Broadcasting on trees near criticality
Name
2005.07801.pdf
Description
Submitted version
Size
195.1 KB
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Unknown
Checksum (MD5)
95b9a0b669d6fd5e552b411a53f51a65
Author(s)
Gu, Yuzhou
Polyanskiy, Yury
Hosseini Roozbehani, Hajir
Date Issued
June 2020
Journal
IEEE International Symposium on Information Theory - Proceedings
Publisher
IEEE
Citation
Gu, Yuzhou, Roozbehani, Hajir and Polyanskiy, Yury. 2020. "Broadcasting on trees near criticality." IEEE International Symposium on Information Theory - Proceedings, 2020-June.
Version
Original manuscript
Abstract
© 2020 IEEE. We revisit the problem of broadcasting on d-ary trees: starting from a Bernoulli(1/2) random variable X 0 at a root vertex, each vertex forwards its value across binary symmetric channels BSC δ to d descendants. The goal is to reconstruct X 0 given the vector X Lh of values of all variables at depth h. It is well known that reconstruction (better than a random guess) is possible as h →∞ if and only if δ < δ c (d). In this paper, we study the behavior of the mutual information and the probability of error when δ is slightly subcritical. The innovation of our work is application of the recently introduced less-noisy channel comparison techniques. For example, we are able to derive the positive part of the phase transition (reconstructability when δ < δ c ) using purely information-theoretic ideas. This is in contrast with previous derivations, which explicitly analyze distribution of the Hamming weight of X Lh (a so-called Kesten-Stigum bound).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/isit44484.2020.9174464
