Generalized Cut-Set Bounds for Broadcast Networks

TL;DR

This paper introduces new, tighter network coding bounds for broadcast networks by using diverse set operations on cuts, improving upon traditional bounds and demonstrated through application to combination networks.

Contribution

It presents a novel set of bounds for broadcast networks that utilize various set operations and are derived solely from Shannon entropy's submodularity.

Findings

New bounds are tighter than traditional cut-set bounds.

Bounds are applicable to general broadcast networks.

Application to combination networks demonstrates their effectiveness.

Abstract

A broadcast network is a classical network with all source messages collocated at a single source node. For broadcast networks, the standard cut-set bounds, which are known to be loose in general, are closely related to union as a specific set operation to combine the basic cuts of the network. This paper provides a new set of network coding bounds for general broadcast networks. These bounds combine the basic cuts of the network via a variety of set operations (not just the union) and are established via only the submodularity of Shannon entropy. The tightness of these bounds are demonstrated via applications to combination networks.