Solving the error correcting code is an important goal with regard to communication theory. To reveal the error correcting code characteristics, several researchers have applied a statistical-mechanical approach to this problem. In our research, we have treated the error correcting code as a Bayes inference framework. Carrying out the inference in practice, we have applied the NMF (naive mean field) approximation to the MPM (maximizer of the posterior marginals) inference, which is a kind of Bayes inference. In the field of artificial neural networks, this approximation is used to reduce computational cost through the substitution of stochastic binary units with the deterministic continuous value units. However, few reports have quantitatively described the performance of this approximation. Therefore, we have analyzed the approximation performance from a theoretical viewpoint, and have compared our results with the computer simulation.

In this paper, we describe an implementation of analog neural network system with on-line learning capability. A learning rule using the simultaneous perturbation is adopted. Compared with usage of the ordinary back-propagation method, we can easily implement the simultaneous perturbation learning rule. The neural system can monitor weight values and an error value. The exclusive OR problem and a simple function problem are shown.

This paper describes a neuro-based optimization algorithm for three dimensional (3-D) rectangular puzzles which are the problems to arrange the irregular-shaped blocks so that they perfectly fit into a fixed three dimensional rectangular shape. First, the fitting function of the 3-D block, which means the fitting degree of each irregular block to the neighboring block and the rectangular configuration, is described. Next, the energy function for the 3-D rectangular puzzles is proposed, where the horizontal rotation of the block is also considered. Finally, our optimization method is applied to several examples using the 3-D analog neural array and it is shown that our algorithm is useful for solving 3-D rectangular puzzles.

This paper describes a neuro-based optimization algorithm for three dimensional (3-D) cylindric puzzles which are problems to arrange the irregular-shaped slices so that they perfectly fit into a fixed three dimensional cylindric shape. First, the idea to expand the 2-dimensional tiling technique to 3-dimensional puzzles is described. Next, to energy function with the fitting function of each polyomino is introduced, which is available for 3-D cylindric puzzles. Furthermore our algorithm is applied to several examples using the analog neural array. Finally, it is shown that our algorithm is useful for solving 3-D cylindric puzzles.