[IEEE Trans. on Information Theory, March 2008, pp. 1287-1291]
Network Coding Capacity with a Constrained Number of Coding Nodes
Jillian Cannons and Kenneth Zeger
Abstract
We study network coding capacity under a constraint on the total number of
network nodes that can perform coding. That is, only a certain number of
network nodes can produce coded outputs, whereas the remaining nodes are
limited to performing routing. We prove that every non-negative, monotonically
non-decreasing, eventually constant, rational-valued function on the
non-negative integers is equal to the capacity as a function of the number of
allowable coding nodes of some directed acyclic network.