Vector Quantizer Design Research Articles

Dynamic Logarithmic Vector Quantizer Design for Stochastic Continuous Time Linear Systems With State Feedback Control

This paper addresses logarithmic vector quantizers with dynamic sensitivity design for stochastic continuous time linear system with a feedback control law. Logarithmic vector quantization is adopted so that the coarsest density of quantization and data compression efficiency are both guaranteed. In addition, the problem of quantizer saturation is treated with the mechanism of dynamic sensitivity. The dynamic of the sensitivity during “zoom-in” / “zoom-out” stages is proposed. It is shown that with the proposed algorithm, a single input continuous time linear system can be stabilized in the sense of mean square by quantized feedback control via adopting sensitivity varying algorithm. Results from theoretical analysis are verified through simulation at the end of the paper.

Logarithmic Pyramid Vector Quantization—Design and Theoretical Analysis

Vector quantization is an integral part of modern speech and audio codecs. This study proposes the logarithmic pyramid vector quantizer (LPVQ), which is a gain-shape vector quantizer specifically designed for the quantization of Laplace distributed memoryless sources. The objective of the study is a theoretical analysis of the LPVQ: We determine the distortion of the shape quantizer with respect to rate and vector dimension for the quantization of an i.i.d. Laplace source. Furthermore, we derive formulas for the quantization signal-to-noise ratio (SNR) of the shape quantizer and the quantization SNR of the LPVQ, giving reliable results for an effective bit rate per vector coordinate of 2bits and higher. We study the SNR-behavior of the LPVQ for infinite dimensions and compare it with the maximal achievable SNR according to the rate-distortion bound. After having proposed a strategy for the allocation of the bit rate for the gain quantization and the quantization of the shape vector, respectively, we verify the derived formulas by simulations.

Stochastic Circuit Design and Performance Evaluation of Vector Quantization for Different Error Measures

Vector quantization (VQ) is a general data compression technique that has a scalable implementation complexity and potentially a high compression ratio. In this paper, a novel implementation of VQ using stochastic circuits is proposed and its performance is evaluated against conventional binary designs. The stochastic and binary designs are compared for the same compression quality, and the circuits are synthesized for an industrial 28-nm cell library. The effects of varying the sequence length of the stochastic representation are studied with respect to throughput per area (TPA) and energy per operation (EPO). The stochastic implementations are shown to have higher EPOs than the conventional binary implementations due to longer latencies. When a shorter encoding sequence with 512 bits is used to obtain a lower quality compression measured by the $L^{1}$ -norm, squared $L^{2}$ -norm, and third-law errors, the TPA ranges from 1.16 to 2.56 times than that of the binary implementation with the same compression quality. Thus, although the stochastic implementation underperforms for a high compression quality, it outperforms the conventional binary design in terms of TPA for a reduced compression quality. By exploiting the progressive precision feature of a stochastic circuit, a readily scalable processing quality can be attained by halting the computation after different numbers of clock cycles.

Codebook Calibration Method for Vector Quantizers Implemented at the Focal Plane of CMOS Imagers

We have recently designed and tested a CMOS imager fabricated in a 0.35- $\mu \text{m}$ CMOS technology, with focal-plane image compression using vector quantization (VQ) for texture representation. In Lloyd-Max VQ design theory, the input space partition is matched to the codebook and vice versa, by means of well-known partition and centroid conditions. Although both the partition and codebook were designed with vectors extracted from the same digital image base, only the partition is nonideally implemented, owing to mismatches and errors produced by the fabrication process. Whereas this paper does not have a focus on hardware or system architecture, some hardware details are described, to illustrate the most important error sources. In this paper, we introduce a method for updating the codebook as binary indices are experimentally generated by the camera, so that texture reconstruction with smaller mean squared error is consistently obtained. We illustrate the method by means of experiments carried out with captured and improved photographs.

