Voronoi Shaping for Lattices With Efficient Encoding

In this letter, we propose a Voronoi shaping method for shaping lattices, Λ _s, and coding lattices, Λ _c, satisfying Λ _s ⊆ K\mathbb Zⁿ ⊆ Λ _c ⊆ \mathbb Zⁿ, with K being an integer diagonal matrix. This assumption is easily satisfied for lattices obtained from error-correcting codes. For these lattices, using the proposed strategy, lattice encoding complexity is reduced to the encoding complexity of the underlying error-correcting code. Our proposal is illustrated for Construction-D lattices with Gosset ( E₈) and Leech ( Λ ₂₄) lattices as shaping lattices.