On achievable rates for analog computing real-valued functions over the wireless channel

In this work, a recently proposed analog transmission scheme is considered, which harnesses interference for reliably and efficiently computing real-valued functions over a wireless channel. To better understand the corresponding trade-off between the conflicting demands of reliability and efficiency, in this paper we choose an information theoretic perspective by analyzing the scheme within the framework of computation coding. Towards this end, we first adapt the standard notions of a computation code and an achievable computation rate to our specific needs and then provide rate expressions for some simple but insightful examples. It turns out that the achievable computation rates not only depend on the function to be computed but also on the desired accuracy and the number of concurrently active transmitters.