Noisy network coding with causal channel state information

Abstract

This paper considers a noisy network coding scheme for relay noisy networks with causal channel state information (CSI). We mainly focus on two models: discrete memoryless multicast network (DM-MN) and discrete memoryless network (DMN). Two different situations are investigated: 1) causal CSI only at the relay nodes, 2) causal CSI at all the nodes. The second situation is easily specialized to other cases: causal CSI at both the source and relay nodes; causal CSI at both the destination and relay nodes. Typically, causal CSI at the transmitter is only used for precoding, known as Shannon strategy. However, in our scheme causal CSI is compressed and transmitted with message information. Wyner-Ziv binning is used for compression and Shannon strategy is exploited to transmit both the message and CSI. It is a channel coding problem with respect to the message. On the other hand, it is a distributed source coding problem for sharing the CSI. We are the first to characterize noisy network coding inner bound with causal CSI. We also recover the result for relay channel (RC) as special case of DM-MN. And we indicate that our bound contains others in previous work. We also discuss some cases in which our scheme is strictly better.