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Zig-zag and replacement product graphs and LDPC codes


Kelley, C; Sridhara, D; Rosenthal, J (2008). Zig-zag and replacement product graphs and LDPC codes. Advances in Mathematics of Communications, 2(4):347-372.

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.

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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5 citations in Web of Science®
9 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:09 Feb 2009 16:01
Last Modified:05 Apr 2016 12:57
Publisher:American Institute of Mathematical Sciences
ISSN:1930-5338
Publisher DOI:10.3934/amc.2008.2.347
Related URLs:http://arxiv.org/abs/cs/0611155v2
Permanent URL: http://doi.org/10.5167/uzh-12668

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