Compress-forward strategy with non-causal channel state information at the relay

In this paper we consider relay channel (RC) with non-causal channel state information (CSI) only at the relay. Three compress-forward (CF) lower bounds were established. The first one is obtained by letting the relay transmit compressed CSI and message information directly. The second bound is a special case of the first one, which is achieved by letting the relay only transmit CSI regardless of message. It is equivalent to the first one under some cases. To achieve the third bound we introduce a new coding scheme, which makes more use of the non-causal CSI. The third bound contains all previous bounds. In our scheme, the non-causal CSI is compressed and transmitted with message information. The transmission of CSI has twofold effect. On the one hand, it may reduce the message rate sent by the relay. On the other hand, the destination can decode the CSI and use it to improve decoding message from both the source and the relay. We find that our scheme is equivalent to CF strategy with Gelfand-Pinsker (GP) coding, in which the non-causal CSI is only used to improve decoding the message from the relay. Note that if the channel between the relay and destination is good enough, the relay can transmit all the message information it got and use the extra capacity to transmit compressed CSI. In this situation the transmission of CSI doesn´t reduce the message rate to be relayed, and our scheme outperforms CF strategy with GP coding.