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

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.