"The Information Bottleneck: A Unified Information Theoretic View"

This presentation focuses on connections between relatively recent notions and variants of the
Information Bottleneck and classical information theoretic frameworks, such as:
Remote Source-Coding; Information Combining; Common Reconstruction; The Wyner-Ahlswede-Korner Problem;
The Efficiency of Investment Information; CEO Source Coding under Log-Loss,
Hypothesis Testing Error Exponent and others.
We overview the uplink Cloud Radio Access Networks (CRAN) with oblivious processing, which is
an attractive model for future wireless systems and highlight the basic connections to distributed
Gaussian information bottleneck framework. For this setting, the optimal trade-offs
between rates (i.e.  complexity) and information (i.e. accuracy) in the discrete and vector Gaussian
schemes is determined, taking an information-estimation viewpoint.
Further, the performance cost of the simple 'oblivious' universal processing in CRAN systems is
exemplified via novel bounding techniques.
The concluding overview and outlook addresses in a unified way the dual problem of the
privacy funnel and recent observations on the additive noise channels with a helper.
Connections to the finite block length bottleneck features (related to the Courtade-Kumar conjecture)
and entropy complexity measures (rather than mutual information) are shortly discussed.
Some challenging problems are mentioned such as the characterization of the
optimal power limited inputs (`features') maximizing the `relevance' for the Gaussian
information bottleneck, under `complexity' constraints.
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The talk is based mainly on joint research with A. Zaidi, I.E. Auguerri, G. Caire, O. Simeone
and S-H. Park.
The research of S. Shamai is supported by the European Union's Horizon 2020 Research and Innovation
Programme: No. 694630.
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