  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.
