Performance-Rate Functions for Dynamically Quantized Feedback Systems

This paper studies the performance of dynamically quantized feedback systems. In particular, we examine the relationship between the minimum summed squared quantization error and the rate at which feedback measurements are quantized. The closed loop system's performance can vary greatly for a given bit rate, depending on how the quantization bits are allocated. This paper derives the bit assignment policy that minimizes the summed squared quantization level achievable under a constant bit rate. The proof of the bit assignment's optimality allows us to identify "performance-rate" functions that bound the best achievable performance as a function of the bit rate