Causal Rate Distortion Function on Abstract Alphabets: Optimal Reconstruction and Properties

TL;DR

This paper formulates a causal rate distortion function on abstract alphabets, derives an optimal causal reconstruction kernel, and establishes properties and a coding theorem for the function.

Contribution

It introduces a general framework for causal rate distortion on abstract alphabets and proves the existence and optimality of the reconstruction kernel.

Findings

Optimal causal reconstruction kernel derived

Existence of minimizing kernel established

Properties of the causal rate distortion function presented

Abstract

A causal rate distortion function with a general fidelity criterion is formulated on abstract alphabets and a coding theorem is derived. Existence of the minimizing kernel is shown using the topology of weak convergence of probability measures. The optimal reconstruction kernel is derived, which is causal, and certain properties of the causal rate distortion function are presented.