Robust Data Compression: Variable Length Codes and Burst Errors

This paper characterizes factors affecting the accuracy of the correlation coefficient (CC) template matching algorithm, as applied to motion tracking from two-dimensional real-time coronary artery magnetic resonance images. The performance of this algorithm is analyzed in the presence of both random and systematic error. In the presence of random error, it is shown that a necessary and sufficient condition for accurate motion tracking is a large CC difference-to-noise ratio (CCDNR). The CCDNR itself is in turn affected by five factors: image and template size, image and template structure, and the magnitude of the noise. Techniques are introduced for manipulating some of these factors in order to increase the CCDNR for greater motion tracking accuracy. In the presence of superimposed systematic error it is shown that, while large CCDNR is necessary, it alone is not sufficient to ensure accurate motion tracking. Techniques are developed for improving motion tracking accuracy that minimize the effects of systematic error, while maintaining an adequate CCDNR level. The ability of these techniques to improve motion tracking accuracy is demonstrated both in phantoms and in coronary artery images.

In this paper, a comparative analysis of switching-based calibration algorithms for DACs is presented. The algorithms are compared by the static nonlinearity reduction in presence of random and systematic errors. The influence of the following parameters is considered: a type of constructed array, a resolution of the primary array, numbers of folding and decoupling operations. Fully unarized arrays reduce INL and cannot enhance DNL, unlike fully binarized ones. All algorithms improve nonlinearity in presence of random errors better than in presence of systematic errors.

Variable length codes (VLC) have found widespread use for efficient encoding of symbols with unequal probabilities in many practical situations. However, bit errors can cause a loss of decoder synchronism that often leads to error propagation. Recent advances in the development of VLC that limit the effect of error propagation, such as reversible VLC and self-synchronising VLC, contribute further to their popularity. However, it is still important to model the performance of various VLC code sets so that comparisons can be made between different coding schemes and for different applications. Communicating sequential processes (CSP) is a well-established formal description technique that allows one to analyse the behaviour of concurrently evolving processes. It has been successfully applied to industrial-scale problems. The paper describes how CSP can be applied to the modelling of the resync process of VLC. This approach offers three main advantages. First, a complete model comprises processes and events as basic building blocks, making this approach highly scalable. Second, different semantic models provide different level of abstraction. Third, tools are available for automatic generation of sync sequences, which also provide a measure of sync performance. This facilitates comparisons of different VLC schemes in addition to code sets obtained using a given coding scheme.

Joint source-channel decoding of variable length codes (VLC) for image and video streaming transmission over unreliable links, such as wireless networks, is a subject of increasing interest. Much more residual source redundancy can be exploited when both types of correlation: (i) the correlation between bits inside a VLC codeword as well as; (ii) the correlation between VLC codewords of a VLC sequence unit (e.g. corresponding to one image block), are taken into account. The paper (Hang Nguyen et al, IEEE Int. Conf. on Acoustics, Speech, and Sigpro., 2004) proposes an optimum maximum likelihood (ML) decoder of VLC sequences which can exploit these two kinds of correlation and outperforms the existing VLC decoders. This paper proposes a reduced complexity version of this optimal VLC decoder. Simulation results show that the complexity is reduced by 5 in terms of number of possible candidates, while the performance is only slightly sub-optimal compared with the optimal version of the Hang Nguyen paper.

In multiple-user communications, the bursty nature of the packet arrival times cannot be divorced from the analysis of the transmission process. However, in traditional information theory the random arrival times are smoothed out by appropriated source coding and no consideration is made for the end-to-end delay. In this thesis, using tools from network theory, we investigate simple models that consider the end-to-end delay and/or the variability of the packet arrivals as important parameters, while staying in a information theoretic framework. First, we simplify the problem and focus on the transmission of a bursty source over a single-user channel. We introduce a new measure of channel features that enable us to incorporate the possibility to code among several packets in a scheduling problem. In this setup, we look for policies that minimize the average packet delay. Assuming that the packets are independent and sufficiently large to perform capacity achieving coding, we then consider the problem of allocating rates among a finite number of users communicating through a multiple-user channel. Following the previous work in the context of multiple-access channel, we formulate a scheduling problem in which the rate of each user is chosen from the capacity region of the multiple-user channel. Here, the goal is to find a scheduling policy that minimizes the sum of the transmitter queue lengths, such a policy is called delay optimal. In particular settings, for the additive Gaussian multiple-access channel we show the delay optimality of the Longer Queue Higher Rate policy introduced by Yeh. And, when the users communicate through a symmetric broadcast channel, we propose and show the delay optimality of a Best User Highest Possible Rate policy, among a large class of admissible policies. Finally, in the last part of this thesis, we look at the multiple-user channel coding problem from the perspective of the receivers. By measuring the transmission rates at the receivers, we are able to define variable length codes and to characterize the region of achievable rates when the receivers can decode their intended messages at different instants of time. For the two-user degraded broadcast channel and for the two-user multiple-access channel, we show that the gain in using variable length codes essentially comes from the possibility for the receivers to decode the transmitted messages in non-overlapping periods of time.

