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 a priori information about the lattice
structure lead to a simplification of the model.