Networked embedded control systems are present almost everywhere. A recent trend is to introduce wireless sensor networks in these systems, to take advantage of the added mobility and flexibility offered by wireless solutions. In such networks, the sensor observations are typically quantized and transmitted over noisy links. Concerning the problem of closed-loop control over such non-ideal communication channels, relatively few works have appeared so far. This thesis contributes to this field, by studying some fundamentally important problems in the design of joint source--channel coding and optimal control. The main part of the thesis is devoted to joint design of the coding and control for scalar linear plants, whose state feedbacks are transmitted over binary symmetric channels. The performance is measured by a finite-horizon linear quadratic cost function. The certainty equivalence property of the studied systems is utilized, since it simplifies the overall design by separating the estimation and the control problems. An iterative optimization algorithm for training the encoder--decoder pairs, taking channel errors into account in the quantizer design, is proposed. Monte Carlo simulations demonstrate promising improvements in performance compared to traditional approaches. Event-triggered control strategies are a promising solution to the problem of efficient utilization of communication resources. The basic idea is to let each control loop communicate only when necessary. Event-triggered and quantized control are combined for plants affected by rarely occurring disturbances. Numerical experiments show that it is possible to achieve good control performance with limited control actuation and sensor communication. / QC 20101109

This thesis treats the problem of source coding in situations where the encoded data is subject to errors. The typical scenario is a communication system, where source data such as speech or images should be transmitted from one point to another. A problem is that most communication systems introduce some sort of error in the transmission. A wireless communication link is prone to introduce individual bit errors, while in a packet based network, such as the Internet, packet losses are the main source of error. The traditional approach to this problem is to add error correcting codes on top of the encoded source data, or to employ some scheme for retransmission of lost or corrupted data. The source coding problem is then treated under the assumption that all data that is transmitted from the source encoder reaches the source decoder on the receiving end without any errors. This thesis takes another approach to the problem and treats source and channel coding jointly under the assumption that there is some knowledge about the channel that will be used for transmission. Such joint source--channel coding schemes have potential benefits over the traditional separated approach. More specifically, joint source--channel coding can typically achieve better performance using shorter codes than the separated approach. This is useful in scenarios with constraints on the delay of the system. Two different flavors of joint source--channel coding are treated in this thesis; multiple description coding and channel optimized vector quantization. Channel optimized vector quantization is a technique to directly incorporate knowledge about the channel into the source coder. This thesis contributes to the field by using channel optimized vector quantization in a couple of new scenarios. Multiple description coding is the concept of encoding a source using several different descriptions in order to provide robustness in systems with losses in the transmission. One contribution of this thesis is an improvement to an existing multiple description coding scheme and another contribution is to put multiple description coding in the context of channel optimized vector quantization. The thesis also presents a simple image coder which is used to evaluate some of the results on channel optimized vector quantization. / QC 20101108

<p>Broadcasting correlated Gaussians is one of the cases where separate source-channel coding is suboptimal. In this dissertation, we will study the distortion region of sending correlated Gaussian sources over an AWGN-BC using hybrid digital-analog coding approach, where each receiver wishes to reconstruct one source component subject to the mean squared error distortion constraint.</p> <p>First of all, the problem of transmitting m independent Gaussian source components over an AWGN-BC is studied. We show this problem setup is closely related to broadcasting correlated Gaussian sources with genie-aided receivers. Moreover, the separate source-channel coding approach is proven to be optimal in these setups.</p> <p>Second, we consider two new scenarios and find the achievable distortion regions for both cases, where three Gaussian source components are sent to three receivers. The difference is that for the first scenario, the first two source components are correlated and they are independent of the third one while for the second scenario, the last two source components are correlated and they are independent of the first one. Inner bounds based on hybrid analog-digital coding and outer bounds based on genie-aided arguments are proposed for both cases and the optimality is proven.</p> <p>Finally, we study two cases where side information is presented at one receiver. Hybrid analog-digital coding schemes are used and the optimality is proven.</p> / Master of Applied Science (MASc)

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / A joint source-channel coding scheme (JSCCS) used in applications, like sending images, voice, music etc. over internet/ wireless networks, involves source coding to compress the information and channel coding to detect/ correct errors, introduced by the channel. In this paper, we investigate the unequal error protection (UEP) capability of a class of low-density parity-check (LDPC) codes in a JSCCS. This class of irregular LDPC codes is constructed from cyclic difference families (CDFs).

