Polytope of correct (linear programming) decoding and low-weight pseudo-codewords

@article{Chertkov2011PolytopeOC,
  title={Polytope of correct (linear programming) decoding and low-weight pseudo-codewords},
  author={Michael Chertkov and Mikhail G. Stepanov},
  journal={2011 IEEE International Symposium on Information Theory Proceedings},
  year={2011},
  pages={1648-1652}
}
We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowest-weight pseudo-codeword as a non-convex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the… CONTINUE READING
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