Self-organizing maps for the design of multiple description vector quantizers

Multiple description coding is an appealing tool to guarantee graceful signal degradation in the presence of unreliable channels. While the principles of multiple description scalar quantization are well-understood and solid guidelines exist to design effective systems, the same does not hold for vector quantization, especially at low bit-rates, where burdensome and unsatisfactory design techniques discourage its use altogether in applications.In this work we use the self-organizing maps to design multiple description VQ codebooks. The proposed algorithm is flexible, fast and effective: it deals easily with a large variety of situations, including the case of more than two descriptions, with a computational complexity that remains fully affordable even for large codebooks, and a performance comparable to that of reference techniques.A thorough experimental analysis, conducted in a wide range of operating conditions, proves the proposed technique to perform on par with well-known reference methods based on greedy optimization, but with a much lower computational burden. In addition, the resulting codebook can be itself optimized, thus providing even better performance. All experiments are fully reproducible, with all software and data available online for the interested researchers.

Designing Optimal Multiresolution Quantizers with Error Detecting Codes

This paper investigates the design of optimal multiresolution vector quantizers for broadcast channels with cyclic redundancy checks (CRC). Given a CRC-coded broadcast system with multiresolution vector quantization (MRVQ), a closed-form formula for the weighted end-to-end distortion (EED) is first derived under random index assignment. The closed-form expression is then further utilized to identify necessary optimality conditions to minimize the EED, from which an iterative algorithm is proposed for quantization design. Experiments conducted under both the point-to-point and broadcast channels demonstrate that for a wide range of channel error probability, inclusion of CRC significantly reduces the EED without sacrificing bandwidth. Further analyses are conducted to determine the best tradeoff between bits allocated for source quantization and CRC error detection.

Performance Analysis of Distributed Beamforming in a Spectrum Sharing System

In this paper, we consider a distributed beamforming scheme (DBF) in a spectrum sharing system where multiple secondary users share the spectrum with some licensed primary users under an interference temperature constraint. We assume that the DBF is applied at the secondary users. We first consider optimal beamforming and compare it with the user selection scheme in terms of the outage probability and bit error rate performance metrics. Since perfect feedback is difficult to obtain, we then investigate a limited feedback DBF scheme and develop an analysis for a random vector quantization design algorithm. Specifically, the approximate statistics functions of the squared inner product between the optimal and quantized vectors are derived. With these statistics, we analyze the outage performance. Furthermore, the effects of channel estimation error and number of primary users on the system performance are investigated. Finally, optimal power adaptation and cochannel interference are considered and analyzed. Numerical and simulation results are provided to illustrate our mathematical formalism and verify our analysis.

IMAGE COMPRESSION USING SELF-ORGANIZING FEATURE MAP AND WAVELET TRANSFORMATION

In this paper, a new method of vector quantizer design for image compression using Generic codebook and wavelet transformation is proposed. In the proposed method, Self Organizing Feature Map (SOFM) is used for initial codebook generation. A new scheme of wavelet transformation based Vector Quantization (VQ) technique is proposed to replace the SOFM code vectors by VQ code vectors. The proposed wavelet transform is used to generate wavelet coefficients which are then converted into VQ code vectors. Discrete Cosine Transformation based vector quantization technique is proposed in the existing image compression algorithms with low quality images with greater amount of information loss. Hence to increase the psycho visual quality of the reconstructed image wavelet transformation based vector quantization technique is proposed in this paper. Performance of the proposed work is tested with varying codebook size and various training images. Experimental results show that the reconstructed images obtained by the proposed method are of good quality with better compression ratio and higher Peak Signal–to– Noise Ratio.

Geometric piecewise uniform lattice vector quantization of the memoryless Gaussian source

The aim of this paper is to find a quantization technique that has low implementation complexity and asymptotic performance arbitrarily close to the optimum. More specifically, it is of interest to develop a new vector quantizer design procedure for a memoryless Gaussian source that yields vector quantizers with excellent performance and the structure required for fast quantization. To achieve this, we combined a fast lattice-encoding algorithm with a geometric approach to generate a model of a geometric piecewise-uniform lattice vector quantizer. Expressions for granular distortion and the optimal number of outputs points in each region were derived. Both exact and approximative asymptotic analyses were carried out. During this process, the constant probability density function of the input signal vector was kept inside the whole region. The analysis demonstrated the existence of piecewise-constant approximations to the input-vector probability density function, which is optimal for the proposed geometric piecewise-uniform vector quantizer. The considered quantization technique is near optimal for a memoryless Gaussian source. In other words, this paper proposes a method for a near-optimum, low-complex vector quantizer design based on probability density function discretization. The presented methodology gives a signal-to-quantization noise ratio that in some cases differs from the optimum by 0.1 dB or less. Improvements of the considered model in performance and complexity over some of the existing techniques are also demonstrated.

