An Equivalence between Network Coding and Index Coding

TL;DR

This paper establishes a general equivalence between network coding and index coding problems, including both linear and non-linear codes, through an efficient reduction that preserves feasibility.

Contribution

It introduces a comprehensive reduction method that demonstrates the equivalence of network coding and index coding in the general case, extending previous linear-only results.

Findings

Network coding and index coding are equivalent in the general setting.

The reduction preserves feasibility between the two problems.

Previous connections were limited to linear codes.

Abstract

We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and non-linear codes. Specifically, we present an efficient reduction that maps a network coding instance to an index coding one while preserving feasibility. Previous connections were restricted to the linear case.