In this thesis, different aspects of lattice-based precoding and decoding for the transmission of digital and analog data over MIMO fading channels are investigated: 1) Lattice-based precoding in MIMO broadcast systems: A new viewpoint for adopting the lattice reduction in communication over MIMO broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior of the symbol-error-rate for the lattice-reduction-aided precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum-rate is analyzed. It is shown that the lattice-reduction-aided method, using LLL algorithm, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). 2) Lattice-based decoding in MIMO multiaccess systems and MIMO point-to-point systems: Diversity order and diversity-multiplexing tradeoff are two important measures for the performance of communication systems over MIMO fading channels. For the case of MIMO multiaccess systems (with single-antenna transmitters) or MIMO point-to-point systems with V-BLAST transmission scheme, it is proved that lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, it is proved that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity in V-BLAST systems. On the other hand, the inherent drawbacks of the naive lattice decoding for general MIMO fading systems is investigated. It is shown that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal diversity-multiplexing tradeoff. 3) Lattice-based analog transmission over MIMO fading channels: The problem of finding a delay-limited schemes for sending an analog source over MIMO fading channels is investigated in this part. First, the problem of robust joint source-channel coding over an additive white Gaussian noise channel is investigated. A new scheme is proposed which achieves the optimal slope for the signal-to-distortion-ratio (SDR) curve (unlike the previous known coding schemes). Then, this idea is extended to MIMO channels to construct lattice-based codes for joint source-channel coding over MIMO channels. Also, similar to the diversity-multiplexing tradeoff, the asymptotic performance of MIMO joint source-channel coding schemes is characterized, and a concept called diversity-fidelity tradeoff is introduced in this thesis.

In this thesis, different aspects of lattice-based precoding and decoding for the transmission of digital and analog data over MIMO fading channels are investigated: 1) Lattice-based precoding in MIMO broadcast systems: A new viewpoint for adopting the lattice reduction in communication over MIMO broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior of the symbol-error-rate for the lattice-reduction-aided precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum-rate is analyzed. It is shown that the lattice-reduction-aided method, using LLL algorithm, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). 2) Lattice-based decoding in MIMO multiaccess systems and MIMO point-to-point systems: Diversity order and diversity-multiplexing tradeoff are two important measures for the performance of communication systems over MIMO fading channels. For the case of MIMO multiaccess systems (with single-antenna transmitters) or MIMO point-to-point systems with V-BLAST transmission scheme, it is proved that lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, it is proved that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity in V-BLAST systems. On the other hand, the inherent drawbacks of the naive lattice decoding for general MIMO fading systems is investigated. It is shown that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal diversity-multiplexing tradeoff. 3) Lattice-based analog transmission over MIMO fading channels: The problem of finding a delay-limited schemes for sending an analog source over MIMO fading channels is investigated in this part. First, the problem of robust joint source-channel coding over an additive white Gaussian noise channel is investigated. A new scheme is proposed which achieves the optimal slope for the signal-to-distortion-ratio (SDR) curve (unlike the previous known coding schemes). Then, this idea is extended to MIMO channels to construct lattice-based codes for joint source-channel coding over MIMO channels. Also, similar to the diversity-multiplexing tradeoff, the asymptotic performance of MIMO joint source-channel coding schemes is characterized, and a concept called diversity-fidelity tradeoff is introduced in this thesis.

<p>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.</p><p>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.</p><p>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.</p>

<p>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.</p><p>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.</p><p>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.</p>

