Reducing Quantization Error by Matching Pseudoerror Statistics

We investigate the use of an adaptive processor (a quantizer pseudoinverse) and the statistics of the associated pseudoerror signal to reduce quantization error in scalar quantizers when a small amount of prior knowledge about the signal x is available. This approach uses both the quantizer representation points and the thresholds at the receiver. No increase in the transmitted data rate is required. We discuss examples that use low-pass, high-pass, and band-pass signals along with an adaptive processor that consists of a set of filters and clippers. Matching a single pseudoerror statistic to a target value is sufficient to attain modest reductions in quantization error in situations with one degree of freedom. Adaptive processing based on a pair of pseudoerror statistics allows for quantization noise reduction in problems with two degrees of freedom.