  We propose a new decentralized average consensus algorithm with compressed
communication that scales linearly with the network size n. We prove that the
proposed method converges to the average of the initial values held locally by
the agents of a network when agents are allowed to communicate with compressed
messages. The proposed algorithm works for a broad class of compression
operators (possibly biased), where agents interact over arbitrary static,
undirected, and connected networks. We further present numerical experiments
that confirm our theoretical results and illustrate the scalability and
communication efficiency of our algorithm.
