A vector quantizer is a system for mapping a sequence of continuous or discrete vectors into a digital sequence suitable for communication over or storage in a digital channel. The goal of such a system is data compression: to reduce the bit rate so as to minimize communication channel capacity or digital storage memory requirements while maintaining the necessary fidelity of the data. The mapping for each vector may or may not have memory in the sense of depending on past actions of the coder, just as in well established scalar techniques such as PCM, which has no memory, and predictive quantization, which does. Even though information theory implies that one can always obtain better performance by coding vectors instead of scalars, scalar quantizers have remained by far the most common data compression system because of their simplicity and good performance when the communication rate is sufficiently large. In addition, relatively few design techniques have existed for vector quantizers. During the past few years several design algorithms have been developed for a variety of vector quantizers and the performance of these codes has been studied for speech waveforms, speech linear predictive parameter vectors, images, and several simulated random processes. It is the purpose of this article to survey some of these design techniques and their applications.

Vector quantization

Quantization is a process that maps a continous or discrete set of values into approximations that belong to a smaller set. Quantization is a lossy: some information about the original data is lost in the process. The key to a successful quantization is therefore the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.

Quantization

Digital Coding of Waveforms

Quantization, the process of approximating continuous-amplitude signals by digital (discrete-amplitude) signals, is an important aspect of data compression or coding, the field concerned with the reduction of the number of bits necessary to transmit or store analog data, subject to a distortion or fidelity criterion. The independent quantization of each signal value or parameter is termed scalar quantization, while the joint quantization of a block of parameters is termed block or vector quantization. This tutorial review presents the basic concepts employed in vector quantization and gives a realistic assessment of its benefits and costs when compared to scalar quantization. Vector quantization is presented as a process of redundancy removal that makes effective use of four interrelated properties of vector parameters: linear dependency (correlation), nonlinear dependency, shape of the probability density function (pdf), and vector dimensionality itself. In contrast, scalar quantization can utilize effectively only linear dependency and pdf shape. The basic concepts are illustrated by means of simple examples and the theoretical limits of vector quantizer performance are reviewed, based on results from rate-distortion theory. Practical issues relating to quantizer design, implementation, and performance in actual applications are explored. While many of the methods presented are quite general and can be used for the coding of arbitrary signals, this paper focuses primarily on the coding of speech signals and parameters.

Vector quantization in speech coding

An iterative descent algorithm based on a Lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed. These entropy-constrained vector quantizers (ECVQs) can be used in tandem with variable-rate noiseless coding systems to provide locally optimal variable-rate block source coding with respect to a fidelity criterion. Experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates (about 1 bit/sample) under the squared error distortion measure, about 1.6 dB improvement in the signal-to-noise ratio can be expected over the best scalar and lattice quantizers when block entropy-coded with block length 4. Even greater gains are made over other forms of entropy-coded vector quantizers. For pattern recognition, it is shown that the ECVQ algorithm is a generalization of the k-means and related algorithms for estimating cluster means, in that the ECVQ algorithm estimates the prior cluster probabilities as well. Experiments on multivariate Gaussian distributions show that for clustering problems involving classes with widely different priors, the ECVQ outperforms the k-means algorithm in both likelihood and probability of error. >

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Entropy-constrained vector quantization

This paper describes the 8 kb/s speech coding algorithm G.729 which has been standardized by ITU-T. The algorithm is based on a conjugate-structure algebraic CELP (CS-ACELP) coding technique and uses 10 ms speech frames. The codec delivers toll-quality speech (equivalent to 32 kb/s ADPCM) for most operating conditions. This paper describes the coder structure in detail and discusses the reasons behind certain design choices. A 16-b fixed-point version has been developed as part of Recommendation G.729 and a summary of the subjective test results based on a real-time implementation of this version are presented.

Design and description of CS-ACELP: a toll quality 8 kb/s speech coder

Code-Excited Linear Prediction (CELP) produces high quality synthetic speech at low bit rate. However the basic scheme leads to huge computational loads. The paper describes a related scheme, which allows real time implementation on current DSP chips. The very efficient search procedure in the codebook is achieved by means of a new technique called "backward filtering" and the use of algebraic codes. RSB performances are reported for a variety of conditions.

Fast CELP coding based on algebraic codes

The application of algebraic code excited linear prediction (ACELP) coding to wideband speech is presented An algebraic codebook with a 20 bit address can be used without any storage requirements and, more importantly, with a very efficient search procedure which allows for real-time implementation The authors describe an efficient procedure for searching such a large codebook deploying a focused search strategy, where less than 01% of the codebook is searched with performance very close to that of a full search High-quality speech at a bit rate of 13 kbps was obtained >

16 kbps wideband speech coding technique based on algebraic CELP

A general framework is introduced which allows both fast search and freedom in designing codebooks with good statistical properties. Several previously proposed schemes are compared from this viewpoint. A backward filtering formulation is given to show that sparse algebraic codes (SACs) (i.e., with few nonzero components) offer distinct advantages. It is shown that they reduce the optimal-search computation per codeword. They also allow control of the statistical properties of the codebook in the time and frequency domains. This control can be dynamic in the sense that it can be made to evolve as a function of the linear predictive coding model A(z). The algebraic-code excited linear prediction (ACELP) technology which allows full duplex operation on a single TMS320C25 at rates between 4.8 and 16 kb/s and which is based on SAC-driven dynamic codebooks is described. >

On reducing computational complexity of codebook search in CELP coder through the use of algebraic codes

A toll quality speech codec at 8 kb/s suitable for the future personal communications system is presented. The codec is currently under standardization by the ITU-T (successor of CCITT) where the codec terms of reference were mainly determined considering PCS application. The encoding algorithm is based on algebraic code-excited linear prediction (ACELP) and has a speech frame of 10 ms. Efficient pitch and codebook search strategies, along with efficient quantization procedures, have been developed to achieve toll quality encoded speech with a complexity implementable on current fixed-point DSP chips. Formal subjective listening tests, performed by ITU-T SG 12, showed that the codec quality is equivalent to that of G.726 ADPCM at 32 kb/s in error-free conditions and it outperforms G.726 under error conditions. The codec performs adequately under tandeming conditions, and can support a frame erasure rate up to 3% with a degradation in its performance that is still worse than the ITU-T requirements, and this is one subject of study for the next phase. The algorithm has been implemented on a single fixed-point DSP for the ITU-T subjective rest, and required about 29 MIPS. An optimized version, however, requires 24 MIPS without any speech quality degradation. >

J.-P. Adoul

Papers

Design and description of CS-ACELP: a toll quality 8 kb/s speech coder

Fast CELP coding based on algebraic codes

16 kbps wideband speech coding technique based on algebraic CELP

On reducing computational complexity of codebook search in CELP coder through the use of algebraic codes

A toll quality 8 kb/s speech codec for the personal communications system (PCS)