An upper bound on the sum-rate distortion function and its corresponding rate allocation schemes for the CEO problem

We consider a distributed sensor network in which several observations are communicated to the fusion center using limited transmission rate. The observation must be separately encoded so that the target can be estimated with minimum average distortion. We address the problem from an information theoretic perspective and establish the inner and outer bound of the admissible rate-distortion region. We derive an upper bound on the sum-rate distortion function and its corresponding rate allocation schemes by exploiting the contra-polymatroid structure of the achievable rate region. The quadratic Gaussian case is analyzed in detail and the optimal rate allocation schemes in the achievable rate region are characterized. We show that our upper bound on the sum-rate distortion function is tight for the quadratic Gaussian CEO problem in the case of same signal-to-noise ratios at the sensors.