Boolean Functions: Noise Stability, Non-interactive Correlation Distillation, and Mutual Information
Name
1801.04462.pdf
Description
Accepted version
Size
259.61 KB
Format
Adobe PDF
Checksum (MD5)
923e3828b897c2cecefb6d2f0c0cebb3
Author(s)
Li, Jiange
Medard, Muriel
Date Issued
2021
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
© 1963-2012 IEEE. Let T be the noise operator acting on Boolean functions f:{0,1nto 0, 1 , where in [0, 1/2] is the noise parameter. Given α >1 and fixed mean E f , which Boolean function f has the largest α -th moment E(Tf)α ? This question has close connections with noise stability of Boolean functions, the problem of non-interactive correlation distillation, and Courtade-Kumar's conjecture on the most informative Boolean function. In this paper, we characterize maximizers in some extremal settings, such as low noise (=(n) close to 0), high noise (=(n) close to 1/2), as well as when α =α (n) is large. Analogous results are also established in more general contexts, such as Boolean functions defined on discrete torus (Z/p Z)n and the problem of noise stability in a tree model.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TIT.2020.3041028
