Structural Routability of n-Pairs Information Networks

Information does not generally behave like a flow in communication networks with multiple sources and sinks. However, it is often conceptually and practically useful to be able to associate separate data streams with each source-sink pair, with only routing and no coding performed at the network nodes. This raises the question of whether there is a nontrivial class of network topologies for which achievability is always equivalent to ‘routability’, for any combination of source signals and positive channel capacities. This chapter considers possibly cyclic, directed, errorless networks with n source-sink pairs and mutually independent source signals. The concept of downward matching is introduced and it is shown that, if the network topology is downward matched, then a given combination of source signals, demand rates and channel capacities is achievable if and only if there is a feasible multicommodity flow.