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. 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.
- Decision feedback
- Differential pulse-code modulation (DPCM)
- Entropy coded dithered quantization (ECDQ)
- Minimum mean-square error (MMSE) estimation
- Shannon lower bound
- Test channel