On Transform Coding with Dithered Quantizers

This paper is concerned with optimal transform coding in conjunction with dithered quantization. While the optimal deterministic quantizer´s error is uncorrelated with the reconstructed value, the dithered quantizer yields quantization errors that are correlated with the reconstruction but are white and independent of the source. These properties offer potential benefits, but also have implications on the optimization of the rest of the coder. We derive the optimal transform for consequent dithered quantization. For fixed rate coding, we show that the transform derived for dithered quantization is universally optimal (for all sources), unlike the conventional quantization case where optimality of the Karhunen-Loeve transform is guaranteed for Gaussian sources. Moreover, we establish variable rate coding optimality for Gaussian sources.