Entropy vectors and network codes

TL;DR

This paper explores the connection between entropy functions and network coding, showing how non-Shannon inequalities can improve bounds on network capacity and highlighting limitations of linear codes.

Contribution

It introduces an entropy-based framework for analyzing network coding problems and demonstrates the importance of non-Shannon inequalities in capacity bounds.

Findings

Entropy functions relate to network multicast solvability.

Non-Shannon inequalities tighten capacity bounds.

Linear network codes are insufficient in some cases.

Abstract

We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and abelian) network codes and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions.