Consider a communication network consisting of a complete regular tree
whose edges are independent noisy channels. A value is transmitted down
the tree from the root. For what values of the channel noise parameters
can the transmitted value be reconstructed from the values observed at
the leaves? Reconstruction problems on trees have been widely studied
in both communication theory and genetics.
In this talk I will present a simple criterion for determining bounds on
the range of parameter values for which reconstruction is not possible.
This leads to easy, unified proofs of known bounds, and occasionally to
slight improvements, for a number of channels.
Joint work with Fabio Martinelli and Dror Weitz.

Keywords:

Phase Transition;Computation;Reconstruction

Lecture #10862

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