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In this paper, we investigate the performance of low-density parity-check (LDPC) product codes in a multisource relay network where multiple sources transmit data to a same destination with the help of a noisy relay. We consider an LDPC product code resulting from the concatenation of Multiple Serially Concatenated Multiple Parity-Check (M-SC-MPC) codes. Every source encodes its data using the same M-SC-MPC code and broadcasts the codeword to relay and destination. The relay decodes and stores all codewords from sources in the rows of a matrix and encodes the columns using another M-SC-MPC code. Only the redundancy part generated by the relay is forwarded to the destination. At the destination, the codewords from the sources and the redundancy part from the relay form an observation of a product codeword whose parity check matrix is sparse. This LDPC product code can be iteratively decoded at destination using the low complexity sum-product algorithm. Since there are errors at the input of the relay-destination channel, an appropriate log-likelihood ratio is used in the LDPC decoding at destination in order to reduce the error propagation effect. The system error performance is given on the additive white Gaussian noise (AWGN) channel and the Rayleigh flat fading channel.