Optimum pre- and post-filters for robust scalar quantization

An N-level scalar quantization system for continuous alphabet i.i.d. sources with a pre- and post-filter as suggested by Popat and Zeger (see IEEE Trans. Commun., vol.40, no.11, p.1670, 1992) is considered. The idea is that the pre-filter changes the distribution of the source to approximately Gaussian, which is then quantized by a Lloyd-Max (1960, 1982) quantizer for Gaussian random variables. For many sources, the overall system outperforms one that directly quantizes the sources. We propose an iterative algorithm for designing the optimum filters, to minimize the overall mean squared error between the input and output of the quantization system. It is found experimentally that the design algorithm always converges very rapidly to a solution where the optimum pre- and post-filters are all pass filters. We prove the convergence of the design algorithm for the N=2 case, and conjecture that convergence to the same solution always holds for any N