Rate Loss in the CEO Problem
Proceedings of the 39th Conference on Information Sciences and Systems (CISS 2005), Baltimore, MD, March 2005.
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Abstract
The quadratic Gaussian CEO problem has a known sum rate distortion function. Furthermore, the loss with respect to a remote rate distortion function that has access to all observations at a joint encoder is easily derived, and both the sum rate and rate loss increase asymptotically as number of agents $M \to \infty$. Does this limiting behavior change if the source is no longer Gaussian? By adapting a technique in [6], this paper reveals an upper bound to the rate loss in the CEO problem. When the source is observed through additive white Gaussian noise and the distortion is mean squared error, this bound can be evaluated by solving a single-letter MMSE estimation problem. For this case, it turns out that the limiting behavior of both the sum rate distortion and rate loss cannot be worse than for certain cases, can be better.