  An error correcting code using a tree-like multilayer perceptron is proposed.
An original message $\mbi{s}^0$ is encoded into a codeword $\boldmath{y}_0$
using a tree-like committee machine (committee tree) or a tree-like parity
machine (parity tree). Based on these architectures, several schemes featuring
monotonic or non-monotonic units are introduced. The codeword $\mbi{y}_0$ is
then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by
noise. The analytical performance of these schemes is investigated using the
replica method of statistical mechanics. Under some specific conditions, some
of the proposed schemes are shown to saturate the Shannon bound at the infinite
codeword length limit. The influence of the monotonicity of the units on the
performance is also discussed.
