Universal Quantization for Separate Encodings and Joint Decoding of Correlated Sources

TL;DR

This paper extends Ziv's universal quantization scheme to multi-user correlated source coding, providing bounds on redundancy and establishing inner and outer bounds on the rate-distortion region without prior knowledge of the rate region.

Contribution

It generalizes a single-user universal coding scheme to multi-user scenarios and derives bounds on redundancy and the rate-distortion region.

Findings

Redundancy can be kept within 0.754 bits per sample per user.

Achieves bounds without prior knowledge of the multi-user rate region.

Provides inner and outer bounds on the rate-distortion achievable region.

Abstract

We consider the multi-user lossy source-coding problem for continuous alphabet sources. In a previous work, Ziv proposed a single-user universal coding scheme which uses uniform quantization with dither, followed by a lossless source encoder (entropy coder). In this paper, we generalize Ziv's scheme to the multi-user setting. For this generalized universal scheme, upper bounds are derived on the redundancies, defined as the differences between the actual rates and the closest corresponding rates on the boundary of the rate region. It is shown that this scheme can achieve redundancies of no more than 0.754 bits per sample for each user. These bounds are obtained without knowledge of the multi-user rate region, which is an open problem in general. As a direct consequence of these results, inner and outer bounds on the rate-distortion achievable region are obtained.