Noisy beeping networks

Beeping networks consist of exceedingly simple computational devices whose communication is based on beeps and silence. In this work, we introduce noisy beeping networks, where the observed communication is noisy with some fixed probability of error. We show how to transform any algorithm over a noiseless beeping network into a noise-resilient version while incurring a multiplicative overhead of essentially O(log⁡n) in its round complexity, with high probability. Our coding is optimal for some (short) tasks, such as the node-coloring of cliques. Interestingly, in the case of coloring, our technique achieves the same complexity as the standard beeping model while being noise resilient. We further show how to simulate a large family of algorithms designed for distributed networks in the CONGEST(B) model over a noisy beeping network, with a multiplicative overhead of O(B⋅Δ⋅min⁡(n,Δ²)) in the round complexity, where Δ is the maximum degree of the network.