# Universal Sampling Rate Distortion

## TL;DR

This paper introduces universal sampling and compression schemes for correlated sources that do not require prior knowledge of source distributions, providing optimal rate-distortion trade-offs in various sampling scenarios.

## Contribution

It presents the first single-letter characterizations of universal sampling rate distortion functions for different sampling methods, including fixed-set and random sampling.

## Key findings

- Universal schemes perform robustly without knowing source distributions.
- Successive sampling mechanisms improve reconstruction quality.
- New joint source learning and compression schemes are developed.

## Abstract

We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within a specified level of distortion. The combined sampling mechanism and rate distortion code are universal in that they are devised to perform robustly without exact knowledge of the underlying joint probability distribution of the sources. In Bayesian as well as nonBayesian settings, single-letter characterizations are provided for the universal sampling rate distortion function for fixed-set sampling, independent random sampling and memoryless random sampling. It is illustrated how these sampling mechanisms are successively better. Our achievability proofs bring forth new schemes for joint source distribution-learning and lossy compression.