Achieving the Gaussian Rate–Distortion Function by Prediction

The ldquowater-fillingrdquo 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 ldquotest-channelrdquo realization. We provide an alternative time-domain realization for the rate-distortion function, based on linear prediction. The predictive test channel 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 intersymbol interference (ISI) channels.