Bounds on the Capacity of the Relay Channel with States at the Source

We consider a state-dependent full-duplex relay channel with the channel states available non-causally at only the source, i.e., neither at the relay nor at the destination. For the discrete memoryless (DM) case, we establish lower and upper bounds on the channel capacity. The lower bound is obtained by a coding scheme at the source that uses a Gel'fand-Pinsker like binning scheme at the source, and is based on partial decode-and-forward at the relay. The upper bound improves upon that obtained by assuming that the channel state is available at the source, the relay, and the destination. For the Gaussian case also, we establish lower and upper bounds on the capacity. The lower bound is obtained by a coding scheme that consists in a superposition of generalized dirty paper coding (GDPC) and standard DPC at the source, and partial decode-and-forward at the relay. In this case also, the upper bound is better than that obtained by assuming that the channel state is available at the source, the relay, and the destination. For the general Gaussian RC and the degraded Gaussian RC, the lower bound and the upper bound meet, and so give the capacity, for some extreme cases, and so the capacity is obtained for these cases,