Date of this Version
Random Structures & Algorithms
A periodic tree Tn consists of full n-level copies of a finite tree T. The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjacent vertices to have the same label is 1−ϵ. This model simulates noisy propagation of a bit from the root, and has significance both in communication theory and in biology. Our aim is to find an algorithm which decides for every set of values of the boundary bits of T, if the root is more probable to be 0 or 1. We want to use this algorithm recursively to reconstruct the value of the root of Tn with a probability bounded away from ½ for all n. In this paper we find for all T, the values of ϵ for which such a reconstruction is possible. We then compare the ϵ values for recursive and nonrecursive algorithms. Finally, we discuss some problems concerning generalizations of this model.
This is the peer reviewed version of the following article: Mossel, E. (1998), Recursive reconstruction on periodic trees. Random Struct. Alg., 13: 81–97., which has been published in final form at doi: 10.1002/(SICI)1098-2418(199808)13:1<81::AID-RSA5>3.0.CO;2-O. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms.
Mossel, E. (1998). Recursive Reconstruction on Periodic Trees. Random Structures & Algorithms, 13 (1), 81-97. http://dx.doi.org/10.1002/(SICI)1098-2418(199808)13:1<81::AID-RSA5>3.0.CO;2-O
Date Posted: 27 November 2017
This document has been peer reviewed.