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Multiple nodes sensing the common target is the most popular application of the Wireless Sensor Networks (WSNs). Pure distributed compression of multiple correlated sources has been discussed much in the related literature, while taking the noisy communication channels into account is more suitable for the actual scenario. In this paper, a practical Distributed Joint Source-Channel Coding (DJSCC) scheme for multiple correlated sources is proposed. Besides considering the noisy channels and multiple sources, the processing of the noisy side information is also investigated here. By combining the Shannon theorem and the Slepian-Wolf theorem, the theoretical limits of the proposed DJSCC scheme are derived. An efficient coding strategy with a single Low-Density Parity Check (LDPC) code is designed based on the theory to cope with both source and channel coding. The simulation results demonstrate the desired efficiency of our scheme.