One-Shot Wyner-Ziv Compression of a Uniform Source

TL;DR

This paper investigates the one-shot Wyner-Ziv compression problem for a uniform source, deriving bounds on entropy-distortion functions with scalar quantization and noisy side information, especially at high compression rates.

Contribution

It introduces bounds on entropy-distortion functions for uniform sources in one-shot Wyner-Ziv compression with noisy side information, highlighting their tightness at high rates.

Findings

Derived upper and lower bounds for entropy-distortion functions.

Bounds are tight at high compression rates.

Applicable to sources with low-dimensional features in high-dimensional spaces.

Abstract

In this paper, we consider the one-shot version of the classical Wyner-Ziv problem where a source is compressed in a lossy fashion when only the decoder has access to a correlated side information. Following the entropy-constrained quantization framework, we assume a scalar quantizer followed by variable length entropy coding. We consider compression of a uniform source, motivated by its role in the compression of processes with low-dimensional features embedded within a high-dimensional ambient space. We find upper and lower bounds to the entropy-distortion functions of the uniform source for quantized and noisy side information, and illustrate tightness of the bounds at high compression rates.