LP Pseudocodewords of Cycle Codes are Half-Integral
Combinatorics
2012-12-13 v1 Information Theory
math.IT
Abstract
In his Ph.D. disseration, Feldman and his collaborators define the linear programming decoder for binary linear codes, which is a linear programming relaxation of the maximum-likelihood decoding problem. This decoder does not, in general, attain maximum-likelihood performance; however, the source of this discrepancy is known to be the presence of non-integral extreme points (vertices) within the fundamental polytope, vectors which are also called nontrivial linear programming pseudocodewords. Restricting to the class of cycle codes, we provide necessary conditions for a vector to be a linear programming pseudocodeword. In particular, the components of any such pseudocodeword can only assume values of zero, one-half, or one.
Cite
@article{arxiv.1212.2953,
title = {LP Pseudocodewords of Cycle Codes are Half-Integral},
author = {Nathan Axvig},
journal= {arXiv preprint arXiv:1212.2953},
year = {2012}
}
Comments
13 pages