A new method is given for performing approximate maximum-likelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor graph or parity-check representation of the code. The resulting… (More)
Fig. 2. The equivalence of the polytopes and Q in three dimensions. The polytope is defined as the set of points inside the unit hypercube with l distance at least one from all odd-weight hypercube vertices. The polytope Q is the convex hull of even-weight hypercube vertices.