The Influence of Probability Density Function Discretization on Geometric Lattice Quantizer Design for Memoryless Gaussian Source

摘要

In this paper the geometric cubic lattice quantizer design based on the PDF discretization is analyzed for the two-dimensional Gaussian source. Particularly, inside the regions, obtained by the geometric support partition, the constant PDF of the input signal vector is supposed. For this input vector PDF approximation and for the given quantizer rate, the granular distortion is optimized in order to get the manner of total points number distribution per regions. Also, the expression for the granular distortion is determined and used to estimate the performance of the proposed model. The SQNR of the proposed quantizer is compared with the known optimal ratio and on these bases it is concluded, among the other things, under which condition the suggested approximation can be applied.