Optimizing Dither Distributions for Noisy Quantization Systems
Morriel Kasher, Michael Tinston, Predrag Spasojević · 2023
We consider the design of non-subtractive dither distributions for improving the performance of quantizers in the presence of additive white Gaussian noise. By formulating the dither optimization as a maximum-likelihood (ML) deconvolution problem, we are able to apply the Lucy-Richardson deconvolution method to recover an estimate of the optimal (in the ML sense) dither distribution which should be used in the presence of Gaussian noise with a known variance. We present this resultant optimized dither distribution over a wide range of quantizer noise levels and show that it consistently succeeds in producing a close approximation of the desired output distribution after convolution with the noise distribution. This is then proven through numerical simulations to significantly reduce the overall mean square error of the quantization while maintaining comparable or better results in other critical quantizer linearity metrics including Total Harmonic Distortion and Spurious-Free Dynamic Range (when compared to traditional unoptimized dithering). This technique has wide-ranging applications in communication, audio processing, and data compression, all of which rely on quantizers for their analog-to-digital conversion and each of which typically contain some implicit system-level Gaussian noise.