Variable length codes (VLCs), used in data compression, are very sensitive to error propagation in the presence of noisy channels. To address this problem, several joint source channel turbo techniques have been proposed in the literature. In this paper, we focus on pairs of source/VLC of low redundancy, i.e., when there is a good match between the source statistics and the length distribution of the VLC. It is a case not considered extensively in the literature so far and the classical concatenation of a VLC and a convolutional code is not satisfying. Through EXIT chart and interleaving gain analysis, we show that the introduction of a repetition code between the VLC and the convolutional code considerably improves global performance. In particular, excellent symbol error rates are obtained with reversible VLCs which are used in recent source codecs.

A concurrent variable length coding (VLC) decoder, introduced in Hsieh and Kim (1996) and Shaw-Min Lei and Ming-Ting Sun (1989), can achieve high system performance by decoding VLC codes concurrently by exploiting the principle of variable-length coding statistical characteristics, shorter codewords appear often. For concurrent VLC decoding, the better the decoding throughput, the more complicated the hardware and control. Therefore, a compromise should be made between performance and cost. In this paper, a systematic approach based on mathematical models for a concurrent VLC decoder is proposed. The tradeoff between system performance and hardware cost is investigated.

A scheme for the synchronization of variable length codes

The recent H.264 video coding standard adopted context-based adaptive variable length coding (CAVLC) as the entropy coding tool. By combining adaptive variable length coding (VLC) with context modeling, we can achieve a high degree of redundancy reduction. However, CAVLC in H.264 has a problem that correctness of VLC table prediction is low. In this paper, we propose a new VLC table prediction algorithm using both the correlation of coding mode and the statistics of mode distribution in both intra and inter frames. Experimental results show that the proposed algorithm reduces the bit rate by 0.94% on average.

An efficient architecture of variable length coding (VLC) is developed for recent multimedia applications, such as video and image compression. VLC plays a crucial part in these applications in that it provides a very effective coding gain. In this paper, we will describe an architecture design of VLC encoder. It can produce VLC codeword and amplitude, and pack them in order to achieve the constant word-length output. In addition, in this pipeline architecture, the VLC codeword and the amplitude can be processed in one clock cycle such that the input data rate of VLC encoder can reach as high as the sampling rate of video/image data. Therefore, it is very suitable for very high data rate video and image compression applications.

The error recovery capability of variable length code (VLC) has been considered as an important performance and design criterion in addition to its coding efficiency. However, almost all of the existing methods for evaluating the error recovery capability of VLC assume that the transmission fault is a random single bit inversion. In this paper, we consider a more generalized problem of precisely evaluating the error recovery capability of VLC in the case that the encoded bit stream is transmitted over a BSC with arbitrary crossover probability. By making use of the Perron-Frobenius Theorem, we derive a very simple expression for the exact mean symbol error rate (MSER) in Levenshtein distance sense. We also prove that in the very low crossover probability region, the mean error propagation length (MEPL) derived for single inversion error case approaches a scaled value of MSER. In addition, we briefly discuss the error recovery of VLC over Gilbert-Elliott channel, which is one of the simplest and practical models for a channel with memory.

We address the optimization of joint source-channel coding schemes for iterative source-channel decoding (ISCD) of first-order Markov sources. The optimization requires source encoders, providing code words with a minimum Hamming distance dmin ges 2. Usually, specifically designed variable- length codes (VLCs) are applied for this purpose, leading, however, to an increased complexity of the decoder. In this paper, we propose a novel concept: a single parity-check code is employed for mapping the quantized source symbols to a binary representation. The additional redundancy introduced by this mapping is afterwards compensated by an inner channel code with rate R > 1. Simulation results for the AWGN channel show that the proposed scheme is superior to VLC- based approaches, while leading to a significantly reduced complexity at the same time.

