Theoretical analysis of the high-rate vector quantization of LPC parameters

The paper presents a theoretical analysis of high-rate vector quantization (VQ) systems that use suboptimal, mismatched distortion measures, and describes the application of the analysis to the problem of quantizing the linear predictive coding (LPC) parameters in speech coding systems. First, it is shown that in many high-rate VQ systems the quantization distortion approaches a simple quadratically weighted error measure, where the weighting matrix is a “sensitivity matrix” that is an extension of the concept of the scalar sensitivity. The approximate performance of VQ systems that train and quantize using mismatched distortion measures is derived, and is used to construct better distortion measures. Second, these results are used to determine the performance of LPC vector quantizers, as measured by the log spectral distortion (LSD) measure, which have been trained using other error measures, such as mean-squared (MSE) or weighted mean-squared error (WMSE) measures of LEPC parameters, reflection coefficients and transforms thereof, and line spectral pair (LSP) frequencies. Computationally efficient algorithms for computing the sensitivity matrices of these parameters are described. In particular, it is shown that the sensitivity matrix for the LSP frequencies is diagonal, implying that a WMSE measured LSP frequencies converges to the LSD measure in high-rate VQ systems. Experimental results to support the theoretical performance estimates are provided