THEORETICAL-ANALYSIS OF THE HIGH-RATE VECTOR QUANTIZATION OF LPC PARAMETERS

This paper presents a theoretical analysis of high-rate vector quantiz ation (VQ) systems that use suboptimal, mismatched distortion measures , and describes the application of the analysis to the problem of quan tizing the linear predictive coding (LPC) parameters in speech coding systems, First, it is shown that in many high-rate VQ systems the quan tization distortion approaches a simple quadratically weighted error m easure, where the weighting matrix is a ''sensitivity matrix'' that is an extension of the concept of the scalar sensitivity. The approximat e performance of VQ systems that train and quantize using mismatched d istortion measures is derived, and is used to construct better distort ion measures, Second, these results are used to determine the performa nce of LPC vector quantizers, as measured by the log spectral distorti on (LSD) measure, which have been trained using other error measures, such as mean-squared (MSE) or weighted mean-squared error (WMSE) measu res of LPC parameters, reflection coefficients and transforms thereof, and line spectral pair (LSP) frequencies, Computationally efficient a lgorithms for computing the sensitivity matrices of these parameters a re described. In particular, it is shown that the sensivity matrix for the LSP frequencies is diagonal, implying that a WMSE measure of LSP frequencies converges to the LSD measure in high-rate VQ systems, Expe rimental results to support the theoretical performance estimates are provided.