Linear programming bounds on the degree distributions of LDPC code ensembles

This work considers the behavior of the degree distributions of capacity-approaching low-density parity-check (LDPC) code ensembles via linear programming (LP) bounds. These LP bounds are information-theoretic, and they apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. Analytical solutions of these bounds are given in closed form, and the bounds are compared for the BEC with some specific degree distributions of capacity-achieving sequences of LDPC code ensembles. These LP bounds are shown to be informative and are easy to calculate. Due to space limitations, the derivation of the LP bounds is outlined, and the reader is referred to the full paper version for complete proofs and further discussions.