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In this paper, we propose a general framework for Distributed Source Coding (DSC) of multiple sequentially correlated information sources. In particular, we modularize the joint decoding function into a conceptually simple structure by utilizing a notion of "complementarity" on the code space. Assuming a constrained Hamming-distance based correlation, our general framework of DSC achieves arbitrary non-asymmetric-rate compression of multiple sources with a same overall compression rate as asymmetric compression schemes. This DSC framework does not only have flexibility with respect to compression rates, but also accommodates the use of any linear block code and any of its corresponding complements. By investigating the unique connection between syndromes and complementary codewords, we translate the major steps of DSC joint decoding into syndrome decoding followed by channel encoding via a linear block code and also via its complement code. Our aim is to achieve transparency which facilitates practical implementation.