On the quadratic AWGN CEO problem and non-gaussian sources

In the CEO problem, introduced by Berger et al, IEEE Trans. Info. Theory, 1996, a CEO is interested in a source that cannot be observed directly. M agents observe independently noisy versions of the source and, without collaborating, must encode these across noiseless rate-constrained channels to the CEO. The quadratic AWGN CEO problem refers to the class of CEO problems for which the agents view the source through additive white Gaussian noise, and the distortion is squared error. This paper discusses two upper bounds to the CEO sum-rate distortion function for this class of problems. The first follows from elementary arguments. It permits two conclusions. First, the worst case is when the underlying source is Gaussian (for fixed variance). Second, there are source distributions that lead to a significantly better behavior. The second upper bound follows from a new bound on the rate loss between the CEO and the remote rate-distortion function. For certain source distributions and certain ranges of distortion, this bound is better than the first