The asymptotic closed-loop approach to predictive vector quantizerdesign with application in video coding

The basic vector quantization (VQ) technique employed in video coding belongs to the category of predictive vector quantization (PVQ), as it involves quantization of the (motion compensated) frame prediction error. It is well known that the design of PVQ suffers from fundamental difficulties, due to the prediction loop, which have an impact on the convergence and the stability of the design procedure. We propose an approach to PVQ design that enjoys the stability of open-loop design while it ensures ultimate optimization of the closed-loop system. The method is derived for general predictive quantization, and we demonstrate it on video compression at low bit rates, where it provides substantial improvement over standard open and closed loop design techniques. Further, the approach outperforms standard DCT-based video coding.     

Adaptive entropy-coded predictive vector quantization of images

The authors consider 2-D predictive vector quantization (PVQ) of images subject to an entropy constraint and demonstrate the substantial performance improvements over existing unconstrained approaches. They describe a simple adaptive buffer-instrumented implementation of this 2-D entropy-coded PVQ scheme which can accommodate the associated variable-length entropy coding while completely eliminating buffer overflow/underflow problems at the expense of only a slight degradation in performance. This scheme, called 2-D PVQ/AECQ (adaptive entropy-coded quantization), is shown to result in excellent rate-distortion performance and impressive quality reconstructions of real-world images. Indeed, the real-world coding results shown demonstrate little distortion at rates as low as 0.5 b/pixel     

Parallel Viterbi algorithm implementation: breaking theACS-bottleneck

The central unit of a Viterbi decoder is a data-dependent feedback loop which performs an add-compare-select (ACS) operation. This nonlinear recursion is the only bottleneck for a high-speed parallel implementation. A linear scale solution (architecture) is presented which allows the implementation of the Viterbi algorithm (VA) despite the fact that it contains a data-dependent decision feedback loop. For a fixed processing speed it allows a linear speedup in the throughput rate by a linear increase in hardware complexity. A systolic array implementation is discussed for the add-compare-select unit of the VA. The implementation of the survivor memory is considered. The method for implementing the algorithm is based on its underlying finite state feature. Thus, it is possible to transfer this method to other types of algorithms which contain a data-dependent feedback loop and have a finite state property     

Novel Transmit Beamforming Schemes for Time-Selective Fading Multiantenna Systems

Transmit beamforming has been widely adopted for wireless systems with multiple transmit antennas. For a block fading channel, the Grassmannian beamformer has been shown to provide very good performance for finite rate feedback. However, the original Grassmannian beamformer does not take the time domain correlation of the channel fading into consideration. In this paper, based on a first-order autoregressive (AR1) dynamic fading model, we develop two new classes of beamforming algorithms that exploit the interframe correlations in the channel fading. We first introduce an algorithm based on a standard predictive vector quantization (PVQ) approach, and the resulting PVQ beamformer accomplishes superior power delivery at the receiver. However, the error performance of the PVQ beamformer is not satisfactory at high signal-to-noise ratios, and it also has a high implementation complexity. To resolve these issues, we then develop a novel successive beamforming (SBF) algorithm. The new SBF scheme uses the knowledge of the previous fading blocks to aid the beamforming codebook design of the current fading block. The beamforming codebook is constructed based on the successive partition of the surface of a spherical cap. The new SBF scheme accomplishes nearly the same performance as that of the PVQ beamformer, and it has a much simpler implementation. Through numerical simulations, we demonstrate that the proposed beamformers outperform the other previously proposed beamformers at various fading scenarios     

Scalable Linear Array Architecture with Data-Driven Control for Ultrahigh-Speed Vector Quantization

Current and future requirements for adaptive real-time image compression challenge even the capabilities of highly parallel realizations in terms of hardware performance. Previously proposed linear array structures for full-search vector quantization do not offer scalability and adaptivity in this context, because they require separate data/control pins for dynamically updating the codevectors and complicated interlock mechanisms to ensure that the regular data flow is not corrupted as a result of updates. We explore the design space for full-search vector quantizers and propose a novel linear processor array architecture in which global wiring is limited to clock and power supply distribution, thus allowing high-speed processing in spite of only limited communication with the host via the boundary processors. The resulting fully pipelined design is not only area-efficient for VLSI implementation but is also readily scalable and offers extremely high performance.     

