Zig-zag and replacement product graphs and LDPC codes

Christine A. Kelley, Deepak Sridhara, Joachim Rosenthal

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the use of zig-zag and replacement product graphs for the construction of codes on graphs. A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs, and a proof of the expansion property of this modified zig-zag product is presented.

Original languageEnglish (US)
Pages (from-to)347-372
Number of pages26
JournalAdvances in Mathematics of Communications
Volume2
Issue number4
DOIs
Publication statusPublished - Nov 1 2008

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Keywords

  • Codes on graphs
  • Expander graphs
  • LDPC codes
  • Replacement product of a graph
  • Zig-Zag product

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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