Abstract
Abstract 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 Y r | X R , S R . 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.
Highlights
Extensions to multiple user channels were performed by Gel'fand and Pinsker in [5], where it was shown that interference cancellation was possible in the Gaussian broadcast channel (BC) and Gaussian multiple-access channel (MAC)
(3) We show that the exact capacity for the channel with non-causal channel state information at the source and the relay can be characterized if the receiver output Y is a deterministic function of the relay input Xr, the channel state SD, and one of the source inputs XD, i.e., Y = f(XD, Xr, S), and the relay output Yr is restricted to be controlled by only the source input XR and the channel state SR, i.e., the channel from the source to the relay is governed by the conditional probability distribution PY rjXR;SR
4 Semi-deterministic orthogonal relay channel with non-causal channel state information we show that the lower bound derived in Theorem 1 is tight for a class of semi-deterministic orthogonal relay channel, where, the output Y of the destination is a deterministic function of XD, Xr and SD, i.e., Y = f(XD, Xr, SD), and the output Yr of the relay node is controlled only by XR and SR, i.e., the channel from the source to the relay is governed by the conditional distribution PY rjXR;SR
Summary
With the same achievable schemes proposed in [18], the authors [19] obtained two corresponding lower bounds for the state-dependent relay channel with orthogonal components and channel state information known non-causally to the source. A (M, n) code for the state-dependent relay channel with channel state information non-causally known to the source and the relay consists of an encoding function at the source φn : f1; 2;
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