Some Properties of Successive Minima and Their Applications

TL;DR

This paper investigates properties of successive minima in lattices and applies these findings to enhance an algorithm for optimizing the achievable rate in integer-forcing strategies within cloud radio access networks.

Contribution

It introduces new properties of successive minima and uses them to improve an existing algorithm for network optimization.

Findings

Enhanced algorithm for maximizing achievable rate

Improved understanding of lattice successive minima

Potential applications in network optimization

Abstract

A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical applications points of view. In this paper, we first study some properties of successive minima and then employ some of them to improve the suboptimal algorithm for solving an optimization problem about maximizing the achievable rate of the integer-forcing strategy for cloud radio access networks in [1].