<p>In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D).</p><p>In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively.</p><p>In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels.</p><p>Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity.</p><p>These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.</p>

In this thesis we study a scalar uniform and non-uniform quantization of random processes (or signals) in average case setting. Quantization (or discretization) of a signal is a standard task in all nalog/digital devices (e.g., digital recorders, remote sensors etc.). We evaluate the necessary memory capacity (or quantization rate) needed for quantized process realizations by exploiting the correlation structure of the model random process. The thesis consists of an introductory survey of the subject and related theory followed by four included papers (A-D). In Paper A we develop a quantization coding method when quantization levels crossings by a process realization are used for its coding. Asymptotical behavior of mean quantization rate is investigated in terms of the correlation structure of the original process. For uniform and non-uniform quantization, we assume that the quantization cellwidth tends to zero and the number of quantization levels tends to infinity, respectively. In Papers B and C we focus on an additive noise model for a quantized random process. Stochastic structures of asymptotic quantization errors are derived for some bounded and unbounded non-uniform quantizers when the number of quantization levels tends to infinity. The obtained results can be applied, for instance, to some optimization design problems for quantization levels. Random signals are quantized at sampling points with further compression. In Paper D the concern is statistical inference for run-length encoding (RLE) method, one of the compression techniques, applied to quantized stationary Gaussian sequences. This compression method is widely used, for instance, in digital signal and image processing. First, we deal with mean RLE quantization rates for various probabilistic models. For a time series with unknown stochastic structure, we investigate asymptotic properties (e.g., asymptotic normality) of two estimates for the mean RLE quantization rate based on an observed sample when the sample size tends to infinity. These results can be used in communication theory, signal processing, coding, and compression applications. Some examples and numerical experiments demonstrating applications of the obtained results for synthetic and real data are presented.

ABSTRACT DETERMINATION OF STOCHASTIC MODEL PARAMETERS OF INERTIAL SENSORS &Uuml / nver, Alper PhD, Department of Electric Electronic Engineering Supervisor: Prof. Dr. M&uuml / beccel Demirekler January 2013, 82 pages Gyro and accelerometer systematic errors due to biases, scale factors, and misalignments can be compensated via an on-board Kalman filtering approach in a Navigation System. On the other hand, sensor random noise sources such as Quantization Noise (QN), Angular Random Walk (ARW), Flicker Noise (FN), and Rate Random Walk (RRW) are not easily estimated by an on-board filter, due to their random characteristics. In this thesis a new method based on the variance of difference sequences is proposed to compute the powers of the above mentioned noise sources. The method is capable of online or offline estimation of stochastic model parameters of the inertial sensors. Our aim in this study is the estimation of ARW, FN and RRW parameters besides the quantization and the Gauss-Markov noise parameters of the inertial sensors. The proposed method is tested both on the simulated and the real sensor data and the results are compared with the Allan variance method. Comparison shows very satisfactory results for the performance of the method. Computational load of the new method is less than the computational load of the Allan variance on the order of tens. One of the usages of this method is the individual noise characterization. A noise, whose power spectral density has a constant slope, can be identified accurately by the proposed method. In addition to this, the parameters of the GM noise can also be determined. Another idea developed here is to approximate the overall error source as a combination of ARW and some number of GM sources only. The reasons of selecting such a structure is the feasibility of using these models in a Kalman filter framework for error propagation as well as their generality of modeling other noise sources.

With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages. Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.

The area of cooperative communications has received tremendous research interest in recent years. This interest is not unwarranted, since cooperative communications promises the ever-so-sought after diversity and multiplexing gains typically associated with multiple-input multiple-output (MIMO) communications, without actually employing multiple antennas. In this dissertation, we consider several cooperative communication channels, and for each one of them, we develop information theoretic coding schemes and derive their corresponding performance limits. We next develop and design practical coding strategies which perform very close to the information theoretic limits. The cooperative communication channels we consider are: (a) The Gaussian relay channel, (b) the quasi-static fading relay channel, (c) cooperative multiple-access channel (MAC), and (d) the cognitive radio channel (CRC). For the Gaussian relay channel, we propose a compress-forward (CF) coding strategy based on Wyner-Ziv coding, and derive the achievable rates specifically with BPSK modulation. The CF strategy is implemented with low-density parity-check (LDPC) and irregular repeataccumulate codes and is found to operate within 0.34 dB of the theoretical limit. For the quasi-static fading relay channel, we assume that no channel state information (CSI) is available at the transmitters and propose a rateless coded protocol which uses rateless coded versions of the CF and the decode-forward (DF) strategy. We implement the protocol with carefully designed Raptor codes and show that the implementation suffers a loss of less than 10 percent from the information theoretical limit. For the MAC, we assume quasi-static fading, and consider cooperation in the low-power regime with the assumption that no CSI is available at the transmitters. We develop cooperation methods based on multiplexed coding in conjunction with rateless codes and find the achievable rates and in particular the minimum energy per bit to achieve a certain outage probability. We then develop practical coding methods using Raptor codes, which performs within 1.1 dB of the performance limit. Finally, we consider a CRC and develop a practical multi-level dirty-paper coding strategy using LDPC codes for channel coding and trellis-coded quantization for source coding. The designed scheme is found to operate within 0.78 dB of the theoretical limit. By developing practical coding strategies for several cooperative communication channels which exhibit performance close to the information theoretic limits, we show that cooperative communications not only provide great benefits in theory, but can possibly promise the same benefits when put into practice. Thus, our work can be considered a useful and necessary step towards the commercial realization of cooperative communications.

