Geometric techniques in multiterminal communication and estimation
Abstract/Contents
- Abstract
- Since its inception in 1948, one of the main goals in information theory has been to extend its original scope of point-to-point communication to include networks of nodes exchanging information. Towards this goal, we develop tools from high-dimensional geometry to analyze the fundamental limits of communication and statistical estimation tasks in a networked setting. In the first half of the thesis, we describe a problem in network communications -- the relay channel -- and prove a new upper bound on the capacity of this channel which resolves an open problem posed by Thomas Cover in "Open Problems in Communication and Computation", Springer-Verlag, 1987. The proof is highly geometric, with its main ingredient being a new isoperimetric result on high-dimensional spheres that builds on a Riesz-type rearrangement inequality. In the second half of the thesis, we consider a collection of networked statistical estimation problems modeling bandwidth and privacy constraints in distributed and federated learning systems. In these problems, data is distributed across many nodes in a network and must be communicated to a centralized estimator under communication, privacy, or mutual information constraints. We show how a geometric interpretation of Fisher information from the processed statistical samples can derive tight minimax lower bounds for many distributed estimation problems of interest.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Barnes, Leighton Pate |
|---|---|
| Degree supervisor | Özgür, Ayfer |
| Thesis advisor | Özgür, Ayfer |
| Thesis advisor | Osgood, Brad |
| Thesis advisor | Weissman, Tsachy |
| Degree committee member | Osgood, Brad |
| Degree committee member | Weissman, Tsachy |
| Associated with | Stanford University, Department of Electrical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Leighton Pate Barnes. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/vr693cz0711 |
Access conditions
- Copyright
- © 2021 by Leighton Pate Barnes
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