Predictive vector quantization with intrablock prediction supportregion

A predictive vector quantization (PVQ) structure is proposed, where the encoder uses a predictor based on an intrablock support region, followed by a modified vector quantizer stage. Simulation results show that a modification on a previously published PVQ system led to an improvement of 1 dB in PSNR for Lenna.     

Control generation in the design of processor arrays

The problem of mapping algorithms onto regular arrays has received great attention in the past. Results are available on the mapping of regular algorithms onto systolic or wavefront arrays. On the other hand, many algorithms that can be implemented on parallel architectures are not completely regular but are composed of a set of regular subalgorithms. Recently, a class of configurable processor arrays has been proposed that allows the efficient implementation of piecewise regular algorithms. In contrary to pure systolic of wavefront arrays they are distinguished by a dynamic configuration structure. The known trajectories, however, cannot be applied to the design of configurable processor arrays because the functions of the procesing elements and the interconnection structure are time- and space-dependent. In this paper, a systematic procedure is introduced that allows the efficient design of configurable processor arrays including the specification of the processing elements and the generation of control signals. Control signals are propagated through the processor array. The proposed design trajectory can be used for the design of regular arrays or configurable arrays.     

Low-Complexity High-Speed Decoder Design for Quasi-Cyclic LDPC Codes

This paper studies low-complexity high-speed decoder architectures for quasi-cyclic low density parity check (QC-LDPC) codes. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. Enhanced partially parallel decoding architectures are proposed to linearly increase the throughput of conventional partially parallel decoders through introducing a small percentage of extra hardware. Based on the proposed architectures, a (8176, 7154) Euclidian geometry-based QC-LDPC code decoder is implemented on Xilinx field programmable gate array (FPGA) Virtex-II 6000, where an efficient nonuniform quantization scheme is employed to reduce the size of memories storing soft messages. FPGA implementation results show that the proposed decoder can achieve a maximum (source data) decoding throughput of 172 Mb/s at 15 iterations     

Predictive Vector Quantization of Images

The purpose of this paper is to present new image coding schemes based on a predictive vector quantization (PVQ) approach. The predictive part of the encoder is used to partially remove redundancy, and the VQ part further removes the residual redundancy and selects good quantization levels for the global waveform. Two implementations of this coding approach have been devised, namely, sliding block PVQ and block tree PVQ. Simulations on real images show significant improvement over the conventional DPCM and tree codes using these new techniques. The strong robustness property of these coding schemes is also experimentally demonstrated.     

Efficient realizations of the discrete and continuous wavelettransforms: from single chip implementations to mappings on SIMD arraycomputers

This paper presents a wide range of algorithms and architectures for computing the 1D and 2D discrete wavelet transform (DWT) and the 1D and 2D continuous wavelet transform (CWT). The algorithms and architectures presented are independent of the size and nature of the wavelet function. New on-line algorithms are proposed for the DWT and the CWT that require significantly small storage. The proposed systolic array and the parallel filter architectures implement these on-line algorithms and are optimal both with respect to area and time (under the word-serial model). Moreover, these architectures are very regular and support single chip implementations in VLSI. The proposed SIMD architectures implement the existing pyramid and a'trous algorithms and are optimal with respect to time     

A pyramid vector quantizer

The geometric properties of a memoryless Laplacian source are presented and used to establish a source coding theorem. Motivated by this geometric structure, a pyramid vector quantizer (PVQ) is developed for arbitrary vector dimension. The PVQ is based on the cubic lattice points that lie on the surface of anL-dimensional pyramid and has simple encoding and decoding algorithms. A product code version of the PVQ is developed and generalized to apply to a variety of sources. Analytical expressions are derived for the PVQ mean square error (mse), and simulation results are presented for PVQ encoding of several memoryless sources. For large rate and dimension, PVQ encoding of memoryless Laplacian, gamma, and Gaussian sources provides rose improvements of5.64, 8.40, and2.39dB, respectively, over the corresponding optimum scalar quantizer. Although suboptimum in a rate-distortion sense, because the PVQ can encode large-dimensional vectors, it offers significant reduction in rose distortion compared with the optimum Lloyd-Max scalar quantizer, and provides an attractive alternative to currently available vector quantizers.     

