Application of Extended Huffman Coding on Three-Level Scalar Quantizer for Gaussian Source

Abstract

This paper presents design process of the optimal three-level scalar quantizer with extended Huffman coding. The optimal value of the decision threshold is achieved by optimization of the decision threshold depending on the maximum value of signal to quantization noise ratio. The calculation of average bit rate and source entropy, as well as the comparison between these parameters is done. The convergence of the average bit rate to the source entropy is thoroughly analysed for two, three, and four symbol blocks. Performances of the proposed quantizer in terms of signal to quantization noise ratio are estimated by comparing numerical values to the quantizer having two quantization levels for the Gaussian probability density function. Also, analysis of the average bit rate and the source entropy depending on the size of symbol blocks is performed.