Multi-round 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 computation of type-threshold functions which include the maximum, minimum, and indicator functions as special cases. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates tend to zero as the number of sensors increases. In this paper, wireless sensor networks are modeled as fully connected Gaussian networks with equal channel gains, which are termed collocated Gaussian networks. A general multi-round coding scheme exploiting not only the broadcast property but also the superposition property of Gaussian networks 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 even if the number of sensors tends to infinity.