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On the Error-Correcting Capabilities of Cycle Codes of Graphs

Published online by Cambridge University Press:  01 March 1997

LAURENT DECREUSEFOND  and
GILLES ZÉMOR
LAURENT DECREUSEFOND
Affiliation:
Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75 634 Paris Cedex 13, France
GILLES ZÉMOR
Affiliation:
Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75 634 Paris Cedex 13, France
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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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 1 , March 1997 , pp. 27 - 38
Copyright
1997 Cambridge University Press

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