Chapter Summary

Chapter 17 Summary

Key Points

  • 1.

    Wireless-FL pipeline (§17.1): FL over a wireless channel is a three-axis optimization — convergence, per-round MSE, resource cost. Digital vs. AirComp aggregation trade orthogonal-slot bandwidth for noise-limited MSE; pick by nn, integrity need, and privacy model.

  • 2.

    Convergence under aggregation MSE (§17.2): noise floor is ηlr(σg2/n+\ntnmseagg/n2)/(2μ)\eta_{\text{lr}}(\sigma_g^2/n + \ntn{mseagg}/n^2)/(2\mu) for smooth strongly-convex FL. Match \ntnmseagg≈nσg2\ntn{mseagg} \approx n\sigma_g^2 to avoid over-engineering.

  • 3.

    Scheduling and resource allocation (§17.3): threshold scheduling (Theorem 17.3.1) is Pareto-optimal for MSE; α\alpha-fairness adds an MSE cost factor 1/(1−ακ)≈1.5×1/(1 - \alpha\kappa) \approx 1.5\times for Rayleigh channels at α=0.5\alpha = 0.5. Energy-constrained per-user power is water-filling.

  • 4.

    CommIT Contribution 5 (§17.4) (Elkordy-Caire-Avestimehr 2023): IT-secure federated representation learning over AirComp. Sum-zero masks cancel exactly in the aggregate, yielding d2log⁡(1+O(1/(nσm2/σz2)))\tfrac{d}{2}\log(1 + O(1/(n\sigma_m^2/\sigma_z^2))) per-user MI leakage at no MSE overhead. Fifth and final CommIT contribution.

  • 5.

    Golden thread threaded: privacy, robustness, and communication efficiency appear as MSE, fairness, and energy — each with its own axis and sweet spot. The right design matches the three to the target convergence without over-engineering.

IT-Secure Federated Representation Learning (CommIT)Exercises