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 ${\mathbb R}^d$ without the White Noise Hypothesis. In \cite{WX}, Wang and Xu showed that for asymptotically equidistributed unit-norm tight frame the PCM quantization error has an upper bound ${\mathcal O}(\delta^{(d+1)/2})$ and they conjecture the upper bound is sharp. In this note, we confirm the conjecture with employing the asymptotic estimate of the Bessel functions. 
Heng Zhou and Zhiqiang Xu
math.NA cs.IT math.IT