Characterizing per node degrees of freedom in an interference network

We consider the problem of interference alignment in vector subspaces of the available vector space at each communication node. We assume that the communication nodes are divided into two sets, the transmitting nodes and the receiving nodes. A full duplex node may be treated as two nodes split into the transmitting node and a receiving node. We consider only a part of communication network that is defined by the set of links from the transmitting node to receiving nodes that are considered to generate interference at their receiving nodes. The interference network is defined as this subset of the links and their transmitting and receiving nodes. The goal is to maximize the size of subspaces of the available vector space at each node that is interference free, i.e., at the transmitting node this subspace may be freely used for the transmission and at a receiving point this subspace may be freely used for reception. We provide a computable necessary and sufficient condition for the achievablility of such subspaces in an arbitrary network. therefore, given a topology for an interference network and the size of vector spaces available at each node (the number of antennas), we can provide a definite answer if a set of subspaces with a given size (degrees of freedom per node) is achievable or not.