Zig-zag and Replacement Product Graphs and LDPC Codes
Christine A. Kelley, Deepak Sridhara, and Joachim Rosenthal
TL;DR
This paper explores how zig-zag and replacement product graphs can be used to construct LDPC codes with good expansion properties, introducing a modified zig-zag product for unbalanced bipartite graphs.
Contribution
It introduces a modified zig-zag product for unbalanced biregular bipartite graphs and analyzes their application in LDPC code construction.
Findings
New family of expander graphs from zig-zag and replacement products
Modified zig-zag product for unbalanced bipartite graphs
Potential for improved LDPC code performance
Abstract
The performance of codes defined from graphs depends on the expansion property of the underlying graph in a crucial way. Graph products, such as the zig-zag product and replacement product provide new infinite families of constant degree expander graphs. The 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.
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Taxonomy
TopicsError Correcting Code Techniques · Cooperative Communication and Network Coding · Advanced Wireless Communication Techniques