A Low-Power Encoder For Pyramid Vector Quantization of Subband Coefficients

A real-time, low-power video encoder design for pyramid vector quantization (PVQ) has been presented. The quantizer is estimated to dissipate only 2.1 mW for real-time video compression of images of 256 × 256 pixels at 30 frames per second in standard 0.8-micronCMOS technology with a 1.5 V supply. Applying this quantizer to subband decomposed images, the quantizer performs better than JPEG on average. We achieve this high level of power efficiency with image quality exceeding that of variable rate codes through algorithmic and architectural reformulation. The PVQ encoder is well-suited for wireless, portable communication applications.     

An Integrated Systolic Array Design for Video Compression

This paper presents an integrated systolic array design for implementing full-search block matching, 2-D discrete wavelet transform, and full-search vector quantization on the same VLSI architecture. These functions are the prime components in video compression and take a great amount of computation. To meet the real-time application requirements, many systolic array architectures are proposed for individually performing one of those functions. However, these functions contain similar computational procedure. The matrix-vector product forms of the three functions are quite analogous. After extracting the common computation component, we design an integrated one-dimensional systolic array that can perform aforementioned three functions. The proposed architecture can efficiently perform three typical functions: (1) the full-search block matching with block of size 16 × 16 and the search are from –8 to 7; (2) the 2-D 2 level Harr transform with block of size 8 × 8; and (3) the full-search vector quantization with input vector of size 2 × 2. A utilization rate of 100% to 97% is achieved in the course of executing full-search block matching and full-search vector quantization. When it comes to perform 2-D discrete wavelet transform, the utilization rate is about 32%. The proposed integrated architecture has lowered hardware cost and reduced hardware structure. It befits the VLSI implementation for video/image compression applications.     

Optical computing techniques for image/video compression

The advantage of optics is its capability of providing highly parallel operations in a three-dimensional space. In this paper, we propose optical architectures to execute various image compression techniques. We optically implement the following compression techniques: transform coding, vector quantization, video coding. We show many generally used transform coding methods, for example, the cosine transform, can be implemented by a simple optical system. The transform coding can be carried out in constant time. Most of this paper is concerned with an innovative optical system for vector quantization using holographic associative matching. Limitations of conventional vector quantization schemes are caused by a large number of sequential searches through a large vector space. Holographic associative matching provided by multiple exposure holograms can offer advantageous techniques for vector-quantization-based compression schemes. Photorefractive crystals, which provide high-density recording in real time, are used as our holographic media. The reconstruction alphabet can be dynamically constructed through training or stored in the photorefractive crystal in advance. Encoding a new vector can be carried out by holographic associative matching in constant time. An extension to interframe coding using optical block matching methods is also discussed     

Predictive vector quantizer design using deterministic annealing

A new approach is proposed for predictive vector quantizer (PVQ) design, which is inherently probabilistic, and is based on ideas from information theory and analogies to statistical physics. The approach effectively resolves three longstanding fundamental shortcomings of standard PVQ design. The first complication is due to the PVQ prediction loop, which has a detrimental impact on the convergence and the stability of the design procedure. The second shortcoming is due to the piecewise constant nature of the quantizer function, which makes it difficult to optimize the predictor with respect to the overall reconstruction error. Finally, a shortcoming inherited from standard VQ design is the tendency of the design algorithm to terminate at a locally, rather than the globally, optimal solution. We propose a new PVQ design approach that embeds our previous asymptotic closed-loop (ACL) approach within a deterministic annealing (DA) framework. The overall DA-ACL method profits from its two main components in a complementary way. ACL is used to overcome the first difficulty and offers the means for stable quantizer design as it provides an open-loop design platform, yet allows the PVQ design algorithm to asymptotically converge to optimization of the closed-loop performance objective. DA simultaneously mitigates or eliminates the remaining design shortcomings. Its probabilistic framework replaces hard quantization with a differentiable expected cost function that can be jointly optimized for the predictor and quantizer parameters, and its annealing schedule allows the avoidance of many poor local optima. Substantial performance gains over traditional methods have been achieved in the simulations.     

