Author:
DECREUSEFOND LAURENT,ZÉMOR GILLES
Abstract
We are interested in a function f(p) that
represents the probability that a random subset of edges of a
Δ-regular graph G contains half the edges of some cycle
of G. f(p) is also the probability that a codeword
is corrupted beyond recognition when words of the cycle code of
G are submitted to the binary symmetric channel. We derive a
precise upper bound on the largest p for which
f(p) can vanish when the number of edges of
G goes to infinity. To this end, we introduce the notion of
fractional percolation on trees, and calculate the related critical
probabilities.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
10 articles.
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