Information alignment for consensus with interference

This paper studies distributed averaging of arbitrary vectors in the presence of network interference by casting an algebraic structure over the interference. While communicating locally with its neighbors for consensus, each agent causes an additive interference, lying on a low-dimensional subspace, in other communication links. We consider a particular case when this interference subspace depends only on the inter-ferer, referred to as uniform outgoing interference. We show that consensus is possible in a low-dimensional subspace of the initial conditions whose dimension is complimentary to the largest interference subspace across all of the agents. In this context, we derive a global information alignment and a local pre-conditioning, followed by local consensus iterations to ensure subspace consensus. We further provide the conditions under which this subspace consensus recovers the exact average. The analytical results are illustrated graphically to describe the setup and the information alignment scheme.