Analysis of high rate LPC vector quantizers designed by minimizing suboptimal error measures

For the quantization of the linear predictive coding (LPC) parameters in speech coding systems, the log spectral distortion (LSD) measure is often cited as the performance measure most correlated with speech quality. However, most practical quantization schemes use simpler error measures, such as mean squared error (MSE) or weighted mean squared error (WMSE) measures between the quantized and unquantized LPC coefficients, reflection coefficients, arcsine coefficients, area ratios, or line spectral pair frequencies (LSPs). This paper develops analytical expressions for performance of high rate vector quantization (VQ) schemes which are trained by minimizing suboptimal distortion measures, and applies these results to the problem of quantizing the LPC parameters. In particular, the theory is developed to evaluate the performance, as measured by one distortion measure, of a vector quantizer which has been trained by minimizing a different distortion measure. Using this analysis, the performance, in LSD, of vector quantizers trained by minimizing MSE and WMSE measures is theoretically evaluated