Hostname: page-component-5d59c44645-mrcq8 Total loading time: 0 Render date: 2024-03-02T22:37:45.363Z Has data issue: false hasContentIssue false

On the Error-Correcting Capabilities of Cycle Codes of Graphs

Published online by Cambridge University Press:  01 March 1997

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

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
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)