  This paper studies distributed strategies for average-consensus of arbitrary
vectors in the presence of network interference. We assume that the underlying
communication on any \emph{link} suffers from \emph{additive interference}
caused due to the communication by other agents following their own consensus
protocol. Additionally, no agent knows how many or which agents are interfering
with its communication. Clearly, the standard consensus protocol does not
remain applicable in such scenarios. In this paper, we cast an algebraic
structure over the interference and show that the standard protocol can be
modified such that the average is reachable in a subspace whose dimension is
complimentary to the maximal dimension of the interference subspaces (over all
of the communication links). To develop the results, we use \emph{information
alignment} to align the intended transmission (over each link) to the
null-space of the interference (on that link). We show that this alignment is
indeed invertible, i.e. the intended transmission can be recovered over which,
subsequently, consensus protocol is implemented. That \emph{local} protocols
exist even when the collection of the interference subspaces span the entire
vector space is somewhat surprising.
