The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels
Christian Borgs
Jennifer Chayes
Elchanan Mossel
Sebastien Roch
This paper appears in: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Publication Date: Oct. 2006
On page(s): 518-530
Location: Berkeley, CA,
ISSN: 0272-5428
ISBN: 0-7695-2720-5
INSPEC Accession Number: 9297321
Digital Object Identifier: 10.1109/FOCS.2006.76
Current Version Published: 2006-12-19
Abstract
We establish the exact threshold for the reconstruction problem for a binary asymmetric channel on the b-ary tree, provided that the asymmetry is sufficiently small. This is the first exact reconstruction threshold obtained in roughly a decade. We discuss the implications of our result for Glauber dynamics, phylogenetic reconstruction, noisy communication and the so-called "replica symmetry breaking" in spin glasses and random satisfiability problems
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