Voronoi Shaping for Lattices With Efficient Encoding

摘要

In this letter, we propose a Voronoi shaping method for shaping lattices, Lambda(s), and coding lattices, Lambda(c), satisfying Lambda(s) subset of KZ(n) subset of Lambda(c) subset of Z(n), 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 (E-8) and Leech (Lambda(24)) lattices as shaping lattices.