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Discrete Isoperimetric Inequalities and the Probability of a Decoding Error

Published online by Cambridge University Press:  14 February 2001

JEAN-PIERRE TILLICH  and
GILLES ZÉMOR
JEAN-PIERRE TILLICH
Affiliation:
LRI, bâtiment 490, Université Paris-Sud, 91405 Orsay, France (e-mail: tillich@lri.fr)
GILLES ZÉMOR
Affiliation:
École Nationale Supérieure des Télécommunications, 75 634 Paris 13, France (e-mail: zemor@infres.enst.fr)
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Abstract

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We derive improved isoperimetric inequalities for discrete product measures on the n-dimensional cube. As a consequence, a general theorem on the threshold behaviour of monotone properties is obtained. This is then applied to coding theory when we study the probability of error after decoding.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 5 , September 2000 , pp. 465 - 479
Copyright
2000 Cambridge University Press