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In this paper, we present a distributed joint source-channel (DJSC) coding approach for a pair of correlated binary sources transmitted over independent binary symmetric channels. This problem is of interest in wireless sensor network applications, where encoders with low complexity and delay may be required. In the proposed method, a judiciously chosen fraction of information bits and a fraction of parity bits obtained by puncturing the output of a systematic channel code are transmitted for each source. We obtain the achievable rate region for the proposed coding scheme and show that it coincides with the Slepian-Wolf lower bound as the channel error probability approaches zero. Experimental results obtained with a practical implementation based on LDPC codes are also presented which demonstrate that for short coding block lengths (or low delay coding), the proposed DJSC coding method outperforms separate distributed source coding and channel coding.