Compress-and-forward strategy for relay channel with causal and non-causal channel state information

The discrete memoryless state-dependent relay channel (SD-RC) is considered in this study. Two main cases are investigated: SD-RC with non-causal channel state information (CSI) and SD-RC with causal CSI. In each case, the SD-RC with partial CSI at the source and the relay is considered. As special cases it includes three different situations in which perfect CSI is available: (i) only at the source, (ii) only at the relay and (iii) both at the source and the relay. For the non-causal situation, the authors establish lower bound on capacity (achievable rate) of the SD-RC, using Gel’fand-Pinsker coding at the nodes informed of CSI and compress-andforward (CF) strategy at the relay. Using the Shannon’s strategy and CF relaying, the authors derive lower bound on capacity of SD-RC in the causal case. Furthermore, in order to compare their derived bounds with the previously obtained results, which are based on the decode-and-forward (DF) strategy, the authors consider general Gaussian relay channel (RC) with additive independent and identically distributed Gaussian state and noise, and obtain lower bounds on capacity for the cases in which perfect CSI is available noncausally at the source or at the relay. They also present cases in which their lower bounds outperform DFbased bounds, and can achieve rates close to the upper bound. For causal case, a numerical example of the binary fading Gaussian RC with additive noise is provided.