Universal Wyner-Ziv Coding for Distortion Constrained General Side-Information

TL;DR

This paper introduces a universal Wyner-Ziv coding framework for sources with side-information generated by unknown channels within a certain class, providing bounds and conditions for optimal rate-distortion performance.

Contribution

It defines a new universal rate-distortion function for non-stationary, non-ergodic channels and establishes bounds and conditions for its optimality.

Findings

Derived upper and lower bounds on the rate-distortion function.

Established a matching condition for the bounds to coincide.

Discussed the relation to the Heegard-Berger problem.

Abstract

We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and the side-information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound and a lower bound on the rate-distortion function, and derive a matching condition such that the upper and lower bounds coincide. The relation between the new rate-distortion function and the rate-distortion function of the Heegard-Berger problem is also discussed.