Naive Mean Field Approximation for the Error Correcting Code

Brain Research Institute, RIKEN(Dated: February 2, 2008)Solving the error correcting code is an important goal with regard to communication theory. To reveal theerror correcting code characteristics, several researchers have applied a statistical-mechanical approach to thisproblem. In our research, we have treated the error correcting code as a Bayes inference framework. Carryingout the inference in practice, we have applied the NMF (naive mean field) approximation to the MPM (maxi-mizer of the posterior marginals) inference, which is a kind of Bayes inference. In the field of artificial neuralnetworks, this approximation is used to reduce computational cost through the substitution of stochastic binaryunits with the deterministic continuous value units. However, few reports have quantitatively described the per-formance of this approximation. Therefore, we have analyzed the approximation performance from a theoreticalviewpoint, and have compared our results with the computer simulation.I. INTRODUCTION