Cut-Set Bounds on Network Information Flow

TL;DR

This paper introduces a new method using irreducible sets to derive computable outer bounds on the capacity region of network information flow, improving upon existing bounds especially for correlated sources.

Contribution

It develops a novel framework based on irreducible sets to characterize and compute outer bounds for network capacity, applicable to both correlated and independent sources.

Findings

New bounds outperform existing graph-theoretic bounds.

Irreducible sets effectively identify information bottlenecks.

Method applicable to networks with correlated and independent sources.

Abstract

Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general. Characterizing the network coding capacity region requires determination of the set of all entropic vectors. Furthermore, computing the explicitly known linear programming bound is infeasible in practice due to an exponential growth in complexity as a function of network size. This paper focuses on the fundamental problems of characterization and computation of outer bounds for networks with correlated sources. Starting from the known local functional dependencies induced by the communications network, we introduce the notion of irreducible sets, which characterize implied functional dependencies. We provide recursions for computation of all maximal irreducible sets. These sets act as information-theoretic bottlenecks, and provide an easily computable outer bound. We extend the notion of irreducible sets (and resulting outer bound) for networks with independent sources. We compare our bounds with existing bounds in the literature. We find that our new bounds are the best among the known graph theoretic bounds for networks with correlated sources and for networks with independent sources.