Network Coding Capacity: A Functional Dependence Bound

TL;DR

This paper introduces a new, easily computable outer bound for network coding capacity based on functional dependencies, which is tighter than some existing bounds and addresses the complexity issues in capacity region determination.

Contribution

The paper presents a novel outer bound on network coding capacity derived from functional dependencies, improving computational feasibility and tightness over previous bounds.

Findings

The new bound is computationally easier to evaluate.

It is tighter than some existing bounds.

The approach leverages functional dependence characterization.

Abstract

Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors $\Gamma^{*}$, which is known to be an extremely hard problem. On the other hand, calculating the explicitly known linear programming bound is very hard in practice due to an exponential growth in complexity as a function of network size. We give a new, easily computable outer bound, based on characterization of all functional dependencies in networks. We also show that the proposed bound is tighter than some known bounds.