References & Further Reading

References

B. Nazer and M. Gastpar, Computation Over Multiple-Access Channels, 2007
Foundational AirComp paper: introduced computation over MACs as an information-theoretic primitive.
M. Goldenbaum, H. Boche, and S. Stanczak, Harnessing Interference for Analog Function Computation in Wireless Sensor Networks, 2013
The practical treatment of AirComp with nomographic functions — characterizes the function class computable in one channel use.
A. N. Kolmogorov, On the Representation of Continuous Functions of Many Variables by Superposition of Continuous Functions of One Variable and Addition, 1957
The original 1957 superposition theorem — guarantees every continuous aggregate admits a nomographic representation. Foundational for §16.3.
D. A. Sprecher, On the Structure of Continuous Functions of Several Variables, 1965
Constructive form of Kolmogorov's theorem with explicit universal functions.
O. Abari, H. Rahul, and D. Katabi, Over-the-Air Function Computation in Sensor Networks, 2016
Practical AirComp implementations for WSN and FL settings; detailed hardware-level synchronization considerations.
X. Cao, G. Zhu, J. Xu, and K. Huang, Optimized Power Control Design for Over-the-Air Federated Edge Learning, 2020
AirComp power control for FL; derives zero-forcing MSE and threshold user selection.
W. Liu, X. Zang, Y. Li, and B. Vucetic, Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws, 2020
MMSE receivers for AirComp; high-SNR scaling laws.
K. Yang, T. Jiang, Y. Shi, and Z. Ding, Federated Learning via Over-the-Air Computation, 2020
The canonical reference for AirComp-based FL. Practical scheduling, power control, convergence analysis.
M. Seif, W.-T. Chang, and R. Tandon, Wireless Federated Learning with Local Differential Privacy, 2020
AirComp with local DP: $\sqrt{n}$-amplification result and per-user MI privacy bounds. Basis for §16.4.
D. Liu and O. Simeone, Privacy for Free: Wireless Federated Learning via Uncoded Transmission With Adaptive Power Control, 2021
"Privacy for free" perspective on AirComp; refined DP analysis under adaptive power control.
K. Bonawitz et al., Practical Secure Aggregation for Privacy-Preserving Machine Learning, 2017
Baseline secure aggregation for FL. Compared with AirComp in the cmp-aircomp-vs-secagg table.
H. B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, Communication-Efficient Learning of Deep Networks from Decentralized Data, 2017
The FedAvg paper. Motivating application for AirComp aggregation of gradients.