Causal Rate Distortion Function on Abstract Alphabets and Optimal Reconstruction Kernel

TL;DR

This paper formulates a causal rate distortion function on abstract alphabets, deriving the optimal reconstruction kernel as a product of causal kernels and establishing existence via weak*-convergence.

Contribution

It introduces a general framework for causal rate distortion on abstract spaces and derives the structure of the optimal kernel, extending prior work to more general settings.

Findings

Optimal reconstruction kernel is a product of causal kernels.

Existence of the minimizing kernel is proven using weak*-convergence.

Properties of the causal rate distortion function are characterized.

Abstract

A Causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and the optimal reconstruction kernel is derived, which consists of a product of causal kernels. In the process, general abstract spaces are introduced to show existence of the minimizing kernel using weak*-convergence. Certain properties of the causal rate distortion function are presented.