Design and Analysis of Optimal Noisy Channel Quantization With Random Index Assignment

This paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance. Given a tandem source-channel coding system with vector quantization, block channel coding, and random index assignment, a closed-form formula is first derived for computing the average end-to-end distortion (EED) of the system, which reveals a structural factor called the scatter factor of a noisy channel quantizer. Based on this formula, we propose a noisy-channel quantization design method by minimizing the EED. Experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the EED when compared with quantizers designed separately without reference to channel conditions, which reveals a practical and effective design for noisy-channel quantization as to simplify the channel model by considering a random index assignment. Furthermore, we have presented the high rate asymptotic analysis of the EED for the tandem system, while convergence analysis of the iterative algorithm is included in the Appendix.

VECTOR QUANTIZATION BASED ON STEADY-STATE MEMETIC ALGORITHM

A novel memetic algorithm (MA) for the design of vector quantizers (VQs) is presented in this paper. The algorithm uses steady-state genetic algorithm (GA) for the global search and K-means algorithm for the local improvement. As compared with the usual MA using the generational GA for global search, the proposed MA dramatically reduces the computational time for VQ training. In addition, it attains a near global optimal solution, and its performance is insensitive to the selection of initial codewords. Numerical results show that it can save more than 70% of computation time while maintaining a comparable performance as previous MA.

Concentric Permutation Source Codes

Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the simplicity of encoding while increasing the number of rate-distortion operating points, improving the convex hull of operating points, and increasing design complexity. We show that when the subcodes are designed with the same composition, optimization of the codebook reduces to a lower-dimensional vector quantizer design within a single cone. Heuristics for reducing design complexity are presented, including an optimization of the rate allocation in a shape-gain vector quantizer with gain-dependent wrapped spherical shape codebook.

FPGA implementation of genetic vector quantizers

This paper presents a novel hardware architecture for genetic vector quantizer (VQ) design. It is based on steady-state genetic algorithm (GA) and adopts shift registers for accelerating mutation and crossover operations while reducing area cost. It also uses a pipeline for fitness evaluation. The proposed architecture has been embedded in a softcore CPU for physical performance measurement. Experimental results show that it is an effective alternative for VQ optimization attaining both high performance and low computational time.

An Efficient Distributed Genetic Algorithm Architecture for Vector Quantizer Design

This paper presents a novel distributed genetic algorithm (GA) architecture for the design of vector quantizers. The design is based on a multi-core architecture, where each island of the GA is associated with a hardware accelerator and a softcore processor for independent genetic evolutions. An on-chip RAM with a mutex circuit is adopted for the migration of genetic strings among different islands. This allows a simple and flexible migration for the implementation of hardware distributed GA. Experimental results shows that the proposed architecture has significantly lower computational time as compared with its software counterparts running on multicore processors with multithreading for GA-based optimization.

Hyperplane-Based Vector Quantization for Distributed Estimation in Wireless Sensor Networks

This paper considers distributed estimation of a vector parameter in the presence of zero-mean additive multivariate Gaussian noise in wireless sensor networks. Due to stringent power and bandwidth constraints, vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information, which is then forwarded to a fusion center where a final estimate of the vector parameter is obtained. Within such a context, this paper focuses on a class of hyperplane-based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization. It is shown that the key of the vector quantization design is to find a compression vector for each sensor. Under the framework of the Cramer-Rao bound (CRB) analysis, the compression vector design problem is formulated as an optimization problem that minimizes the trace of the CRB matrix. Such an optimization problem is extensively studied. In particular, an efficient iterative algorithm is developed for the general case, along with optimal and near-optimal solutions for some specific but important noise scenarios. Performance analysis and simulation results are carried out to illustrate the effectiveness of the proposed scheme.

