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 all previous bounds. This upper bound is proved using traditional weak converse techniques involving mutual information inequalities and identification of auxiliary random variables via past and future channel random variable sequences. We show that it 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 are all obtained using non-traditional geometric proof techniques. We then develop an upper bound on the capacity of the relay channel with orthogonal receiver components which utilizes an auxiliary receiver and show that it is tighter than the bound by Tandon and Ulukus on the capacity of the relay channel with i.i.d. relay output sequence. 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.