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Logarithmic Pyramid Vector Quantization-Design and Theoretical Analysis

Authors:
Sohn, C. ,  Krüger, H.Vary, P.
Journal:
IEEE Transactions on Information Theory
Page(s):
3732 - 3744
Date:
2019
ISSN:
1557-9654
DOI:
10.1109/TIT.2019.2947502
Language:
English

Abstract

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-tonoise 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 2 bits 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.

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