Optimal design of quantization gains and update rules

Investigate optimal design methods for the static quantization gain \(\gamma_0\) and the update rule for the time-varying quantization gain \(\gamma_1\), using appropriately defined objective functions for reliable dynamic-key LWE-based encrypted state-feedback control.

Background

The paper derives admissible lower and upper bounds for the static gain $\gamma_0$ and the time-varying gain $\gamma_1(k)$ to ensure asymptotic stability and prevent plaintext overflow in a dynamic-key LWE-based encrypted state-feedback control system. The remark discusses practical parameter-selection heuristics: $\gamma_0$ should be as small as possible while preserving stability of the encoded gain, whereas $\gamma_1$ should be as large as possible to improve quantization accuracy.

Beyond these empirical guidelines, the authors identify a concrete unresolved direction: developing systematic optimization-based methods for selecting $\gamma_0$ and the update rule governing $\gamma_1$, with respect to suitably defined objective functions. Such methods would provide principled encoder design rather than relying only on admissibility bounds and heuristic choices.