  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.
