Logarithmic Pyramid Vector Quantization—Design and Theoretical Analysis

Vector quantization is an integral part of modern speech and audio codecs. This study proposes the logarithmic pyramid vector quantizer (LPVQ), which is a gain-shape vector quantizer specifically designed for the quantization of Laplace distributed memoryless sources. The objective of the study is a theoretical analysis of the LPVQ: We determine the distortion of the shape quantizer with respect to rate and vector dimension for the quantization of an i.i.d. Laplace source. Furthermore, we derive formulas for the quantization signal-to-noise ratio (SNR) of the shape quantizer and the quantization SNR of the LPVQ, giving reliable results for an effective bit rate per vector coordinate of 2bits and higher. We study the SNR-behavior of the LPVQ for infinite dimensions and compare it with the maximal achievable SNR according to the rate-distortion bound. After having proposed a strategy for the allocation of the bit rate for the gain quantization and the quantization of the shape vector, respectively, we verify the derived formulas by simulations.