Spectral Graph Theory Lecture 12 Expander Codes

Our construction of error-correcting codes will exploit bipartite expander graphs (as these give a much cleaner construction than the general case). Let’s begin by examining what a bipartite expander graph should look like. It’s vertex set will have two parts, U and V , each having n vertices. Every vertex will have degree d, and every edge will go from a vertex in U to a vertex in V . In the same way that we view ordinary expanders as approximations of complete graphs, we will view bipartite expanders as approximations of complete bipartite graphs1. That is, if we let Kn,n denote the complete bipartite graph, then we want a d-regular bipartite graph G such that