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In this paper the problem of compressing multiple correlated sources is addressed. It is assumed that the m sources are given as a sequence where an assumption is made only on the correlation between neighbouring sources. The correlation assumption is deterministic and Hamming-distance based (so-called ldquoconstrained correlationrdquo in the literature). The problem of compressing such a sequence of correlated sources is easily solved by repeatedly applying the asymmetric distributed source coding (DSC) for two sources, as in the DISCUS framework of (S.S. Pradhan et al., 2003). In this paper we present an alternative, more general, framework that achieves the same overall compression rate but allows for more flexible compression rates per source. The proposed encoder employs a channel code with a parity check matrix that does not need to be systematic. The proposed decoder consists of three steps. Firstly, difference patterns between sources are recovered from the compressed data via a channel decoder. Subsequently, this information is combined with other parts of the compressed data. Finally, by solving a linear equation and adding difference patterns, the original messages are reconstructed. We show that, for m = 2, several DSC coding schemes from the literature are special cases. We illustrate our framework for a sequence of 3 sources through a (15, 7) BCH code with a non-systematic parity check matrix.