Neural Lattice Decoders

TL;DR

This paper introduces neural lattice decoders that leverage geometric properties of lattices, including a no-learning optimal decoder and learned decoders with regularization, enhancing decoding efficiency and structure utilization.

Contribution

It presents the first neural lattice decoder based on Voronoi-reduced bases and introduces learned decoders that incorporate lattice structure for improved performance.

Findings

Optimal decoder requires no learning

Regularization simplifies neural decoders

Voronoi-reduced basis enhances decoding efficiency

Abstract

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.