Achieving uniform side information gain with multilevel lattice codes over the ring of integers

TL;DR

This paper introduces a novel lattice coding scheme for index coding problems, leveraging Construction π_A lattices over integers to optimize broadcast efficiency and achieve uniform side information gain.

Contribution

It proposes CRT lattice index coding using Construction π_A over integers, providing bounds and conditions for uniform side information gain, with theoretical analysis and design examples.

Findings

Derived an upper bound for side information gain.

Established conditions for uniform gain.

Demonstrated efficiency through theoretical analysis and examples.

Abstract

The index coding problem aims to optimise broadcast communication by taking advantage of receiver-side information to improve transmission efficiency. In this letter, we explore the application of Construction $\pi_A$ lattices to index coding. We introduce a coding scheme, named \textit{CRT lattice index coding}, using Construction $\pi_A$ over $\mathbb{Z}$ to address the index coding problem. It is derived an upper bound for side information gain of a CRT lattice index code and conditions for the uniformity of this gain. The efficiency of this approach is shown through theoretical analysis and code design examples.