The lower bound of the PCM quantization error in high dimension

In this note, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for R without the White Noise Hypothesis. In [4], Wang and Xu showed that for asymptotically equidistributed unit-norm tight frame the PCM quantization error has an upper bound O(δ(d+1)/2) and they conjecture the upper bound is sharp. In this note, we confirm the conjecture with employing the asymptotic estimate of the Bessel functions.