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The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels

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4 Author(s)

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

Published in:

2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)

Date of Conference:

Oct. 2006