  The distributed remote source coding (so-called CEO) problem is studied in
the case where the underlying source, not necessarily Gaussian, has finite
differential entropy and the observation noise is Gaussian. The main result is
a new lower bound for the sum-rate-distortion function under arbitrary
distortion measures. When specialized to the case of mean-squared error, it is
shown that the bound exactly mirrors a corresponding upper bound, except that
the upper bound has the source power (variance) whereas the lower bound has the
source entropy power. Bounds exhibiting this pleasing duality of power and
entropy power have been well known for direct and centralized source coding
since Shannon's work. While the bounds hold generally, their value is most
pronounced when interpreted as a function of the number of agents in the CEO
problem.
