Noisy Beeping Networks

TL;DR

This paper introduces noisy beeping networks with limited communication and noise, providing noise-resilient algorithms that transform existing noiseless algorithms with minimal overhead, applicable to sensor and biological systems.

Contribution

It develops noise-resilient algorithms for beeping networks, transforming noiseless algorithms with only logarithmic overhead, and demonstrates optimality and simulation of distributed algorithms under noise.

Findings

Noise-resilient algorithms with O(log n) overhead for arbitrary networks.

Optimal coding schemes for node-coloring in cliques.

Simulation of CONGEST($B$) algorithms over noisy beeping networks with tight bounds.

Abstract

We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed probability when sensing the channel, which amounts to deducing a noisy received transmission. Such noisy networks have implications for ultra-lightweight sensor networks and biological systems. We show how to compute tasks in a noise-resilient manner over noisy beeping networks of arbitrary structure. In particular, we transform any algorithm that assumes a noiseless beeping network (of size $n$) into a noise-resilient version while incurring a multiplicative overhead of only $O(\log n)$ in its round complexity, with high probability. We show that our coding is optimal for some tasks, such as node-coloring of a clique. 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. The simulation succeeds with high probability and incurs an asymptotic multiplicative overhead of $O(B\cdot \Delta \cdot \min(n,\Delta^2))$ in the round complexity, where $\Delta$ is the maximal degree of the network. The overhead is tight for certain graphs, e.g., a clique. Further, this simulation implies a constant overhead coding for constant-degree networks.