Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with N Gaussian inputs and P deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, α = P/N, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to α ∼ O(1). The most relevant results are: 1) the simulation supports the validity of the analytical prediction, and 2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of α.