Error-resilient pyramid vector quantization for image compression

Pyramid vector quantization (PVQ) uses the lattice points of a pyramidal shape in multidimensional space as the quantizer codebook. It is a fixed-rate quantization technique that can be used for the compression of Laplacian-like sources arising from transform and subband image coding, where its performance approaches the optimal entropy-coded scalar quantizer without the necessity of variable length codes. In this paper, we investigate the use of PVQ for compressed image transmission over noisy channels, where the fixed-rate quantization reduces the susceptibility to bit-error corruption. We propose a new method of deriving the indices of the lattice points of the multidimensional pyramid and describe how these techniques can also improve the channel noise immunity of general symmetric lattice quantizers. Our new indexing scheme improves channel robustness by up to 3 dB over previous indexing methods, and can be performed with similar computational cost. The final fixed-rate coding algorithm surpasses the performance of typical Joint Photographic Experts Group (JPEG) implementations and exhibits much greater error resilience.     

Predictive residual vector quantization [image coding]

This paper presents a new vector quantization technique called predictive residual vector quantization (PRVQ). It combines the concepts of predictive vector quantization (PVQ) and residual vector quantization (RVQ) to implement a high performance VQ scheme with low search complexity. The proposed PRVQ consists of a vector predictor, designed by a multilayer perceptron, and an RVQ that is designed by a multilayer competitive neural network. A major task in our proposed PRVQ design is the joint optimization of the vector predictor and the RVQ codebooks. In order to achieve this, a new design based on the neural network learning algorithm is introduced. This technique is basically a nonlinear constrained optimization where each constituent component of the PRVQ scheme is optimized by minimizing an appropriate stage error function with a constraint on the overall error. This technique makes use of a Lagrangian formulation and iteratively solves a Lagrangian error function to obtain a locally optimal solution. This approach is then compared to a jointly designed and a closed-loop design approach. In the jointly designed approach, the predictor and quantizers are jointly optimized by minimizing only the overall error. In the closed-loop design, however, a predictor is first implemented; then the stage quantizers are optimized for this predictor in a stage-by-stage fashion. Simulation results show that the proposed PRVQ scheme outperforms the equivalent RVQ (operating at the same bit rate) and the unconstrained VQ by 2 and 1.7 dB, respectively. Furthermore, the proposed PRVQ outperforms the PVQ in the rate-distortion sense with significantly lower codebook search complexity.     

Algorithme de quantification vectorielle sphérique à partir du réseau de Gosset d’ordre 8

Regular point lattices find applications both for the design of waveform quantizers and the design of modulation signal sets. Algebraic spherical vector quantization is a technique recently proposed [1] for speech coding applications. It makes use of spherical subsets from regular point lattices. The article concerns itself with algebraic spherical vector quantization based on the so-called Gosset lattice in eight dimensions. An optimal algorithm is detailed which allows an efficient nearest neighbour search within a Gosset spherical set and computes the rank of this nearest neighbour within the set. The performances of such quantizer for the white Gaussian process are given and compared to the information theory limits. Comparing the merits of the statistical and the algebraic approaches to vector quantization leads to the design of hybrid structures which can combine these two techniques.     

Iterative Decoding of Concatenated Convolutional Codes: Implementation Issues

This tutorial paper gives an overview of the implementation aspects related to turbo decoders, where the term turbo generally refers to iterative decoders intended for parallel concatenated convolutional codes as well as for serial concatenated convolutional codes. We start by considering the general structure of iterative decoders and the main features of the soft-input soft-output algorithm that forms the heart of iterative decoders. Then, we show that very efficient parallel architectures are available for all types of turbo decoders allowing high-speed implementations. Other implementation aspects like quantization issues and stopping rules used in conjunction with buffering for increasing throughput are considered. Finally, we perform an evaluation of the complexities of the turbo decoders as a function of the main parameters of the code.     

Adaptive entropy-coded pruned tree-structured predictive vectorquantization of images

Simpler versions of a previously introduced adaptive entropy-coded predictive vector quantization (PVQ) scheme where the embedded entropy constrained vector quantizer (ECVQ) is replaced by a pruned tree-structured VQ (PTSVQ) are described. The resulting encoding scheme is shown to result in drastically reduced complexity at only a small cost in performance. Coding results for selected real-world images are given