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. 1. A factor graph for the (7; 4; 3) Hamming code. The nodes f1; 2; 3; 4; 5; 6; 7g drawn in open circles correspond to variable nodes, whereas nodes fA;B;Cg in black squares correspond to check nodes.