On the Capacity of the Half-Duplex Diamond Channel Under Fixed Scheduling

The diamond channel is a dual-hop communication system composed of a source, and a destination connected through two noninterfering relays. Operating in the half-duplex mode, relays are not capable of simultaneous transmission and reception of signals. This paper studies coding and scheduling schemes achieving within constant gap from the maximum achievable rate possible assuming the scheduling is fixed for all messages and known to all nodes prior to transmission. It is shown that under constant power constraints, a simple transmission scheme for relays is within 0.71 bits of the optimum rate. It is also demonstrated that the proposed scheme can attain the optimum rate, when channels satisfy a certain property. Furthermore, it is proved that under average power constraints, the same scheme can be used to achieve within 3.6 bits of the optimum rate.