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Broadcasting on trees near criticality
Name
2005.07801.pdf
Description
Submitted version
Size
195.1 KB
Format
Adobe PDF
Checksum (MD5)
95b9a0b669d6fd5e552b411a53f51a65
Author(s)
Gu, Yuzhou
Roozbehani, Hajir
Polyanskiy, Yury
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).
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DOI of Published Version
10.1109/isit44484.2020.9174464
