Asymptotically Optimal Distribution Preserving Quantization for Stationary Gaussian Processes

Distribution preserving quantization (DPQ) has been proposed as a lossy coding tool that yields superior quality over conventional quantization, when applied to perceptually relevant signals. DPQ aims at the optimal rate-distortion trade-off, subject to preserving the source probability distribution. In this article we investigate the optimal DPQ for stationary Gaussian processes and the mean squared error (MSE). A lower bound on the optimal performance is derived. A quantization scheme is proposed and proven to asymptotically reach the lower bound. For the sake of applicability, the scheme is simplified, though without affecting its asymptotic rate-distortion behavior. While this simplification sacrifices the exact preservation of the probability distribution, it strictly preserves the power spectral density (PSD) of the source. This leads to the consideration of another type of quantization: PSD preserving quantization (PSD-PQ). It is shown that the optimal rate-distortion trade-off for PSD-PQ equals that for DPQ, although it has a weaker constraint. The proposed quantizer is applied to audio coding and compared to a conventional method that is optimized for a rate-distortion trade-off without the distribution preserving constraint. The results demonstrate that the new method leads to better perceptual quality.