Achieving the Gaussian Rate-Distortion Function by Prediction

TL;DR

This paper presents a time-domain realization of the Gaussian rate-distortion function using linear prediction, offering insights into optimal coding schemes and their duality with equalization methods.

Contribution

It introduces a novel time-domain approach for the Gaussian rate-distortion function based on linear prediction, expanding beyond traditional frequency domain solutions.

Findings

Pre/post filtered vector-quantized DPCM is optimal at all distortion levels.

The approach reveals a duality with decision-feedback equalization for ISI channels.

Provides a new perspective on Gaussian source coding in the time domain.

Abstract

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.