Interactive Computation of Type-Threshold Functions in Collocated Gaussian Networks

In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on the class of type-threshold functions, e.g., the maximum and indicator functions. A simple network model capturing both the broadcast and superposition properties of wireless channels is considered: the collocated Gaussian network. A general multi-round coding scheme exploiting superposition and interaction (through broadcast) is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity.