An algebraic mincut-maxflow theorem

Abstract

Can we design a communication network just like a huge linear time-invariant filter? To answer this question, we generalize the celebrated mincut-maxflow theorem to linear time-invariant networks where edges are labeled with transfer functions instead of integer capacity constraints. We prove that when the transfer functions are linear time-invariant, the fundamental design limit, mincut, is achievable by a linear time-invariant scheme regardless of the topology of the network. Whereas prior works are based on layered networks, our proof has a novel way of converting an arbitrary relay network to an equivalent acyclic single-hop relay network, which we call Network Linearization. This theorem also reveals a strong connection between network coding and linear system theory.