The multimedia watermarking techniques are evolved very quickly in the last years with the increase in the use of internet. The evolution of the internet makes the copyright issues very important and many different approaches are appeared to protect the digital content. On the other hand, holography is the method to store the 3-D information of an object but it is very applicable to use as a watermark because of the nature of the holographic data. The 3-D object can be reconstructed from the hologram even if the hologram is cropped or occluded. However, watermarking of an image with a hologram is a very novel approach and there are only a few works in the literature which are not very robust against the attacks like filtering or compression. In this thesis, we propose to embed the phase of the hologram to an image using quantization index modulation (QIM). QIM is utilized to make the watermarking scheme blind and degrade the host image as low as possible. The robustness of the proposed technique is also tested against several attacks such as filtering, compression, etc. The evaluated performance of this system is compared with the existing methods in the literature which uses either holograms or logos as the secret mark. Furthermore, the characteristics of the holograms are investigated and the findings about the hologram compression are reported in this work.

Covariance Matrix in target tracking algorithms has a critical role at multi- sensor track fusion systems. This matrix reveals the uncertainty of state es- timates that are obtained from diferent sensors. So, many subproblems of track fusion usually utilize this matrix to get more accurate results. That is why this matrix should be interchanged between the nodes of the multi-sensor tracking system. This thesis mainly deals with analysis of approximations of the covariance matrix that can best represent this matrix in order to efectively transmit this matrix to the demanding site. Kullback-Leibler (KL) Distance is exploited to derive some of the representations for Gaussian case. Also com- parison of these representations is another objective of this work and this is based on the fusion performance of the representations and the performance is measured for a system of a 2-radar track fusion system.

The first explored area in this thesis is the proposed data hiding method, TCQ-IS. The method is based on Trellis Coded Quantization (TCQ), whose initial state selection is arbitrary. TCQ-IS exploits this fact to hide data. It is a practical multi-dimensional that eliminates the prohibitive task of designing high dimensional quantizers. The strength and weaknesses of the method are stated by various experiments. The second contribution is the proposed data hiding method, Forbidden Zone Data Hiding (FZDH), which relies on the concept of &ldquo / forbidden zone&rdquo / , where host signal is not altered. The main motive of FZDH is to introduce distortion as much as needed, while keeping a range of host signal intact depending on the desired level of robustness. FZDH is compared against Quantization Index Modulation (QIM) as well as DC-QIM and ST-QIM. FZDH outperforms QIM even in 1-D and DC-QIM in higher dimensions. Furthermore, FZDH is comparable with ST-QIM for certain operation regimes. The final contribution is the video data hiding framework that includes FZDH, selective embedding and Repeat Accumulate (RA) codes. De-synchronization due to selective embedding is handled with RA codes. By means of simple rules applied to the embedded frame markers, certain level of robustness against temporal attacks is introduced. Selected coefficients are used to embed message bits by employing multi-dimensional FZDH. The framework is tested with typical broadcast material against common video processing attacks. The results indicate that the framework can be utilized in real life applications.

A covariant Wigner-Weyl quantization formalism on the manifold that uses pseudo-differential operators is proposed. The asymptotic product formula that leads to the symbol calculus in the presence of gauge and gravitational fields is presented. The new definition is used to get covariant differential operators from momentum polynomial symbols. A covariant Wigner function is defined and shown to give gauge-invariant results for the Landau problem. An example of the covariant Wigner function on the 2-sphere is also included.

<p>With the simple means of a digitized map and the wheel speed signals, it is possible to position a vehicle with an accuracy comparable to GPS. The positioning problem is a non-linear filtering problem and a particle filter has been applied to solve it. Two new approaches studied are the Auxiliary Particle Filter (APF), that aims at lowerering the variance of the error, and Rao-Blackwellization that exploits the linearities in the model. The results show that these methods require problems of higher complexity to fully utilize their advantages.</p><p>Another aspect in this thesis has been to handle off-road driving scenarios, using dead reckoning. An off road detection mechanism has been developed and the results show that off-road driving can be detected accurately. The algorithm has been successfully implemented on a hand-held computer by quantizing the particle filter while keeping good filter performance.</p>