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

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2 Author(s)
Lifshitz, A. ; Sch. of Electr. Eng., Tel Aviv Univ., Ramat Aviv, Israel ; Be'ery, Y.

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.

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Communications, IEEE Transactions on  (Volume:60 ,  Issue: 4 )