On minimal pseudo-codewords

The performance of linear-programming decoding of a binary linear code described by a parity-check matrix depends on the set of pseudo-codewords associated to this matrix and in particular, on the set of minimal pseudo-codewords. This paper attempts to provide an algebraic characterization of the minimal pseudo-codewords. It also provides a connection between the fundamental cone of a Tanner graph and the fundamental cone of its Forney-style factor graph.