Linear network coding for two-unicast-Z networks: A commutative algebraic perspective and fundamental limits

摘要

We consider a two-unicast-Z network over a directed acyclic graph of unit capacitated edges; the two-unicast-Z network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast-Z networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and nonlinear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous result of Wang et. al. regarding feasibility of rate (1,1) in the network.