To efficiently compute linear functions of the measurements in sensor networks, it was recently shown that the superposition property of the wireless multiple-access channel can profitably be exploited. Using suitable pre- and post-processing functions operating on real sensor readings and on the superimposed signal received by a fusion center, respectively, the natural computation property of the wireless channel can be adapted such that a much larger class of functions is efficiently computable as well. In this paper, we analyze the space of functions which are in principle computable, or at least approximable, in an analog fashion via a wireless multiple-access channel and show to what extend this impacts the communication pattern and the complexity of nodes. Finally, we change the transmission scenario to a sequence of successively received channel outputs and observe that the resulting questions on the computability of functions are related to the famous 13th Hilbert problem.     «

To efficiently compute linear functions of the measurements in sensor networks, it was recently shown that the superposition property of the wireless multiple-access channel can profitably be exploited. Using suitable pre- and post-processing functions operating on real sensor readings and on the superimposed signal received by a fusion center, respectively, the natural computation property of the wireless channel can be adapted such that a much larger class of functions is efficiently computabl...     »