Digital communications have now become a fundamental part of modern society. In communications, channel coding is an effective way to reduce the information rate down to channel capacity so that the information can be transmitted reliably through the channel. This thesis is devoted to studying the mathematical theory and analysis of channel codes that possess a useful diagonal structure in the parity-check and generator matrices. The first aspect of these codes that is studied is the ability to describe the parity-check matrix of a code with sliding diagonal structure using polynomials. Using this framework, an efficient new method is proposed to obtain a generator matrix G from certain types of parity-check matrices with a so-called defective cyclic block structure. By the nature of this method, G can also be completely described by a polynomial, which leads to efficient encoder design using shift registers. In addition, there is no need for the matrices to be in systematic form, thus avoiding the need for Gaussian elimination. Following this work, we proceed to explore some of the properties of diagonally structured lowdensity parity-check (LDPC) convolutional codes. LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. The first crucial property studied is the minimum free distance of LDPC convolutional code ensembles, an important parameter contributing to the error-correcting capability of the code. Here, asymptotic methods are used to form lower bounds on the ratio of the free distance to constraint length for several ensembles of asymptotically good, protograph-based LDPC convolutional codes. Further, it is shown that this ratio of free distance to constraint length for such LDPC convolutional codes exceeds the ratio of minimum distance to block length for corresponding LDPC block codes. Another interesting property of these codes is the way in which the structure affects the performance in the infamous error floor (which occurs at high signal to noise ratio) of the bit error rate curve. It has been suggested that “near-codewords” may be a significant factor affecting decoding failures of LDPC codes over an additive white Gaussian noise (AWGN) channel. A near-codeword is a sequence that satisfies almost all of the check equations. These nearcodewords can be associated with so-called ‘trapping sets’ that exist in the Tanner graph of a code. In the final major contribution of the thesis, trapping sets of protograph-based LDPC convolutional codes are analysed. Here, asymptotic methods are used to calculate a lower bound for the trapping set growth rates for several ensembles of asymptotically good protograph-based LDPC convolutional codes. This value can be used to predict where the error floor will occur for these codes under iterative message-passing decoding.

In digital video compression, apart from storage, successful transmission of the compressed video data over the bandwidth limited erroneous channels is another important issue. To enable a video codec for broadcasting application, it is required to implement the corresponding coding tools (e.g. error-resilient coding, rate control etc.). They are normally non-normative parts of a video codec and hence their specifications are not defined in the standard. In Dirac as well, the original codec is optimized for storage purpose only and so, several non-normative part of the encoding tools are still required in order to be able to use in other types of application. Being the "Research and Developments of the Dirac Video Codec" as the research title, phase I of the project is mainly focused on the error-resilient transmission over a noisy channel. The error-resilient coding method used here is a simple and low complex coding scheme which provides the error-resilient transmission of the compressed video bitstream of Dirac video encoder over the packet erasure wired network. The scheme combines source and channel coding approach where error-resilient source coding is achieved by data partitioning in the wavelet transformed domain and channel coding is achieved through the application of either Rate-Compatible Punctured Convolutional (RCPC) Code or Turbo Code (TC) using un-equal error protection between header plus MV and data. The scheme is designed mainly for the packet-erasure channel, i.e. targeted for the Internet broadcasting application. But, for a bandwidth limited channel, it is still required to limit the amount of bits generated from the encoder depending on the available bandwidth in addition to the error-resilient coding. So, in the 2nd phase of the project, a rate control algorithm is presented. The algorithm is based upon the Quality Factor (QF) optimization method where QF of the encoded video is adaptively changing in order to achieve average bitrate which is constant over each Group of Picture (GOP). A relation between the bitrate, R and the QF, which is called Rate-QF (R-QF) model is derived in order to estimate the optimum QF of the current encoding frame for a given target bitrate, R. In some applications like video conferencing, real-time encoding and decoding with minimum delay is crucial, but, the ability to do real-time encoding/decoding is largely determined by the complexity of the encoder/decoder. As we all know that motion estimation process inside the encoder is the most time consuming stage. So, reducing the complexity of the motion estimation stage will certainly give one step closer to the real-time application. So, as a partial contribution toward realtime application, in the final phase of the research, a fast Motion Estimation (ME) strategy is designed and implemented. It is the combination of modified adaptive search plus semi-hierarchical way of motion estimation. The same strategy was implemented in both Dirac and H.264 in order to investigate its performance on different codecs. Together with this fast ME strategy, a method which is called partial cost function calculation in order to further reduce down the computational load of the cost function calculation was presented. The calculation is based upon the pre-defined set of patterns which were chosen in such a way that they have as much maximum coverage as possible over the whole block. In summary, this research work has contributed to the error-resilient transmission of compressed bitstreams of Dirac video encoder over a bandwidth limited error prone channel. In addition to this, the final phase of the research has partially contributed toward the real-time application of the Dirac video codec by implementing a fast motion estimation strategy together with partial cost function calculation idea.

