Abstract
State of the art wireless network solutions are mainly concerned with forwarding human generated high-resolution image, audio, and video content. In doing so, interference is usually seen as a limitation to overcome so that the channel access of users is coordinated in time or frequency. In many emerging technologies, however, forwarding raw data messages is not necessary and should be avoided for efficiency improvements. Instead, there is a need for a reliable and efficient computation of functions thereof (e.g., computing the maximum flue gas concentration for fire detection, the average frequency drift in a Smart Grid, the minimum humidity in a greenhouse). This chapter deals with this type of problems and provides an overview of some recent results. In particular, it is demonstrated that for reliably computing real-valued functions over the wireless channel, harnessing interference rather than avoiding or canceling it can lead to huge performance gains. It is shown which real-valued functions can be essentially computed by following this paradigm and why this question is closely related to the famous 13th Hilbert problem. Then, the question is addressed of how efficiently such computations can be done in terms of the number of transmissions needed per function value. Subsequently, corresponding encoding and decoding strategies are presented and evaluated in its performance. The chapter concludes with a brief discussion of related and open problems.
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Notes
- 1.
Note that the results reviewed in this chapter show that this statement does not apply to the wireless multiple-access channel.
- 2.
Note that for neither of the two problems we introduced a probability distribution on the source symbols, which is in contrast to the standard information theoretic setting. From the perspective of a communications engineer, however, the problem statements given here are more relevant as any practical coding scheme has to work for any choice of source symbols.
- 3.
The ideal WMAC is noiseless so that it is not necessary to incorporate input cost constraints (i.e., channel inputs and outputs can be arbitrarily scaled without performance degradation).
- 4.
Optimal in the sense that a given desired function cannot be distinguished from its implementation.
- 5.
Note that \(b\in \mathbb {N}\) is a crucial design parameter that dictates the quantization error.
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Acknowledgments
The work summarized in this chapter was mainly supported by the German Research Foundation (DFG) under grants STA 864/3-1, STA 864/3-2, and BO 1743/20-1, respectively.
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Goldenbaum, M., Stańczak, S., Boche, H. (2016). Interference-Aware Analog Computation over the Wireless Channel: Fundamentals and Strategies. In: Utschick, W. (eds) Communications in Interference Limited Networks. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-22440-4_5
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