Introduction . This article analyzes the possibility of implementing highly efficient fault-tolerant algorithms for resolving the ambiguity of phase measurements in Russian and foreign global navigation satellite systems. Nominal values of the GLONASS carrier frequencies with code division of signals are proposed, which ensure an increase in its efficiency by implementing the technology of non-multiple scales. Algorithms for resolving the ambiguity of phase measurements are considered. These algorithms are based on a system of residual classes to calculate the integer value of the number of phase cycles of carrier frequencies in the obtained unambiguity range. The simulation results are presented, and the stability of the proposed algorithms to systematic and random errors of phase measurements is shown. Aim . To improve the efficiency of global navigation satellite systems in determining the position of consumer navigation equipment using phase measurements. Materials and methods . The MATLAB modeling environment was used to process phase measurements from RINEX files. This environment has proven efficient in resolving a wide range of scientific problems of varying complexity in industrial and research settings. To achieve the research aim, the mathematical apparatus of number theory and the system of residual classes were employed. Results . For the GLONASS system with code division of signals, new nominal values of carrier frequencies are proposed; a highly efficient fault-tolerant algorithm for resolving the ambiguity of phase measurements is developed and simulated. The stability of non-multiple scales to systematic errors causing a shift of scales relative to each other is shown, and the operability and reliability of ambiguity resolution algorithms in the presence of random errors not exceeding the value of the specified limiting error of phase measurements is confirmed. Conclusion . The conducted analysis has shown the possibility of forming non-multiple phase metric scales in consumer navigation equipment using signals with code division of GLONASS, GPS, Galileo, and BeiDou systems.

The variable length code (VLC) tables in MPEG-1/2/4 and H.26X are fixed and optimized for a limited range of bit-rates, and they cannot handle a variety of applications. The universal variable length code (UVLC) is a new scheme to encode syntax elements and has some configurable capabilities. It is being considered in the ITU-T H.26L. However, the configurable feature of UVLC has not been well explored. In this paper we describe a VLC scheme which uses configurations as parameters to adapt UVLC to different symbol distributions of different applications. We also propose a method to automatically determine the configuration parameters based on a genetic algorithm (GA). Experimental results show that our method can achieve very good coding efficiency while drastically simplifying the encoding and decoding process, and is applicable to a variety of applications.

A ray theoretical traveltime inversion method in two dimensional arbitrarily dipping layers has been developed and applied to synthetic and real field data. The method is based on Durbaum's formula and may be applied to single-fold as well as CMP raw data. The advantage of Durbaum's formula is that we can estimate dipping angles as well as accurate velocities in dipping layers. In addition, the number of traces which can be utilized for velocity estimations is drastically increased. Also, a statistical method can be used to estimate normal incident times (t$\sb{\rm o}$) and the take-off angles at the surface (B$\sb{\rm o}$) which are measured manually from a stacked section in other methods. Basically, two different statistical ways of interval parameter estimations are discussed. One is Gauss-Newton's nonlinear least squares which applies to sampled traveltime data. The other is the coherency measures technique which does not need picking. To visualize the coherency measures, three different types of plotting are proposed depending on which parameter is fixed with respect to the others. The velocity-B$\sb{\rm o}$ analysis display which plots semblance coefficients on the axes of Vnmo and B$\sb{\rm o}$ at a fixed t$\sb{\rm o}$ is the most efficient method of presentation. An analytical method and an iterative method for velocity inversion from interval parameters are discussed. A computer algorithm to trace rays efficiently in arbitrarily dipping plane layers is also presented because both inversion methods need ray tracing to solve the inversion equation. The accuracy of inversion is studied through models. This study shows that velocity-B$\sb{\rm o}$ analysis is superior to Dix's and Hubral's method for estimating the interval velocities, depths, and dipping angles. Even in the presence of random errors, the method gives a better prediction than the others. The inversion from curved layers and the effect of multiples and diffractions on velocity-B$\sb{\rm o}$ analysis are examined. Application of Velocity-B$\sb{\rm o}$ analysis to real seismic data shows that it successfully predicts both velocity and dipping angle. These accurate velocities and dipping angles are essential in subsequent processing stages.