Efficient memetic vector quantizer design based on reconfigurable hardware and softcore processor

This paper presents a novel hardware architecture for memetic vector quantizer (VQ) design. The architecture uses steady-state genetic algorithm (GA) for global search, and C-Means algorithm for local refinement. It adopts a shift register based circuit for accelerating mutation and crossover operations for steady state CA operations. It also uses a pipeline architecture for the hardware implementation of C-Means algorithm. The proposed architecture is embedded in a softcore CPU, and implemented on a field programmable logic array (FPGA) device for physical performance measurement. Experimental results show that the proposed architecture is an effective method for VQ optimization attaining both high performance and low computational time.

Neuro-Wavelet based vector quantizer design for image compression

This paper presents a novel idea of designing codebook, which is heart of vector quantization scheme based on Kohonens self organizing feature maps (SOFM) and wavelet transform. Being named as neuro wavelet generic codebook for compression of gray images, it can also be extended to the compression of color images and video frames. The code vectors are generated by evaluating the characteristics of the specific image sub samples, which are determined through rigorous mathematical operations and training the selected samples by Kohonen's SOFM artificial neural network with adjustable learning rate and initializations conditions followed by application of discrete wavelet transform. The testing of the codebook is done with variety of images and the compression performance is evaluated by using objective and subjective quality measures such as image fidelity, structural content, mean structural similarity index, universal quality index, spatial frequency measure and spectral activity measure along with PSNR. The proposed design is such that it can be implemented with less complexity and cost using VLSI techniques.

$M$-Description Lattice Vector Quantization: Index Assignment and Analysis

In this paper, we investigate the design of symmetric entropy-constrained multiple description lattice vector quantization (MDLVQ), more specifically, MDLVQ index assignment. We consider a fine lattice containing clean similar sublattices with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -similarity. Due to the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -similarity of the sublattices, an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -fraction lattice can be used to regularly partition the fine lattice with smaller Voronoi cells than a sublattice does. With the partition, the MDLVQ index assignment design can be translated into a transportation problem in operations research. Both greedy and general algorithms are developed to pursue optimality of the index assignment. Under high-resolution assumption, we compare the proposed schemes with other relevant techniques in terms of optimality and complexity. Following our index assignment design, we also obtain an asymptotical close-form expression of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -description side distortion. Simulation results on coding different sources of Gaussian, speech and image are presented to validate the effectiveness of the proposed schemes.

Fuzzy declustering-based vector quantization

Vector quantization is a useful approach for multi-dimensional data compression and pattern classification. One of the most popular techniques for vector quantization design is the LBG (Linde, Buzo, Gray) algorithm. To address the problem of producing poor estimate of vector centroids which are subjected to biased data in vector quantization; we propose a fuzzy declustering strategy for the LBG algorithm. The proposed technique calculates appropriate declustering weights to adjust the global data distribution. Using the result of fuzzy declustering-based vector quantization design, we incorporate the notion of fuzzy partition entropy into the distortion measures that can be useful for classification of spectral features. Experimental results obtained from simulated and real data sets demonstrate the effective performance of the proposed approach.

Redesigning vector quantizers using implicitly estimated probability density functions

Vector quantization is the most general form of quantization, and is a critical step in many compression systems for reducing the bitrate while controlling the distortion in the reconstructed signal. A vector quantizer (VQ) is usually designed using the generalized Lloyd algorithm which requires a training set that is assumed to be drawn from some underlying pdf characterizing the signal to be compressed. We consider here the problem of redesigning an existing VQ for some transformed or repartitioned signal space. Since VQ design is similar to the construction of nonlinear bin histograms, the VQ codebook provides an estimate of the pdf underlying the training set that was originally used to design it. We exploit this observation to synthesize training sets from the VQ codebooks such that they have statistics similar to those of the unknown original training sets. Using the proposed training set synthesis approach, we achieve improvements in performance of between 9.5% and 34% in VQ partitioning and redesign applications compared to a directly repartitioning and transforming the given VQ codebooks.