Zig-zag and Replacement Product Graphs and LDPC Codes
arXiv:cs/0611155
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.
Submitted to Journal of Advances in Mathematics of Communications, Aug. 2007