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.     

Jointly optimized trellis-coded residual vector quantization

The union of residual vector quantization (RVQ) and trellis-coded vector quantization (TCVQ) was considered by various authors where the emphasis was on the sequential design. We consider a new jointly optimized combination of RVQ and TCVQ with advantages in all categories. Necessary conditions for optimality of the jointly optimized trellis-coded residual vector quantizers (TCRVQ) are derived. A constrained direct sum tree structure is introduced that facilitates RVQ codebook partitioning. Simulation results for jointly optimized TCRVQ are presented for memoryless Gaussian, Laplacian, and uniform sources. The rate-distortion performance is shown to be better than RVQ and sequentially designed TCRVQ     

Partial distortion sensitive competitive learning algorithm foroptimal codebook design

An effective competitive learning algorithm based on the partial distortion theorem is proposed for optimal codebook design. Compared with some representative learning algorithms for codebook design, the proposed algorithm has consistently shown the best performance for designing codebooks of different sizes, especially large size codebooks     

Joint optimization of VQ codebooks and QAM signal constellationsfor AWGN channels

A joint design scheme has been proposed to optimize the source encoder and the modulation signal constellation based on the minimization of the end-to-end distortion including both the quantization error and channel distortion. The proposed scheme first optimizes the vector quantization (VQ) codebook for a fixed modulation signal set, and then the modulation signals for the fixed VQ codebook. These two steps are iteratively repeated until they reach a local optimum solution. It has been shown that the performance of the proposed system can be enhanced by employing a new efficient mapping scheme between codevectors and modulation signals. Simulation results show that a jointly optimized system based on the proposed algorithms outperforms the conventional system based on a conventional quadrature amplitude modulation signal set and the VQ codebook designed for a noiseless channel     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

一种稀疏码本多址接入码本优化设计方法

稀疏码多址接入(SCMA)作为一种具有竞争力的非正交多址接入(NOMA)技术,该技术通过高维调制与稀疏扩频的结合,有效地提升了系统的频谱效率。该文针对现有SCMA码本设计中存在的问题,提出一种同时适用于高斯信道和瑞利衰落信道的SCMA码本优化设计方法。在该方法中,首先通过旋转基准星座和母星座,实现母星座在各个维度上投影点间的最小欧氏距离以及叠加在单个资源块上的总星座中与各用户对应的星座图上星座点间的最小欧氏距离的最大化,以提升SCMA码本在高斯信道下的性能;进而在保持总星座上星座点间最小欧氏距离不变的条件下,通过旋转叠加在单个资源块上多个用户的星座,优化叠加在单个资源块上的与各用户对应的星座图中星座点间最小乘积距离和信号空间分集(SSD)阶数,最后结合Q路坐标交织技术获得额外的分集增益,以提升系统抗信道衰落的能力。仿真结果显示:在高斯信道和瑞利衰落信道下,该文设计的SCMA码本的性能均明显优于华为公司提出的SCMA码本和低密度扩频多址接入(LDS-MA)技术。     

Quadtree Optimization for Image and Video Coding

The optimal design of quadtree-based codecs is addressed. Until now, work in this area has focused on the optimization of the quadtree structure for a given set of leaf quantizers while neglecting the design of the quantizers themselves. In cases where the leaf quantizers have been considered, codebooks have been optimized without regard to the ultimate quadtree segmentation. However, it is not sufficient to consider each problem independently, as separate optimization leads to an overall suboptimal solution. Rather, joint design of the quadtree structure and the leaf codebooks must be considered for overall optimality. The method we suggest is a quadtree constrained version of the entropy-constrained vector quantization design method. To this end, a centroid condition for the leaf codebooks is derived that represents a necessary optimality condition for variable-rate quadtree coding. This condition, when iterated with the optimal quadtree segmentation strategy of Sullivan and Baker results in a monotonically descending rate-distortion cost function, and consequently, an (at least locally) optimal quadtree solution.     

Gradient match and side match fractal vector quantizers for images

In this paper, we propose gradient match fractal vector quantizers (GMFVQs) and side match fractal vector quantizers (SMFVQs), which are two classes of finite state fractal vector quantizers (FSFVQs), for the image coding framework. In our previous work, we proposed the noniterative fractal block coding (FBC) technique to improve the decoding speed and the coding performance for conventional FBC techniques. To reduce the number of bits for denoting the fractal code of the range block, the concepts of the gradient match vector quantizers (GMVQs) and the side match vector quantizers (SMVQs) are employed to the noniterative FBC technique. Unlike ordinary vector quantizers, the super codebooks in the proposed GMFVQs and SMFVQs are generated from the affine-transformed domain blocks in the noniterative FBC technique. The codewords in the state codebook are dynamically extracted from the super codebook with the side-match and gradient-match criteria. The redundancy in the affine-transformed domain blocks is greatly reduced and the compression ratio can be significantly increased. Our simulation results show that 15%-20% of the bit rates in the noniterative FBC technique are saved by using the proposed GMFVQs.     

