The lower bound of the PCM quantization error in high dimensions

In this paper, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for RdRd without the White Noise Hypothesis. In [12], Wang and Xu showed that for asymptotically equidistributed unit-norm tight frames the PCM quantization error has an upper bound O(δ(d+1)/2)O(δ(d+1)/2) and they conjecture the upper bound is sharp. In this paper, we confirm the conjecture by employing asymptotic estimates of Bessel functions.