Numerical Comparison of IP Formulations as ML Decoders

For binary linear codes with short and medium block length ML decoding can be achieved by solving the associated integer programming (IP) problem with a general purpose solver. IP also offers algorithms for computing the minimum distance. In this article, we present several IP formulations and computationally compare them on various LDPC and BCH codes. Most of these formulations are obtained by forcing integrality on linear programming (LP) decoding formulations proposed in the literature.