  Communication compression techniques are of growing interests for solving the
decentralized optimization problem under limited communication, where the
global objective is to minimize the average of local cost functions over a
multi-agent network using only local computation and peer-to-peer
communication. In this paper, we propose a novel compressed gradient tracking
algorithm (C-GT) that combines gradient tracking technique with communication
compression. In particular, C-GT is compatible with a general class of
compression operators that unifies both unbiased and biased compressors. We
show that C-GT inherits the advantages of gradient tracking-based algorithms
and achieves linear convergence rate for strongly convex and smooth objective
functions. Numerical examples complement the theoretical findings and
demonstrate the efficiency and flexibility of the proposed algorithm.
