Multiple Relay Channels with Delays: With and without Side Information

In this paper the Multiple Relay Channels (MRC) with delays, with and without channel state information (CSI) are investigated from an information theoretic point of view. For the MRC with unlimited look ahead where the relays can use the whole received block to encode, upper and lower bounds on the capacity are derived which are tight for the degraded case. For the MRC without-delay where the relays have access to the present received symbols in addition to the past symbols, the capacity of the degraded channel is established using Shannon´s strategy for the channels with side information. Then we introduce the state dependent MRC with unlimited look ahead and derive a lower bound on the capacity when the CSI is noncausally available at the sender and relays, using Gel´fand-Pinsker coding technique. Finally, the capacity of the degraded Gaussian MRC with unlimited look ahead and with state noise (dirty paper problem) is established.