Improvement of the lower bound of the PCM quantization error for vectors in R2

Using an asymptotic estimate of the Bessel functions, we investigate the performance of the PCM quantization for vectors in R2 and improve the previous results of Wang and Xu (2012). In particular, we present a lower bound of the PCM quantization error under some mild condition and show that PCM quantization can take the advantage of the redundancy of frames for infinitely many x∈R2 with different magnitudes.