Capacity of a Class of Diamond Channels

We study a special class of diamond channels which was introduced by Schein in 2001. In this special class, each diamond channel consists of a transmitter, a noisy relay, a noiseless relay and a receiver. We prove the capacity of this class of diamond channels by providing an achievability scheme and a converse. The capacity we show is strictly smaller than the cut-set bound. We note that there exists a duality between this diamond channel coding problem and the Kaspi-Berger source coding problem.