Causally and Noncausally Information Bound in Discrete Memoryless Multicast Relay Network

Abstract

The problem of relay channel (RC) with noncausal channel state information (CSI) available at the relay is considered. With the CSI, the relay can help communication in two ways: 1) by relaying message information; 2) by conveying the CSI to help the destination decode. In previous work, Zaidi et al. established a lower bound by letting the relay send message information by performing Gelfand-Pinsker (GP) coding. While in our schemes, we combine the two ways by letting the relay send message information as well as the compressed CSI to the receivers. We investigate three decodeforward (DF) lower bounds. The first two bounds are obtained by transmitting the message information and the CSI directly. We find this scheme is surprisingly equivalent to Zaidi's. The third bound is established by exploiting a new coding scheme. We show that the third bound is tighter than others. We show our optimal scheme for a class of deterministic SD-RC and give the capacity. We also generalize RC to discrete memoryless multicast network (DM-MN). We characterize the DF lower bound for DM-MN with noncausal CSI only at the relay nodes.