Universal Sampling Rate Distortion
This work addresses the challenge of efficient data acquisition and compression for systems with unknown source correlations, though it appears incremental as it builds on existing rate distortion theory.
The paper tackles the problem of sampling and compressing correlated sources without knowing their joint distribution, achieving single-letter characterizations for universal sampling rate distortion functions in Bayesian and non-Bayesian settings.
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.