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. 6. The classical versus fractional distance of the “normal realizations” of the Reed–Muller(n 1, n) codes [31]. The classical distance of these codes is exactly n=2. The upper part of the fractional distance curve follows roughly