An Optimal Linear Coding for Index Coding Problem

TL;DR

This paper presents an optimal linear coding scheme for the index coding problem, providing a unified algebraic approach that is applicable to both unicast and groupcast scenarios, with particular emphasis on groupcast applications.

Contribution

It introduces a linear coding program that is proven to be optimal from a linear perspective for solving index coding problems, including groupcast cases.

Findings

Proved the optimality of the linear coding solution.

Applicable to any number of messages.

Enhanced coding strategies for groupcast index coding.

Abstract

An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding problem is presented. The coding is proved to be the optimal solution from the linear perspective and can be easily utilize for any number of messages. The importance of this work is lying mostly on the usage of the presented coding in the groupcast index coding problem.