Computation in Server-Assisted Noisy Networks

We analyze resilient protocols over noisy networks, focusing on the interesting setting where n computing parties (clients) are supported by a set of k assisting servers. All communication links suffer from random noise, and the goal is to design noise-resilient computations with low round-complexity compared to the noiseless case. We give tight bounds for the case where a constant number of servers is present. We show that Θ(log n) rounds are necessary and sufficient to compute any non-constant function of the clients' inputs, with error probability tending to 0. We further show a lower bound of Ω(log n/k) rounds, for networks with k < O(log n) servers. This lower bound suggests that additional assisting servers could help reducing the overall round complexity.