Improving on the cut-set bound for general primitive relay channels

Consider a primitive relay channel, where, a source X wants to send information to a destination Y with the help of a relay Z and the relay can communicate to the destination via an error-free digital link of rate R
₀
. For the symmetric case, i.e., when Y and Z are conditionally i.i.d. given X, we have recently developed new upper bounds on the capacity of this channel that are tighter than existing bounds, including the celebrated cut-set bound. In this paper, we extend these bounds to the asymmetric case, where Y and Z are conditionally independent given X with arbitrary conditional marginal distributions, for both discrete memoryless and Gaussian channels.