Forward Adaptive Logarithmic Quantizer with New Lossless Coding Method for Laplacian Source

Abstract

The aim of this paper is to improve the G.711 standard, which is widely used, especially in the public switched telephone network (PSTN). Two solutions are proposed. The first solution uses only lossless coder, achieving a bit-rate decrease of 0.82 bits/sample, compared to the G.711 codec. The second solution uses forward adaptation and a lossless coder, further decreasing the bit-rate (by 1.25 bits/sample) and achieving higher average signal-to-quantization noise ratio (SQNR) in comparison with the G.711 codec. Also, the second solution is more robust than the G.711 codec, which means that it has near constant SQNR for a wide range of input signal power. That is very important for signals whose input power varies with time, such as speech and video signals. Our solutions are compatible with the G.711 codec, they have little additional complexity and delay and therefore can be applied in real-time systems, such as PSTN or VoIP. They can also be used in many other systems, such as WiMax and OFDM, as a replacement or improvement of the G.711 codec. Standardization process of the G.711.1 standard (which is a wide-band extension of the G.711 standard) is largely present. Our solutions fulfill all the requirements for that new standard; therefore they can be implemented in its low-frequency part.

Dual-mode quasi-logarithmic quantizer with embedded G.711 codec

“…Let us introduce the mean-squared distortion as a measure of irreversible error incurred during the quantization, which consists of the granular D g and the overload D o component. For the µ-law quantizer and unit variance case, they are given by [16]…”

Semi–logarithmic and hybrid quantization of Laplacian source inwide range of variances

“…Total distortion and SQN R are calculated using expressions (4) and (11). In order to achieve better system performances, total distortion expression can be minimized by using the method of Lagrange multipliers.…”

“…The quality of a quantized signal is generally influenced by the width of a quantizers support region and the number of quantization levels. Although, great number of quantization studies has been published [4][5][6][7][8][9] there is still reasonable need to continue research in this field. Main goal of our research is to find a simply quantization characteristics for quantizer model realization with high quality of performance, with maintaining robustness in wide range of input signals.…”

“…The statistic of input signals: the statistical mean, variance (or the dynamic range), and type of input pdf (probability density function) constantly change with time [1][2][3], [9,10]. Although, great number of quantization studies has been published [4][5][6][7][8][9] there is still reasonable need to continue research in this field.…”

“…Also, for larger number of signal samples, the probability density function of input signal is better represented with Laplacian function [10]. In a number of papers the quantization of memoryless Laplacian source was analyzed since the pdf of the difference signal for an image waveform follows the Laplacian function [10,11]. Concerning Laplacian speech model, there are two logarithmic quantizing characteristics: µ-law quantizing (used in North America & Japan) and A-law quantizing (used in Europe and the rest of the world).…”