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An Overview of the Isoperimetric Method in Coding Theory (Extended Abstract) [Invited Paper]

Jean-Pierre Tillich5 and Gilles Zémor6

(5)  Université Paris-Sud, bâtiment 490, 91405 Orsay, France
(6)  École Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris 13, France
Abstract
When decoding a threshold phenomenon is often observed: decoding deteriorates very suddenly around some critical value of the channel parameter. Threshold behaviour has been studied in many situations outside coding theory and a number of tools have been developped. One of those turns out to be particularly relevant to coding, namely the derivation of isoperimetric inequalities for product measures on Hamming spaces. we discuss this approach and derive consequences.

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