Lower Bounds on the Capacity Regions of the Relay Channel and the Cooperative Relay-Broadcast Channel with Non-Causal Side Information.

In this work, coding for the relay channel (RC) and the cooperative relay broadcast channel (RBC) controlled by random parameters are studied. In the first channel, the RC, information is transferred from the transmitter to the receiver through a multiplicity of nodes which all "simply" act as relays. In the second channel, the cooperative RBC, each intermediate node also acts as a receiver, i.e., it decodes a "private message". For each of these two channels, we consider the situation when side information (SI) Sⁿ on the random parameters is non- causally provided to the transmitter and all the intermediate nodes but not the final receiver, and derive an achievable rate region based on the relays using the decode-and-forward scheme. In the special case when the channels are degraded Gaussian and the side information (SI) is additive i.i.d. Gaussian, we show that 1) the rate regions are tight and provide the corresponding capacity regions and 2) the state Sⁿ does not affect these capacity regions, even though the final receiver has no knowledge of the state. For the degraded Gaussian RC, the results in this paper can be seen as an extension of those by Kim et al. to the case of more than one relay.