On the dimension of certain LDPC codes from q-regular bipartite graphs
Peter Sin
University of Florida

Abstract:

In recent years low density parity check codes have become a topic of practical and theoretical importance in coding theory. These codes can be contructed either randomly or in a systematic way. One such systematic construction was given in a 2004 paper, using certain regular bipartite graphs, first studied by Lazebnik and Ustimenko. The construction open the dimension of these codes, for which a conjecture was proposed. In this talk, I will outline a proof of this conjecture. The conjecture is proved by first showing that the parity check matrices of these codes are submatrices of the incidence matrices of symplectic generalized quadrangles. This allows us to use the geometry and group representation theory associated with these quadrangles to make the necessary calculation.

I will also mention some closely related open problems. .