound on relay channel capacity that surpasses previous bounds, resolving conjectures and improving results for multiple channel classes.

Findings

The new bound is strictly tighter than all previous bounds for Gaussian relay channels.

It resolves Kim's conjecture for relay channels with orthogonal receiver components.

The bound improves upon recent bounds for binary symmetric relay channels.

Abstract

We develop a new upper bound on the capacity of the relay channel that is tighter than previously known upper bounds. This upper bound is proved using traditional weak converse techniques involving mutual information inequalities and Gallager-type explicit identification of auxiliary random variables. We show that the new upper bound is strictly tighter than all previous bounds for the Gaussian relay channel with non-zero channel gains. When specialized to the relay channel with orthogonal receiver components, the bound resolves a conjecture by Kim on a class of deterministic relay channels. When further specialized to the class of product-form relay channels with orthogonal receiver components, the bound resolves a generalized version of Cover's relay channel problem, recovers the recent upper bound for the Gaussian case by Wu et al., and improves upon the recent bounds for the binary symmetric case by Wu et al. and Barnes et al., which were obtained using non-traditional geometric proof techniques. For the special class of a relay channel with orthogonal receiver components, we develop another upper bound on the capacity which utilizes an auxiliary receiver and show that it is strictly tighter than the bound by Tandon and Ulukus. Finally, we show through the Gaussian relay channel with i.i.d. relay output sequence that the bound with the auxiliary receiver can be strictly tighter than our main bound.