  The "water-filling" solution for the quadratic rate-distortion function of a
stationary Gaussian source is given in terms of its power spectrum. This
formula naturally lends itself to a frequency domain "test-channel"
realization. We provide an alternative time-domain realization for the
rate-distortion function, based on linear prediction. This solution has some
interesting implications, including the optimality at all distortion levels of
pre/post filtered vector-quantized differential pulse code modulation (DPCM),
and a duality relationship with decision-feedback equalization (DFE) for
inter-symbol interference (ISI) channels.
