Quantization and coding

The spectral components are quantized and coded with the aim of keeping the noise, which is introduced by quantizing, below the masked threshold. Depending on the algorithm, this step is done in very different ways, from simple block companding to analysis-by-synthesis systems using additional noiseless compression. 

As a special version to enhance the efficiency of the quantization and coding module, an LPC analysis has been proposed to normalize the spectral values [Iwakami et al., 1995],... 

Low resolution filter banks (e.g. 32 subbands), normally combined with a quantization and coding module which works on blocks in time direction. These are frequently called subband coders. 

The following sections describe some of the widely used tools for quantization and coding in more detail. 

The matrixing done in M/S joint stereo coding is invertible. Without the quantization and coding of the matrix output the processing is completely transparent. 

Quantization and Coding. While no major new ideas have been introduced for some time, refinements and variations on the currently used methods for quantization and coding are still an active research topic. Examples include experiments with arithmetic... 

Roberts, 1976] Roberts, L. G. (1976). Picture Coding Using Pseudo-Random Noise. In Jayant, N. S., editor, Waveform Quantization and Coding, pages 145-154. IEEE Press. Reprinted from IEEE Trans, on Information Theory, vol. IT-8, Feb. 1962. 

A bitstream formatter is used to assemble the bitstream, which typically consists of the quantized and coded spectral coefficients and some side information, e.g. bit allocation information. 

The quantization and coding tools in an encoder do the main data-reduction work. As in the case of filter banks, a number of design options are possible and have been explored. 

Noise allocation followed by scalar quantization and Huffman coding. In this method, no explicit bit allocation is performed. Instead, an amount of allowed noise equal to the estimated masked threshold is calculated for each scalefactor band. The scalefactors are used to perform a coloration of the quantization noise (i.e. they modify the quantization step size for all values within a scalefactor band) and are not the result of a normalization procedure. The quantized values are coded using Huffman coding. The whole process is normally controlled by one or more nested iteration loops. The technique is known as analysis-by-synthesis quantization control. It was first introduced for OCF [Brandenburg, 1987], PXFM [Johnston, 1989b] and ASPEC [Brandenburg et al., 1991], In a practical application, the following computation steps are performed in an iterative fashion ... 

Image-transform coding comprises three main components, viz., transformation, quantizer, and symbol encoder. A linear transform is applied to map the pixels onto a set of transform coefficients. These coefficients are then quantized and entropy encoded. The general block diagram of transform-based image coding is shown in Figure 23.1. 

Scalar quantization is the process of mapping the input to a small number of output levels. Since the small number of levels can be coded using shorter codes, the code size of the image is reduced. The quantization and dequantization is performed according to the following equations ... 

The angular momentum of the eleetron is also quantized, and the azimuthal quantum number, I, specifies the permissible values. The number I can assume integer values between zero and (n - 1). Each value of I represents a subshell or sublevel of the principal shell. These subshells are usually identified by an alphabetical code based on old spectroseopie terms. Thus, / = 0 is designated an. y sublevel, / = 1 is ealled a p state, / = 2 is symbolized 2isd,l = 3 eorresponds to an / subshell, and so on in alphabetical order. The electronic distributions associated with various values of the azimuthal quantum number are also identified by this eode. The designation is important because I reflects the shape of these electron clouds. 

We shall establish an upper bound on error probability for the best code of rate B and block length N on this channel by considering a decoder that quantizes the output before decoding. Theorem 4-10 already provides a bound on error probability for such a quantized channel. We then find the limit of this bound as the quantization becomes infinitely fine. 

HPLC is often reported to be the technique of best choice for the quantification of food colorants. According to European Directive 94/36/EC, the quantities of synthetic colorants to be added to foods are restricted and thus reliable methods for their quantification must be established. Approved colorants, defined by E-coded numbers (Table 6.6.2), are permitted for non-alcoholic beverages, confectionery products, and even for caviar (dying fish roe). For example, a specific HPLC chromatographic method for the quantization of 14 synthetic food colorants belonging to azo dye, triphenyhnethane, or quinophthalone classes (E 102,104, 110, 122,123, 124, 127, 128, 129, 131, 132, 133, 142, 151) was reported to check their contents in caviar. ... 

Especially in the case of low bit-rates (implying that a lot of quantization noise is introduced), the filter characteristics of the analysis and synthesis filters as determined by the prototype window / windowing function are a key factor for the performance of a coding system. 

The quantized spectral components are stored and/or transmitted either directly as quantized values according to a bit allocation strategy (including bit packing) or as entropy coded words. 

Vector quantization. In vector quantization, not the individual filter bank output samples are quantized, but n-tuples of values. This technique is used in most current speech and video coding techniques. Recently, vector quantization has been applied in a scheme called TWIN-VQ ([Iwakami et al., 1995]). This system has been proposed for MPEG-4 audio coding (see [MPEG, 1997b]). 

Other coding tools in Layer 3 include a different (nonuniform) quantizer, analysis-by-synthesis control of the quantization noise and Huffman coding of the quantized values to increase the coding efficiency. All these have already been described earlier in this chapter. 

Noiseless Coding. Huffman coding is applied for the quantized spectrum, the differential scalefactors, and directional information. A total of 12 static Huffman codebooks are employed to code pairs or quadruples of spectral values. 

Chou et al. [18] exploit the duality of communication with side-information at the encoder to source coding with side-information at the decoder to derive a watermarking scheme based on trellis-coded quantization. This work can be considered as an extension of the research on practical implementations of Costa s scheme in the direction of high dimensional embedding and reception rules. However, research in this direction is difficult and little progress has been made within the last years. Up to now, performance results that are better than the theoretical capacity limit of ST-SCS propose (see Sec. V) have not been published. Latest results by Chou et al. [19] show at least a slight improvement of turbo coded trellis-based constructions over simple SCS communication using coded modulation techniques. Note also that... 

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