Voronoi Shaping with Efficient Encoding

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 $\Lambdas \subseteq \textbf{K}\mathbb{Z}ⁿ \subseteq \Lambdac$, 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 ($E8$) and Leech ($\Lambda{24}$) lattices as shaping lattices.