Solving problems of maximum likelihood decoding of graph theoretic codes via a Hopfield neural network

The authors present a neural network approach to solving the problem of decoding graph theoretic codes (GTCs). The equivalence relation has first been established between the problem of maximum likelihood decoding (MLD) of graph theoretic codes and that of minimizing an energy function of the Hopfield networks associated with those graphs (J. Bruck and M. Blaum 1989). This, is turn, allows construction of a Hopfield neural network which performs a MLD function in a natural way. However, the existence of the local minima problem, although considerably relaxed in these nets, prevents the completeness of the new decoding approach. Therefore, the authors modify the traditional Hopfield model by adding a detection mechanism to overcome the problem. Statistical analysis and simulations are provided to show the effectiveness of the new model