New Upper Bounds on the Capacity of Primitive Diamond Relay Channels

Consider a primitive diamond relay channel, where a source X wants to send information to a destination with the help of two relays Y
₁
and Y
₂
, and the two relays can communicate to the destination via error-free digital links of capacities C
₁
and C
₂
respectively, while Y
₁
and Y
₂
are conditionally independent given X. In this paper, we develop new upper bounds on the capacity of such primitive diamond relay channels that are tighter than the cut-set bound. Our results include both the Gaussian and the discrete memoryless case and build on the information inequalities recently developed in [6]-[8] that characterize the tension between information measures in a certain Markov chain.