Topics in source and channel coding for audiovisual communication systems are studied. The goal of source coding is to represent a source with the lowest possible rate to achieve a particular distortion, or with the lowest possible distortion at a given rate. Channel coding adds redundancy to quantized source information to recover channel errors. This thesis consists of four topics. Firstly, based on high-rate theory, we propose Karhunen-Loéve transform (KLT)-based classified vector quantization (VQ) to efficiently utilize optimal VQ advantages over scalar quantization (SQ). Compared with code-excited linear predictive (CELP) speech coding, KLT-based classified VQ provides not only a higher SNR and perceptual quality, but also lower computational complexity. Further improvement is obtained by companding. Secondly, we compare various transmitter-based packet-loss recovery techniques from a rate-distortion viewpoint for real-time audiovisual communication systems over the Internet. We conclude that, in most circumstances, multiple description coding (MDC) is the best packet-loss recovery technique. If channel conditions are informed, channel-optimized MDC yields better performance. Compared with resolution-constrained quantization (RCQ), entropy-constrained quantization (ECQ) produces a smaller number of distortion outliers but is more sensitive to channel errors. We apply a generalized γ-th power distortion measure to design a new RCQ algorithm that has less distortion outliers and is more robust against source mismatch than conventional RCQ methods. Finally, designing quantizers to effectively remove irrelevancy as well as redundancy is considered. Taking into account the just noticeable difference (JND) of human perception, we design a new RCQ method that has improved performance in terms of mean distortion and distortion outliers. Based on high-rate theory, optimal centroid density and its corresponding mean distortion are also accurately predicted. The latter two quantization methods can be combined with practical source coding systems such as KLT-based classified VQ and with joint source-channel coding paradigms such as MDC.

<p>In this thesis an approach to joint source-channel coding using direct source to channel mappings is studied. The system studied communicates i.i.d. Gaussian sources on a point-to-point Gaussian memoryless channel with limited feedback (supporting channel state information at most). The mappings, named Shannon-Kotel'nikov (SK) mappings, are memoryless mappings between the source space of dimension M and the channel space of dimension N. Such mappings can be used for error control when M<N, called dimension expansion, and for lossy compression when M>N, called dimension reduction. The SK-mappings operate on amplitude continuous and time discrete signals (meaning that there is no bits involved) through (piecewise) continuous curves or hyper surfaces in general.</p><p>The reason for studying SK-mappings is that they are delay free, robust against varying channel conditions, and have quite good performance at low complexity.</p><p>First a theory for determining and categorizing the distortion using SK-mappings for communication is introduced and developed. This theory is further used to show that SK-mappings can reach the information theoretical bound optimal performance theoretically attainable (OPTA) when their dimension approach infinity.</p><p>One problem is to determine the overall optimal geometry of the SK-mappings. Indications on the overall geometry can be found by studying the codebooks and channel constellations of power constrained channel optimized vector quantizers (PCCOVQ). The PCCOVQ algorithm will find the optimal placing of quantizer representation vectors in the source space and channel symbols in the channel space. A PCCOVQ algorithm giving well performing mappings for the dimension reduction case has been found in the past. In this thesis the PCCOVQ algorithm is modified to give well performing dimension expanding mappings for scalar sources, and 1:2 and 1:3 PCCOVQ examples are given.</p><p>Some example SK-mappings are proposed and analyzed. 2:1 and 1:2 PCCOVQ mappings are used as inspiration for making 2:1 and 1:2 SK-mappings based on the Archimedean spiral. Further 3:1, 4:1, 3:2 and 2:3 SK-mappings are found and analyzed. All example SK-mappings are modeled mathematically using the proposed theory on SK-mappings. These mathematical models are further used to find the optimal coefficients for all the proposed SK-mappings as a function of the channel signal-to-noise ratio (CSNR), making adaptations to varying channel conditions simple.</p>

