Data-Driven Lattices for Vector Quantization

Natalie Lang, Itamar Assaf, Omer Bokobza, Nir Shlezinger

Abstract: Lattice quantization implements vector quantization with a simple structured formulation, that is fully determined by the lattice generator matrix and a distance metric. The conventional approach constructs lattices for quantization by minimizing a bound on the rate-distortion tradeoff, which holds for non-overloaded quantizers, while in practice, overloading prevention typically affects performance. In this work we propose a novel technique for constructing lattice that considers possibly overloaded quantizers, for which we learn the lattice generator matrix by directly evaluating the distortion at its output. For training purposes, we convert the continuous-to-discrete quantizer mapping into a differentiable machine learning model, optimized in an unsupervised manner to best fit the data. Subsequently, the data-driven lattice is fixed and ordinarily combined into the quantization process. We provide numerical studies showing that our method attains improved performance compared with alternative lattice designs for various dimensions, and generalizes well to unseen data.