The capacity of a class of state-dependent relay channel with orthogonal components and side information at the source and the relay

In this paper, a class of state-dependent relay channel with orthogonal channels from the source to the relay and from the source and the relay to the destination is studied. The two orthogonal channels are corrupted by two independent channel states S-R and S-D, respectively, which are known to both the source and the relay. The lower bounds on the capacity are established for the channel either with non-causal channel state information or with causal channel state information. Further, we show that the lower bound with non-causal channel state information is tight if the receiver output Y is a deterministic function of the relay input X-r, the channel state S-D, and one of the source inputs X-D, i.e., Y = f(X-D, X-r, S-D), and the relay output Y-r is restricted to be controlled by only the source input X-R and the channel state S-R, i.e., the channel from the source to the relay is governed by the conditional probability distribution P-Yr vertical bar XR,P-SR. The capacity for this class of semi-deterministic orthogonal relay channel is characterized exactly. The results are then extended to the Gaussian cases, modeling the channel states as additive Gaussian interferences. The capacity is characterized for the channel when the channel state information is known non-causally. However, when the channel state information is known causally, the capacity cannot be characterized in general. In this case, the lower bound on the capacity is established, and the capacity is characterized when the power of the relay is sufficiently large. Some numerical examples of the causal state information case are provided to illustrate the impact of the channel state and the role of the relay in information transmission and in cleaning the channel state.