The source coding game with a cheating switcher

TL;DR

This paper extends the analysis of the source coding game by considering a switcher with non-causal access to source realizations, deriving the rate-distortion function using type covering and switching rules.

Contribution

It introduces the rate-distortion function for an adversarial source with a non-causal switcher, expanding on Berger's causal model with a new proof approach.

Findings

Rate-distortion function characterized for non-causal switcher

Maximization of R(D) over attainable IID distributions

Utilizes type covering lemma and switching rules

Abstract

Berger's paper `The Source Coding Game', IEEE Trans. Inform. Theory, 1971, considers the problem of finding the rate-distortion function for an adversarial source comprised of multiple known IID sources. The adversary, called the `switcher', was allowed only causal access to the source realizations and the rate-distortion function was obtained through the use of a type covering lemma. In this paper, the rate-distortion function of the adversarial source is described, under the assumption that the switcher has non-causal access to all source realizations. The proof utilizes the type covering lemma and simple conditional, random `switching' rules. The rate-distortion function is once again the maximization of the R(D) function for a region of attainable IID distributions.