*Europhys. Lett.*,

**45**(6), pp. 739-744 (1999)

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

Departamento de Física Teórica,
Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain

Received:
3
May
1998

Accepted:
6
January
1999

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, , 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 . 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*.

PACS: 87.10.+e – Biological and medical physics: General theory and mathematical aspects / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems

*© EDP Sciences, 1999*