Optimum switched split vector quantization of LSF parameters

Abstract

We address the issue of rate–distortion (R/D) performance optimality of the recently proposed switched split vector quantization (SSVQ) method. The distribution of the source is modeled using Gaussian mixture density and thus, the non-parametric SSVQ is analyzed in a parametric model based framework for achieving optimum R/D performance. Using high rate quantization theory, we derive the optimum bit allocation formulae for the intra-cluster split vector quantizer (SVQ) and the inter-cluster switching.

For the wide-band speech line spectrum frequency (LSF) parameter quantization, it is shown that the Gaussian mixture model (GMM) based optimum parametric SSVQ method provides 1 bit/vector advantage over the non-parametric SSVQ method.

Introduction

Most of the speech coders use linear prediction (LP) analysis and thus, more effective scheme of quantizing the LP coefficients (LPCs), equivalently line spectrum frequencies (LSFs), is in great demand. Vector quantization (VQ) of LSFs is the best way to reach lowest bitrate, but the prohibitive complexity of a full-search VQ limits its usage. Many different product code VQ methods [1], [2], [3], [4], [5] have been reported for LSF coding, which reduce complexity with a moderate loss of quantization performance. One of the widely reported techniques is split vector quantization (SVQ) method which was first proposed by Paliwal and Atal [6] for telephone-band speech and then further explored for wide-band speech [7], [8], [9]. Recently, So and Paliwal have proposed switched split vector quantization (SSVQ) method [10], [11] which is shown to provide a better R/D performance than the traditional SVQ method, for both telephone-band and wide-band speech cases. The SSVQ is further explored in [12], [13] to show its competitive performance advantage over many other product code VQ methods.

The SSVQ is a non-parametric product code VQ method, where the vector space is divided into non-overlapping Voronoi regions¹ and a separate SVQ is designed for each region. Thus, the SSVQ is composed of multiple SVQs. An input vector to be quantized is first classified to a Voronoi region and then the region specific SVQ is used for quantization. Though the SSVQ provides better rate–distortion (R/D) performance than the SVQ, it does not address the optimality of its R/D performance.

Currently there is a growing interest to develop parametric pdf based quantization methods using Gaussian mixture model (GMM), such that the optimum R/D performance can be achieved at a given bitrate [14], [15], [16], [17]. In this paper, we address the R/D performance optimality of SSVQ in a GMM based framework. We derive the optimum bit allocation criteria for both the stages of quantization, referred to as inter-cluster and intra-cluster bit allocation. We resort to the fixed and variable bitrate schemes of [16] for inter-cluster bit allocation. For intra-cluster bit allocation, we derive the R/D performance expression of the region specific optimum SVQ method using high rate quantization theory. We use square Euclidean distance (SED) as the distortion measure for ease of analysis. Focusing on wide-band speech LSF quantization, we show that the optimum parametric SSVQ method provides 1 bit/vector advantage over the non-parametric SSVQ method.