Abstract
The CEO problem has received much attention since first introduced by Berger et al., but there are limited results on non-Gaussian models with non-quadratic distortion measures. In this work, we extend the quadratic Gaussian CEO problem to two non-Gaussian settings with general rth power of difference distortion. Assuming an identical observation channel across agents, we study the asymptotics of distortion decay as the number of agents and sum-rate, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> , grow without bound, while individual rates vanish. The first setting is a regular source-observation model with rth power of difference distortion, which subsumes the quadratic Gaussian CEO problem, and we establish that the distortion decays at <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-r/2</sup> ) when r ≥ 2. We use sample median estimation after the Berger-Tung scheme for achievability. The other setting is a non-regular source-observation model, including uniform additive noise models, with rth power of difference distortion for which estimation-theoretic regularity conditions do not hold. The distortion decay <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-r</sup> ) when r ≥ 1 is obtained for the non-regular model by midrange estimator following the Berger-Tung scheme. We also provide converses based on the Shannon lower bound for the regular model and the Chazan-Zakai-Ziv bound for the non-regular model, respectively. Lastly, we provide a sufficient condition for the regular model, under which quadratic and logarithmic distortions are asymptotically equivalent by an entropy power relationship as the number of agents grows. This proof relies on the Bernstein-von Mises theorem.
Highlights
Consider a multiterminal source coding problem where the CEO (Chief Executive Officer) of an organization is interested in a sequence of random variables {X(t)}∞ i=1, but does not observe it directly
This paper was presented in part at the 2018 IEEE International Symposium on Information Theory (ISIT) [1] and is based in part on a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering at University of Illinois at Urbana-Champaign
We explore two CEO problems that differ from prior results in that the models have a nonGaussian source-observation pair, and general rth power difference distortion d(x, x) = |x − x|r
Summary
Consider a multiterminal source coding problem where the CEO (Chief Executive Officer) of an organization is interested in a sequence of random variables {X(t)}∞ i=1, but does not observe it directly. VI concludes the paper and mentions a few possible extensions
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