On codes designed via algebraic lifts of graphs

Over the past few years several constructions of protograph codes have been proposed that are based on random lifts of suitably chosen base graphs. More recently, an algebraic analog of this approach was introduced using the theory of voltage graphs. The strength of the voltage graph framework is the ability to analyze the resulting derived graph algebraically, even when the voltages themselves are assigned randomly. Moreover, the theory of voltage graphs provides insight to designing lifts of graphs with particular properties. In this paper we illustrate how the properties of the derived graphs and the corresponding codes relate to the voltage assignments. In particular, we present a construction of LDPC codes by giving an algebraic method of choosing the permutation voltages and illustrate the usefulness of the proposed technique via simulation results.