Compress-and-forward strategy for the relay channel with non-causal State Information

In this paper, we consider a discrete memoryless state-dependent relay channel with non-causal channel state information (CSI). We investigate three different cases in which perfect channel states can be known non-causally: (i) only to the source, (ii) only to the relay or (iii) both to the source and to the relay node. For these three cases we establish lower bounds on the channel capacity (achievable rates) based on using Gel´fand-Pinsker coding at the nodes where the CSI is available and using compress-and-forward (CF) strategy at the relay. Furthermore, for the general Gaussian relay channel with additive independent and identically distributed (i.i.d) states and noise, we obtain lower bounds on the capacity for the cases in which CSI is available at the source or at the relay. We also compare our derived bounds with the previously obtained results which were based on decode-and-forward (DF) strategy, and we show the cases in which our derived lower bounds outperform DF based bounds, and can achieve the rates close to the upper bound.