  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.
