Voronoi Shaping with Efficient Encoding

TL;DR

This paper introduces a Voronoi shaping method that simplifies encoding for certain lattices, making the process more efficient by reducing complexity to linear code encoding, especially for lattices derived from error-correcting codes.

Contribution

It presents a novel Voronoi shaping technique with reduced encoding complexity applicable to specific lattice structures, including construction-D lattices with well-known shapes.

Findings

Encoding complexity is reduced to linear code encoding.

Explicit coset representatives are obtained for the lattices.

Method is demonstrated with E8 and Leech lattices.

Abstract

In this letter, we propose a Voronoi shaping method with reduced encoding complexity. The method works for integer shaping and coding lattices satisfying the chain $\Lambda_s \subseteq \textbf{K}\mathbb{Z}^n \subseteq \Lambda_c$, with $\textbf{K}$ an integer diagonal matrix. This assumption is easily satisfied for lattices obtained from error-correcting codes. For those lattices, using this strategy, an explicit set of coset representatives is obtained and lattice encoding complexity is reduced to the linear code encoding complexity. Our proposal is illustrated in construction-D lattices with Gosset ($E_8$) and Leech ($\Lambda_{24}$) lattices as shaping lattices.