Distributed averaging in the presence of interference

Distributed algorithms, in general, assume that the information sent from a transmitter to a receiver reaches the receiver unharmed and unaltered. However, when the entire network engages in simultaneous such transmissions, it is likely that the intended transmission incurs interference from the transmissions by other transmitter-receiver pairs. In this paper, we study distributed averaging when each transmission is received with an additive unwanted interference component. We model the the interference incurred at each communication link to belong to the range space of a matrix; this matrix may be different across different links. Under this algebraic structure, we outline (local) information alignment strategies such that perfect average is achievable over a subspace complimentary to the network interference subspace.