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 Y1 and Y2, and the two relays can communicate to the destination via error-free digital links of capacities C1 and C2 respectively, while Y1 and Y2 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.