This paper describes the error probability of the second order BAM estimated by a computer simulation and an analytical calculation method. The computer simulation suggests that the iterations to retrieve a library pattern almost converge within four times and the difference between once and twice is much larger than that between twice and four times. The error probability at the output of the second iteration is estimated by the analytical method. The effect of the noise bits is also estimated using the analytical method. The BAM with larger n is more robust for the noise. For example, the noise bits of 0.15n cause almost no degradation of the error probability when n is larger than 100. If the error probability of 10-4 is allowable, the capacity of the second order BAM can be increased by about 40% in the presence of 0.15n noise bits when n is larger than 500.

This paper describes relation between the number of library pairs and error probability to have all the pairs as fixed points for second-order bidirectional associative memory (BAM). To estimate accurate error probability, three methods have been compared; (a) Gaussian approximation, (b) characteristic function method, and (c) Hermite Gaussian approximation (proposed by this paper). Comparison shows that Gaussian approximation is valid for the larger numbers of neurons in both two layers than 1000. While Hermite Gaussian approximation is applicable for the larger number of neurons than 30 when Hermite polynomials up to 8th are considered. Capacity of second-order BAM at the fixed error probability is estimated as the function of the number of neurons.