Network coding has been investigated as a way to improve throughput and power efficiency of wireless networks by mixing of various traffic flows. The scenario under consideration is Y-topology denoise-and-forward relay channel that two sending stations transmit independent data to the receiving station directly and through the relay station. The receiving stations decode the error-correcting coded bits using the extrinsic information. Here, it is important to set the extrinsic information to decode the coded data accurately. In this paper, we present how to set the extrinsic information for belief propagation decoding with network coding to achieve better decoding error rate performance. We calculate the extrinsic information based not only on channels from the relay station to receiving station, but also on all channels from two sending stations to the receiving station when the receiving station decodes error-correcting coded data. When we use turbo code or low-density parity-check (LDPC) code as error-correcting code, we decode the coded data accurately by the use of accurate extrinsic information. We provide computer simulation results and show that the proposed method improves bit error rate performance and decreases the average number of decoding iterations.