  The information bottleneck problem (IB) of jointly stationary Gaussian
sources is considered. A water-filling solution for the IB rate is given in
terms of its SNR spectrum and whose rate is attained via frequency domain
test-channel realization. A time-domain realization of the IB rate, based on
linear prediction, is also proposed, which lends itself to an efficient
implementation of the corresponding remote source-coding problem. A compound
version of the problem is addressed, in which the joint distribution of the
source is not precisely specified but rather in terms of a lower bound on the
guaranteed mutual information. It is proved that a white SNR spectrum is
optimal for this setting.
