[IEEE Trans. on Information Theory, May 2015, pp. 2488-2509 ]
Achievable Rate Regions for Network Coding
Randall Dougherty, Chris Freiling, and Kenneth Zeger
Abstract
Determining the achievable rate region for networks
using routing, linear coding, or non-linear coding
is thought to be a difficult task in general,
and few are known.
We describe the achievable rate regions for four interesting networks
(completely for three and partially for the fourth).
In addition to the known matrix-computation method for proving
outer bounds for linear coding, we present a new method which
yields actual characteristic-dependent linear rank inequalities
from which the desired bounds follow immediately.