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

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.

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Christian Borgs, Jennifer T. Chayes, Elchanan Mossel, Sébastien Roch
• Keywords: Binary Asymmetric Channel, Exact Reconstruction Threshold, Exact Threshold, FOCS 2006, Theoretical Computer Science