The Gaussian CEO Problem for Scalar Sources With Arbitrary Memory

In this paper, we consider the achievable sum-rate/distortion tradeoff for the Gaussian central estimation officer (CEO) problem with a scalar source having arbitrary memory. We describe how the arbitrary memory problem can be fully characterized by using known results for the vector CEO problem, and then we formulate the variational problem of minimizing the sum-rate subject to a distortion constraint. To solve the problem, we extend the conventional Lagrange method and show that if the solution exists, it should consist of a zero part and a non-zero part, where the non-zero part is determined by solving a set of Euler equations. By calculating the second variation of the min-sum-rate problem, a sufficient condition is also found that can be used to determine if the necessary solution results in the minimal sum rate. The special case of two terminals is examined in detail, and it is shown that an analytical solution is possible in this case. Analysis and discussion with examples are provided to illustrate the theoretical results. The general solution obtained in this paper is shown to be compatible with the previous results for cases such as the problem of rate evaluation for sources without memory.

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