Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source

Jelena Nikolić, Danijela Aleksić, Zoran Perić and Milan Dinčić
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Jelena Nikolić: Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia
Danijela Aleksić: Department of Mobile Network Nis, Telekom Srbija, Vozdova 11, 18000 Nis, Serbia
Zoran Perić: Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia
Milan Dinčić: Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia

Mathematics, 2021, vol. 9, issue 23, 1-14

Abstract: Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest uniform quantization with equal bit-rates within both regions. In particular, we assumed a narrow central granular region (CGR) covering the peak of the Laplacian pdf and a wider peripheral granular region (PGR) where the pdf is predominantly tailed. We performed optimization of the widths of CGR and PGR via distortion optimization per border–clipping threshold scaling ratio which resulted in an iterative formula enabling the parametrization of our piecewise uniform quantizer (PWUQ). For medium and high bit-rates, we demonstrated the convenience of our PWUQ over the uniform quantizer, paying special attention to the case where 99.99% of the signal amplitudes belong to the support region or clipping region. We believe that the resulting formulas for PWUQ design and performance assessment are greatly beneficial in neural networks where weights and activations are typically modelled by the Laplacian distribution, and where uniform quantization is commonly used to decrease memory footprint.

Keywords: uniform quantization; piecewise uniform quantizer; border threshold; clipping threshold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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