A Note on Cooperative Multiterminal Source Coding

We consider the multiterminal source coding problem with partially cooperating encoders. In the lossless case, we give a simple proof for a coding theorem that extends the result of Slepian and Wolf for non-cooperating encoders, resulting in a complete characterization of the rate region under this scenario. Then we extend this setup to consider an arbitrary pair of distortions (D1, D2), where we extend the results of Berger and Tung to obtain an inner and an outer bound for the region of achievable rates (R1, R2). Interestingly enough, we find that the rate expressions for the Berger-Tung inner and outer bounds, and for our inner and outer bounds with cooperation, are all identical—the only differences among all four regions lie in the class of probability distributions over which each of these bounds is defined. A close inspection of these classes of distributions reveals two important facts: (a) the uncertainty on whether the Berger-Tung inner and outer bounds are tight or not carries over to our inner and outer bounds with cooperation; (b) cooperation does produce a strict enlargement of the rate-distortion region.