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In the distributed coding of correlated sources, the problem of characterizing the joint probability distribution of a pair of random variables satisfying an n-letter Markov chain arises. The exact solution of this problem is intractable. In this paper, the authors seek a single-letter necessary condition for this n-letter Markov chain. To this end, they propose a new data processing inequality on a new measure of correlation by means of spectrum analysis. Based on this new data processing inequality, they provide a single-letter necessary condition for the required joint probability distribution. They apply the results to two specific examples involving the distributed coding of correlated sources: multi-terminal rate-distortion region and multiple access channel with correlated sources, and propose new necessary conditions for these two problems.
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