Discrete Isoperimetric Inequalities and the Probability of a Decoding Error

Authors:
Jean-Pierre Tillich;Gilles Zémor
Affiliations:
LRI, bâtiment 490, Université Paris-Sud, 91405 Orsay, France (e-mail: tillich@lri.fr);École Nationale Supérieure des Télécommunications, 75 634 Paris 13, France (e-mail: zemor@infres.enst.fr)
Venue:
Combinatorics, Probability and Computing
Year:
2000

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Abstract

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.