Rate-distortion for correlated sources with partially separated encoders

We resolve some open problems concerning the encoding of a pair of correlated sources with respect to a fidelity criterion. Two encoders are used. One encoder observes only the output of the first source, while the other is supplied both with the second source output and with partial information about the first source at some predetermined rate. A general coding theorem is proved which established that{\cal S} \ast, a certain region defined in terms of "single-letter" information theoretic quantities, is an inner bound to the region of all attainable vectors of rates and distortions. For certain cases of interest the converse is proved, too, thereby establishing the rate-distortion region for these cases.