  A distributed average consensus algorithm robust to a wide range of impulsive
channel noise distributions is proposed. This work is the first of its kind in
the literature to propose a consensus algorithm which relaxes the requirement
of finite moments on the communication noise. It is shown that the nodes reach
consensus asymptotically to a finite random variable whose expectation is the
desired sample average of the initial observations with a variance that depends
on the step size of the algorithm and the receiver nonlinear function. The
asymptotic performance is characterized by deriving the asymptotic covariance
matrix using results from stochastic approximation theory. Simulations
corroborate our analytical findings and highlight the robustness of the
proposed algorithm.
