Header

UZH-Logo

Maintenance Infos

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.

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.

Statistics

Citations

Dimensions.ai Metrics
8 citations in Web of Science®
9 citations in Scopus®
12 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

88 downloads since deposited on 09 Feb 2009
2 downloads since 12 months
Detailed statistics

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:18 Feb 2018 10:45
Publisher:American Institute of Mathematical Sciences
ISSN:1930-5338
OA Status:Hybrid
Publisher DOI:https://doi.org/10.3934/amc.2008.2.347
Related URLs:http://arxiv.org/abs/cs/0611155v2

Download

Download PDF  'Zig-zag and replacement product graphs and LDPC codes'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 2)
Size: 394kB
Download PDF  'Zig-zag and replacement product graphs and LDPC codes'.
Preview
Content: Accepted Version
Filetype: PDF (Accepted manuscript, Version 1)
Size: 291kB