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On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes
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