Space-Time Codebook Design for Spread Systems

The problem of designing space-time constellations for communication in spread multiple-antenna wireless systems over Rayleigh fading channel is addressed. Using the asymptotic union bound on error probability as design criterion, codes based on general complex-valued symbols are obtained with a gradient search optimization technique. New space-time constellations are constructed and their performance is assessed. Simulation results show that the proposed technique achieves significant performance gains over existing schemes. Since the designed codebooks do not seem to possess any structure that could reduce the memory requirements for storing the corresponding codebook, the problem of designing structured space-time constellations is also addressed. To overcome this problem, a discrete Fourier transform-based approach is adopted to design structured codebooks and their performance is evaluated. The new structured codebooks also demonstrate significant improvement over state-of-art structured schemes.     

Minimax partial distortion competitive learning for optimalcodebook design

The design of the optimal codebook for a given codebook size and input source is a challenging puzzle that remains to be solved. The key problem in optimal codebook design is how to construct a set of codevectors efficiently to minimize the average distortion. A minimax criterion of minimizing the maximum partial distortion is introduced in this paper. Based on the partial distortion theorem, it is shown that minimizing the maximum partial distortion and minimizing the average distortion will asymptotically have the same optimal solution corresponding to equal and minimal partial distortion. Motivated by the result, we incorporate the alternative minimax criterion into the on-line learning mechanism, and develop a new algorithm called minimax partial distortion competitive learning (MMPDCL) for optimal codebook design. A computation acceleration scheme for the MMPDCL algorithm is implemented using the partial distance search technique, thus significantly increasing its computational efficiency. Extensive experiments have demonstrated that compared with some well-known codebook design algorithms, the MMPDCL algorithm consistently produces the best codebooks with the smallest average distortions. As the codebook size increases, the performance gain becomes more significant using the MMPDCL algorithm. The robustness and computational efficiency of this new algorithm further highlight its advantages.     

Signature optimization for CDMA with limited feedback

We study the performance of joint signature-receiver optimization for direct-sequence code-division multiple access (DS-CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a random vector quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent and identically distributed (i.i.d.) elements, we evaluate the received signal-to-interference plus noise ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear minimum mean-squared error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver, one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.     

Vector quantization with complexity costs

Vector quantization is a data compression method by which a set of data points is encoded by a reduced set of reference vectors: the codebook. A vector quantization strategy is discussed that jointly optimizes distortion errors and the codebook complexity, thereby determining the size of the codebook. A maximum entropy estimation of the cost function yields an optimal number of reference vectors, their positions, and their assignment probabilities. The dependence of the codebook density on the data density for different complexity functions is investigated in the limit of asymptotic quantization levels. How different complexity measures influence the efficiency of vector quantizers is studied for the task of image compression. The wavelet coefficients of gray-level images are quantized, and the reconstruction error is measured. The approach establishes a unifying framework for different quantization methods like K-means clustering and its fuzzy version, entropy constrained vector quantization or topological feature maps, and competitive neural networks     

Multiplication free vector quantization usingL1 distortion measure and its variants

The author considers vector quantization that uses the L (1) distortion measure for its implementation. A gradient-based approach for codebook design that does not require any multiplications or median computation is proposed. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparing the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The author applies the techniques in predictive vector quantization of images and demonstrates the viability of multiplication-free predictive vector quantization of image data.     

