Entropy of quantized data at high sampling rates

This paper considers the entropy of the highly correlated quantized samples resulting from sampling at high rate. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling interval goes to zero. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of infinite-level uniform threshold scalar quantizers and a stationary Gaussian random process whose mean lies at a midpoint of some quantization cell. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on another quantized sample is derived