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In this paper, we consider a distributed sensor network in which sensors communicate their observations to a fusion center (FC) using limited transmission rate. Specifically, we investigate the case where the encoders are partially cooperating; they are connected by communication links with finite capacities. Hence, before the encoders encode and transmit their data, they exchange information to increase the reliability of their information. We address the problem from an information theoretic perspective and determine a lower bound for the sum- rate distortion function of the cooperative CEO problem. We also derive a lower bound for the rate-region of the problem.