Compressed video bitstream transmissions over wireless networks are addressed in this work. We first consider error control and power allocation for transmitting wireless video over CDMA networks in conjunction with multiuser detection. We map a layered video bitstream to several CDMA fading channels and inject multiple source/parity layers into each of these channels at the transmitter. We formulate a combined optimization problem and give the optimal joint rate and power allocation for each of linear minimum mean-square error (MMSE) multiuser detector in the uplink and two types of blind linear MMSE detectors, i.e., the direct-matrix-inversion (DMI) blind detector and the subspace blind detector, in the downlink. We then present a multiple-channel video transmission scheme in wireless CDMA networks over multipath fading channels. For a given budget on the available bandwidth and total transmit power, the transmitter determines the optimal power allocations and the optimal transmission rates among multiple CDMA channels, as well as the optimal product channel code rate allocation. We also make use of results on the large-system CDMA performance for various multiuser receivers in multipath fading channels. We employ a fast joint source-channel coding algorithm to obtain the optimal product channel code structure. Finally, we propose an end-to-end architecture for multi-layer progressive video delivery over space-time differentially coded orthogonal frequency division multiplexing (STDC-OFDM) systems. We propose to use progressive joint source-channel coding to generate operational transmission distortion-power-rate (TD-PR) surfaces. By extending the rate-distortion function in source coding to the TD-PR surface in joint source-channel coding, our work can use the ??equal slope?? argument to effectively solve the transmission rate allocation problem as well as the transmission power allocation problem for multi-layer video transmission. It is demonstrated through simulations that as the wireless channel conditions change, these proposed schemes can scale the video streams and transport the scaled video streams to receivers with a smooth change of perceptual quality.

In this thesis an approach to joint source-channel coding using direct source to channel mappings is studied. The system studied communicates i.i.d. Gaussian sources on a point-to-point Gaussian memoryless channel with limited feedback (supporting channel state information at most). The mappings, named Shannon-Kotel'nikov (SK) mappings, are memoryless mappings between the source space of dimension M and the channel space of dimension N. Such mappings can be used for error control when M&lt;N, called dimension expansion, and for lossy compression when M&gt;N, called dimension reduction. The SK-mappings operate on amplitude continuous and time discrete signals (meaning that there is no bits involved) through (piecewise) continuous curves or hyper surfaces in general. The reason for studying SK-mappings is that they are delay free, robust against varying channel conditions, and have quite good performance at low complexity. First a theory for determining and categorizing the distortion using SK-mappings for communication is introduced and developed. This theory is further used to show that SK-mappings can reach the information theoretical bound optimal performance theoretically attainable (OPTA) when their dimension approach infinity. One problem is to determine the overall optimal geometry of the SK-mappings. Indications on the overall geometry can be found by studying the codebooks and channel constellations of power constrained channel optimized vector quantizers (PCCOVQ). The PCCOVQ algorithm will find the optimal placing of quantizer representation vectors in the source space and channel symbols in the channel space. A PCCOVQ algorithm giving well performing mappings for the dimension reduction case has been found in the past. In this thesis the PCCOVQ algorithm is modified to give well performing dimension expanding mappings for scalar sources, and 1:2 and 1:3 PCCOVQ examples are given. Some example SK-mappings are proposed and analyzed. 2:1 and 1:2 PCCOVQ mappings are used as inspiration for making 2:1 and 1:2 SK-mappings based on the Archimedean spiral. Further 3:1, 4:1, 3:2 and 2:3 SK-mappings are found and analyzed. All example SK-mappings are modeled mathematically using the proposed theory on SK-mappings. These mathematical models are further used to find the optimal coefficients for all the proposed SK-mappings as a function of the channel signal-to-noise ratio (CSNR), making adaptations to varying channel conditions simple.