  In this paper we explore the decision regions of Linear Programming (LP)
decoding. We compare the decision regions of an LP decoder, a Belief
Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We
study the effect of minimal-weight pseudocodewords on LP decoding. We present
global optimization as a method for finding the minimal pseudoweight of a given
code as well as the number of minimal-weight generators. We present a complete
pseudoweight distribution for the [24; 12; 8] extended Golay code, and provide
justifications of why the pseudoweight distribution alone cannot be used for
obtaining a tight upper bound on the error probability.
