English

The Voronoi Region of the Barnes-Wall Lattice $\Lambda_{16}$

Information Theory 2024-10-28 v1 math.IT Metric Geometry

Abstract

We give a detailed description of the Voronoi region of the Barnes-Wall lattice Λ16\Lambda_{16}, including its vertices, relevant vectors, and symmetry group. The exact value of its quantizer constant is calculated, which was previously only known approximately. To verify the result, we estimate the same constant numerically and propose a new very simple method to quantify the variance of such estimates, which is far more accurate than the commonly used jackknife estimator.

Keywords

Cite

@article{arxiv.2301.06092,
  title  = {The Voronoi Region of the Barnes-Wall Lattice $\Lambda_{16}$},
  author = {Daniel Pook-Kolb and Erik Agrell and Bruce Allen},
  journal= {arXiv preprint arXiv:2301.06092},
  year   = {2024}
}

Comments

8 pages, 2 figures. This work has been submitted to the IEEE for possible publication