English

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

Information Theory 2011-06-15 v2 math.IT

Abstract

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.

Keywords

Cite

@article{arxiv.1105.2631,
  title  = {On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes},
  author = {Asi Lifshitz and Yair Be'ery},
  journal= {arXiv preprint arXiv:1105.2631},
  year   = {2011}
}
R2 v1 2026-06-21T18:06:45.975Z