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Book Chapter
An Overview of the Isoperimetric Method in Coding Theory (Extended Abstract) [Invited Paper]
Book Series
Lecture Notes in Computer Science
Publisher
Springer Berlin / Heidelberg
ISSN
0302-9743 (Print) 1611-3349 (Online)
Volume
Volume 1746/1999
Book
Cryptography and Coding
DOI
10.1007/3-540-46665-7
Copyright
1999
ISBN
978-3-540-66887-9
DOI
10.1007/3-540-46665-7_14
Page
798
Subject Collection
Computer Science
SpringerLink Date
Friday, January 01, 1999
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An Overview of the Isoperimetric Method in Coding Theory (Extended Abstract) [Invited Paper]
Jean-Pierre Tillich
5
and Gilles Zémor
6
(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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