Strengthened Cutset Upper Bounds on the Capacity of the Relay Channel and Applications

We establish new upper bounds on the capacity of the relay channel which are tighter than all previous bounds. The upper bounds use traditional weak converse techniques involving mutual information inequalities and identification of auxiliary random variables via past and future channel random variable sequences. For the relay channel without self-interference, we show that the new bound is strictly tighter than all previous bounds for the Gaussian relay channel for every set of non-zero channel gains. When specialized to the class of relay channels 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 extends it to the non-symmetric case, 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.