Achieving the Quadratic Gaussian Rate-Distortion Function for Source Uncorrelated Distortions

TL;DR

This paper demonstrates that the quadratic Gaussian rate-distortion function with uncorrelated distortions can be achieved using high-dimensional lattice quantization and causal coding, with minimal rate loss in finite dimensions.

Contribution

It proves achievability of the uncorrelated distortion RDF using shaped dithered lattice quantization and causal transform coding, extending the understanding of Gaussian source coding.

Findings

Uncorrelated distortion RDF is achievable with high-dimensional lattice quantization.

Causal transform coding can realize the uncorrelated distortion RDF.

Finite-dimensional rate loss is bounded by 0.254 bits/dimension.

Abstract

We prove achievability of the recently characterized quadratic Gaussian rate-distortion function (RDF) subject to the constraint that the distortion is uncorrelated to the source. This result is based on shaped dithered lattice quantization in the limit as the lattice dimension tends to infinity and holds for all positive distortions. It turns out that this uncorrelated distortion RDF can be realized causally. This feature, which stands in contrast to Shannon's RDF, is illustrated by causal transform coding. Moreover, we prove that by using feedback noise shaping the uncorrelated distortion RDF can be achieved causally and with memoryless entropy coding. Whilst achievability relies upon infinite dimensional quantizers, we prove that the rate loss incurred in the finite dimensional case can be upper-bounded by the space filling loss of the quantizer and, thus, is at most 0.254 bit/dimension.