On the error performance of the $A_n$ lattices

TL;DR

This paper derives explicit formulas for the moments of the Voronoi cell of the $A_n$ lattice, enabling precise error probability predictions for lattice codes based on $A_n$.

Contribution

It provides new explicit formulas for Voronoi cell moments of $A_n$ lattices, improving error probability estimation for related lattice codes.

Findings

Explicit formulas for Voronoi cell moments of $A_n$

Accurate prediction of lattice code error probabilities

Enhanced understanding of $A_n$ lattice performance

Abstract

We consider the root lattice $A_n$ and derive explicit formulae for the moments of its Voronoi cell. We then show that these formulae enable accurate prediction of the error probability of lattice codes constructed from $A_n$.