A vector quantizer with minimum visible distortion

A method for designing codebooks for vector quantization (VQ) based on minimum error visibility in a reconstructed picture is described. The method uses objective measurements to define visibility for the picture being coded. The proposed VQ is switched type, i.e., the codebook is divided into subcodebooks, each of which is related to a given subrange of error visibility. Codebook optimization is carried out on the basis of a particular definition of visible distortion of the reconstructed image. Subjective judgment of the test results, carried out at 0.5 b/pel bit rate, indicates that the proposed VQ enables low-distortion images to be reconstructed even when subcodebooks with a small number of codewords are used, thus reducing the codebook search time to about 10% of that required by a fixed VQ (both inside and outside the training set)     

Block transform image coding by multistage vector quantization withoptimal bit allocation

A multistage vector quantization with optimal bit allocation (MVQ-OBA) in the transform domain is presented. A set of bit allocation planes is first obtained by slicing a (scalar) optimal bit allocation map where the number of bits assigned to each coefficient is proportional to the coefficient variance. The set of bit allocation planes determines the coefficients to be used and the codebook size at each stage. The vector dimensionalities are restricted to small values and relatively small codebooks are used, thus reducing both the overhead required for transmitting the codebooks and the complexity in codebook design. The computer simulation results demonstrate that MVQ-OBA is competitive with many other transform coding techniques including variable length transform coding. MVQ-OBA is well suited for progressive transmission     

Enhanced multistage vector quantization by joint codebook design

Multistage vector quantization (MSVQ) can achieve very low encoding and storage complexity in comparison to unstructured vector quantization. However, the conventional stage-by-stage design of the codebooks in MSVQ is suboptimal with respect to the overall performance measure. The authors introduce an algorithm for the joint design of the stage codebooks to optimize the overall performance. The performance improvement, although modest, is achieved with no effect on encoding or storage complexity and only a slight increase in design effort     

Joint source-channel coding for wireless object-based video communications utilizing data hiding.

In recent years, joint source-channel coding for multimedia communications has gained increased popularity. However, very limited work has been conducted to address the problem of joint source-channel coding for object-based video. In this paper, we propose a data hiding scheme that improves the error resilience of object-based video by adaptively embedding the shape and motion information into the texture data. Within a rate-distortion theoretical framework, the source coding, channel coding, data embedding, and decoder error concealment are jointly optimized based on knowledge of the transmission channel conditions. Our goal is to achieve the best video quality as expressed by the minimum total expected distortion. The optimization problem is solved using Lagrangian relaxation and dynamic programming. The performance of the proposed scheme is tested using simulations of a Rayleigh-fading wireless channel, and the algorithm is implemented based on the MPEG-4 verification model. Experimental results indicate that the proposed hybrid source-channel coding scheme significantly outperforms methods without data hiding or unequal error protection.     

Mismatched codebooks and the role of entropy coding in lossy data compression

We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically mismatched to the source distribution), followed by optimal entropy coding that is matched to the quantized codeword distribution. A single-letter formula is derived for the rate achieved by this scheme at a given distortion, in the limit of large codebook dimension. The rate reduction due to entropy coding is quantified, and it is shown that it can be arbitrarily large. In the special case of "almost uniform" codebooks (e.g., an independent and identically distributed (i.i.d.) Gaussian codebook with large variance) and difference distortion measures, a novel connection is drawn between the compression achieved by the present scheme and the performance of "universal" entropy-coded dithered lattice quantizers. This connection generalizes the "half-a-bit" bound on the redundancy of dithered lattice quantizers. Moreover, it demonstrates a strong notion of universality where a single "almost uniform" codebook is near optimal for any source and any difference distortion measure. The proofs are based on the fact that the limiting empirical distribution of the first matching codeword in a random codebook can be precisely identified. This is done using elaborate large deviations techniques, that allow the derivation of a new "almost sure" version of the conditional limit theorem.     

A joint encoder–decoder error control framework for stereoscopic video coding

Stereoscopic video coding (SSVC) plays an important role in various 3D video applications. In SSVC, robust stereoscopic video transmission over error-prone networks is still a challenge problem to be solved. In this paper, we propose a joint encoder–decoder error control framework for SSVC, where error-resilient source coding, transmission network conditions, and error concealment scheme are jointly considered to achieve better error robustness performance. The proposed joint encoder–decoder error control framework includes two parts: an error concealment algorithm at the decoder side and a rate–distortion optimized error resilience algorithm at the encoder side. For error concealment at the decoder side, an overlapped block motion and disparity compensation based error concealment scheme is proposed to adaptively utilize inter-view correlations and temporal correlations. For error resilience at the encoder side, first, the inter-view refreshment is proposed for SSVC to suppress error propagations. Then, an end-to-end distortion model for SSVC is derived, which jointly considers the transmission network conditions, inter-view refreshment, and error concealment tools at the decoder side. Finally, based on the derived end-to-end distortion model, the rate–distortion optimized error resilience algorithm is presented to adaptively select inter-view, inter- or intra-coding for SSVC. The experimental results show that the proposed joint encoder–decoder error control framework has superior error robustness performance for stereoscopic video transmission over error-prone networks.