  Lattice decoders constructed with neural networks are presented. Firstly, we
show how the fundamental parallelotope is used as a compact set for the
approximation by a neural lattice decoder. Secondly, we introduce the notion of
Voronoi-reduced lattice basis. As a consequence, a first optimal neural lattice
decoder is built from Boolean equations and the facets of the Voronoi cell.
This decoder needs no learning. Finally, we present two neural decoders with
learning. It is shown that L1 regularization and {\em a priori} information
about the lattice structure lead to a simplification of the model.
