An Inequality on the Coding Gain of Densest Lattice Packingsin Successive Dimensions

Abstract

A lower bound of the form (\frac{2n}{n+1})^{\frac{1}{n}} γ_{n-1}^{\frac{n-1}{n}} is derived on the coding gainγ_n of the densest n-dimensional (n -D) lattice(s). The bound is obtained based on constructing ann -D lattice which consists of parallel layers. Each layer is selected as a translated version of a densest ( n-1)-D lattice. 0The relative positioning of the layers is adjusted to make the coding gain as large as possible. For large values of n, the bound is improved through tightening Ryskov‘s inequality on covering radius and minimum distance of a lattice.