Lattices from Codes for Harnessing Interference: An Overview and Generalizations

TL;DR

This paper reviews lattice constructions from codes that enable interference management, introduces a new general construction called Construction π_D, and explores lattices over algebraic integers for advanced communication strategies.

Contribution

It presents a unified framework for lattice constructions, including a novel generalization, and extends the concept to algebraic integers, broadening applicability.

Findings

Construction π_D subsumes previous lattice constructions

Lattices over algebraic integers enable new interference harnessing techniques

The overview clarifies algebraic structures needed for efficient lattice-based communication

Abstract

In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D, and Construction $\pi_A$ (previously called product construction) recently proposed by the authors. We then discuss two generalizations where the first one is a general construction of lattices named Construction $\pi_D$ subsuming the above three constructions as special cases and the second one is to go beyond principal ideal domains and build lattices over algebraic integers.