Capacity of a class of semi-deterministic primitive relay channels

We characterize the capacity of a class of primitive relay channels. The primitive relay channel considered in this paper consists of a semi-deterministic broadcast channel to the relay and the decoder. The relay can help the message transmission through an orthogonal finite capacity link to the decoder. We show that the capacity of this class of primitive relay channels is given by the cut-set upper bound, and it can be achieved by the partial decode-and-forward scheme. We also show that the rate achievable by the compress-and-forward scheme is strictly smaller than the capacity.