Network Coding over a Noisy Relay : a Belief Propagation Approach

In recent years, network coding has been investigated as a method to obtain improvements in wireless networks. A typical assumption of previous work is that relay nodes performing network coding can decode the messages from sources perfectly. On a simple relay network, we design a scheme to obtain network coding gain even when the relay node cannot perfectly decode its received messages. In our scheme, the operation at the relay node resembles message passing in belief propagation, sending the logarithm likelihood ratio (LLR) of the network coded message to the destination. Simulation results demonstrate the gain obtained over different channel conditions. The goal of this paper is not to give a theoretical result, but to point to possible interaction of network coding with user cooperation in noisy scenario. The extrinsic information transfer (EXIT) chart is shown to be a useful engineering tool to analyze the performance of joint channel coding and network coding in the network.