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In this paper, we consider a multiple-access relay system with two users, one relay, and one destination. The relay combines the data packets received from these two users and then forwards the data packets to the destination. We consider a novel network coding scheme for information combing at the relay, namely, Low-density parity-check (LDPC) product coding. For LDPC product codes, we propose a joint iterative channel decoding (JICD) scheme based on bipartite graph under the log-likelihood ratio belief propagation (LLR-BP) algorithm resist the interference and fading at the destination. Simulation results show that the packet-error-ratio (PER) performance of LDPC product codes based network coding scheme outperforms the traditional XOR-operation based network coding scheme.