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Mathematical Institute of the Serbian Academy of Sciences and Arts

Mathematical Institute of the Serbian Academy of Sciences and Arts. Design and analysis of the two-level scalar quantizer with extended Huffman coding. Lazar Velimirović , Zoran Perić , Bojan Denić. Abstract.

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Mathematical Institute of the Serbian Academy of Sciences and Arts

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  1. Mathematical Institute of the Serbian Academy of Sciences and Arts Design and analysis of the two-level scalar quantizer with extended Huffman coding Lazar Velimirović, ZoranPerić, Bojan Denić

  2. Abstract We propose a model of the two-level scalar quantizer with extended Huffman coding and variable decision threshold. We decide that the new quantizer model has only two representation levels due to small model complexity and the possibility of the efficient use of the Huffman coding procedure. Variable decision threshold is proposed so the representation levels’ assymetry can be achieved.

  3. The Gaussian probability density function

  4. The quantizer model y1 0 t1 y2 Representation levels are determined from the centroid condition: Variable decision threshold is determined depending on signal quality that wants to be achieved.

  5. Extended Huffman coding Extended Huffman coding is the procedure of determining the optimal length of codewords for blocks of two or more symbols. Probabilities: The probabilities of symbol blocks : The source entropy : The average bit rate :

  6. Extended Huffman coding Example of extended Huffman code construction: forming the tree and assigning the code words

  7. Extended Huffman coding Extended Huffman codebook

  8. Numerical results Performance of the proposed quantizer

  9. Numerical results The dependency of the bit rate and the entropy on the distortion for the proposed quantizer

  10. Numerical results G G SQNR 1 dB R̅ =0.1677 bita L L SQNR 1 dB R̅ =0.4809 bita L G R̅ – R̅ = 0.3132bita

  11. References D. Salomon, A Concise Introduction to Data Compression, Springer, 2008. N. S. Jayant, P. Noll, Digital Coding of Waveforms, Prentice Hall, 1984. Z. Peric, J. Nikolic, “An Effective Method for Initialization of Lloyd-Max’s Algorithm of Optimal Scalar Quantization for Laplacian Source”, Informatica, No. 18(2), pp. 279 - 288, 2007. D. Marco, D. L. Neuhoff, “Low-Resolution Scalar Quantization for Gaussian and Laplacian Sources with Absolute and Squared Error Distortion Measures”, Tech. report, January 7, 2006. ITU-T, Recommendation T.81, Information Technology Digital Compression and Coding of Continuous-tone Still Image Requirements and Guidelines, 1992. Z. Peric, J Nikolic, L. Velimirovic, M. Stanković, D. Aleksić, “Asymmetrical Two-Level Scalar Quantizer with Extended Huffman Coding for Compression of Laplacian Source”, Advances in Electrical and Computer Engineering, No. 13(2), pp. 39-42, 2013.

  12. THANKS A LOT ! Contact e-mail: lazar.velimirovic@mi.sanu.ac.rs

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