Source Coding Problems with Conditionally Less Noisy Side Information
Abstract
A computable expression for the rate-distortion (RD) function proposed by Heegard and Berger has eluded information theory for nearly three decades. Heegard and Berger's single-letter achievability bound is well known to be optimal for \emph{physically degraded} side information; however, it is not known whether the bound is optimal for arbitrarily correlated side information (general discrete memoryless sources). In this paper, we consider a new setup in which the side information at one receiver is \emph{conditionally less noisy} than the side information at the other. The new setup includes degraded side information as a special case, and it is motivated by the literature on degraded and less noisy broadcast channels. Our key contribution is a converse proving the optimality of Heegard and Berger's achievability bound in a new setting. The converse rests upon a certain \emph{single-letterization} lemma, which we prove using an information theoretic telescoping identity {recently presented by Kramer}. We also generalise the above ideas to two different successive-refinement problems.
Cite
@article{arxiv.1212.2396,
title = {Source Coding Problems with Conditionally Less Noisy Side Information},
author = {Roy Timo and Tobias J. Oechtering and Michèle Wigger},
journal= {arXiv preprint arXiv:1212.2396},
year = {2012}
}