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A relay scheme combining network coding with channel coding is proposed for multiple-access relay channel. Via a newly designed network low density parity check code, this scheme permits the relay node to jointly encode the data information from two source nodes. To predict the system performance, a newly generalized Gaussian approximation algorithm is derived, based on which an optimization algorithm is developed to search the degree distribution of the network LDPC code. Simulations show that, in a network with two sources, one relay and one destination, the system with the designed network low density parity check code hold a performance gap less than 0.6 dB from the threshold and a performance gain of about 0.3 dB can be achieved to the same rate XOR network coding scheme at BER = 10-5.