Zig-zag and replacement product graphs and LDPC codes

Christine A. Kelley; Deepak Sridhara; Joachim Rosenthal

doi:10.3934/amc.2008.2.347

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2008, Volume 2, Issue 4: 347-372. Doi: 10.3934/amc.2008.2.347

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Zig-zag and replacement product graphs and LDPC codes

1.
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588
2.
1251 Waterfront Place, Seagate Technology, Pittsburgh, PA 15222
3.
Institut für Mathematik, Universität Zürich, Zürich, CH-8057

Received: August 2007

Revised: August 2008

Published: November 2008

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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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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