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

The concepts of a digital twin and extended reality have recently emerged, which require a massive amount of sensor data to be transmitted with low latency and high reliability. For low-latency communications, joint source-channel coding (JSCC) is an attractive method for error correction coding and compared to highly complex digital systems that are currently in use. I propose the use of complex-valued and quaternionic neural networks (QNN) to decode JSCC codes, where the complex-valued neural networks show a significant improvement over real-valued networks and the QNNs have an exceptionally high performance. Furthermore, I propose mapping encoded JSCC code words to the baseband of the frequency domain in order to enable time/frequency synchronization as well as to mitigate fading using robust estimation theory. Additionally, I perform robust statistical signal processing on the high-dimensional JSCC code showing significant noise immunity with drastic performance improvements at low signal-to-noise ratio (SNR) levels. The performance of the proposed JSCC codes is within 5 dB of the optimal performance theoretically achievable and outperforms the maximum likelihood decoder at low SNR while exhibiting the smallest possible latency. I designed a Bayesian minimum mean square error estimator for decoding high-dimensional JSCC codes achieving 99.96% accuracy. With the recent introduction of electromagnetic reconfigurable intelligent surfaces (RIS), a paradigm shift is currently taking place in the world of wireless communications. These new technologies have enabled the inclusion of the wireless channel as part of the optimization process. In order to decode polarization-space modulated RIS reflections, robust polarization state decoders are proposed using the Weiszfeld algorithm and an generalized Huber M-estimator. Additionally, QNNs are trained and evaluated for the recovery of the polarization state. Furthermore, I propose a novel 64-ary signal constellation based on scaled and shifted Eisenstein integers and generated using media-based modulation with a RIS. The waveform is received using an antenna array and decoded with complex-valued convolutional neural networks. I employ the circular cross-correlation function and a-priori knowledge of the phase angle distribution of the constellation to blindly resolve phase offsets between the transmitter and the receiver without the need for pilots or reference signals. Furthermore, the channel attenuation is determined using statistical methods exploiting that the constellation has a particular distribution of magnitudes. After resolving the phase and magnitude ambiguities, the noise power of the channel can also be estimated. Finally, I tune an Sq-estimator to robustly decode the Eisenstein waveform. / Doctor of Philosophy / This dissertation covers three novel wireless communications methods; analog coding, communications using the electromagnetic polarization and communications with a novel signal constellation. The concepts of a digital twin and extended reality have recently emerged, which require a massive amount of sensor data to be transmitted with low latency and high reliability. Contemporary digital communication systems are highly complex with high reliability at the expense of high latency. In order to reduce the complexity and hence latency, I propose to use an analog coding scheme that directly maps the sensor data to the wireless channel. Furthermore, I propose the use of neural networks for decoding at the receiver, hence using the name neural receiver. I employ various data types in the neural receivers hence leveraging the mathematical structure of the data in order to achieve exceptionally high performance. Another key contribution here is the mapping of the analog codes to the frequency domain enabling time and frequency synchronization. I also utilize robust estimation theory to significantly improve the performance and reliability of the coding scheme. With the recent introduction of electromagnetic reconfigurable intelligent surfaces (RIS), a paradigm shift is currently taking place in the world of wireless communications. These new technologies have enabled the inclusion of the wireless channel as part of the optimization process. Therefore, I propose to use the polarization state of the electromagnetic wave to convey information over the channel, where the polarization is determined using a RIS. As with the analog codes, I also extensively employ various methods of robust estimation to improve the performance of the recovery of the polarization at the receiver. Finally, I propose a novel communications signal constellation generated by a RIS that allows for equal probability of error at the receiver. Traditional communication systems utilize reference symbols for synchronization. In this work, I utilize statistical methods and the known distributions of the properties of the transmitted signal to synchronize without reference symbols. This is referred to as blind channel estimation. The reliability of the third communications method is enhanced using a state-of-the-art robust estimation method.

<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)

Cette thèse est consacrée à l'amélioration des performances de codage/décodage de systèmes de transmission d'images fixes sur des canaux bruités et réalistes. Nous proposons, à cet effet, le développement de méthodes de transmission d'images optimisées en se focalisant sur les deux couches application et physique des réseaux sans fil. Au niveau de la couche application et afin d'assurer une bonne qualité de service, on utilise des algorithmes de compression efficaces permettant au récepteur de reconstruire l'image avec un maximum de fidélité (JPEG2000 et JPWL). Afin d'assurer une transmission sur des canaux sans fil avec un minimum de TEB à la réception, des techniques de transmission, de codage et de modulation avancées sont utilisées au niveau de la couche physique (système MIMO-OFDM, modulation adaptative, CCE, etc). Dans un premier temps, nous proposons un système de transmission robuste d'images codées JPWL intégrant un schéma de décodage conjoint source-canal basé sur des techniques de décodage à entrées pondérées. On considère, ensuite, l'optimisation d'une chaîne de transmission d'images sur un canal MIMO-OFDM sans fil réaliste. La stratégie de transmission d'images optimisée s'appuie sur des techniques de décodage à entrées pondérées et une approche d'adaptation de lien. Ainsi, le schéma de transmission proposé offre la possibilité de mettre en oeuvre conjointement de l'UEP, de l'UPA, de la modulation adaptative, du codage de source adaptatif et de décodage conjoint pour améliorer la qualité de l'image à la réception. Dans une seconde partie, nous proposons un système robuste de transmission de flux progressifs basé sur le principe de turbo décodage itératif de codes concaténés offrant une stratégie de protection inégale de données. Ainsi, l'originalité de cette étude consiste à proposer des solutions performantes d'optimisation globale d'une chaîne de communication numérique pour améliorer la qualité de transmission. / This work is devoted to improve the coding/ decoding performance of a transmission scheme over noisy and realistic channels. For this purpose, we propose the development of optimized image transmission methods by focusing on both application and physical layers of wireless networks. In order to ensure a better quality of services, efficient compression algorithms (JPEG2000 and JPWL) are used in terms of the application layer enabling the receiver to reconstruct the images with maximum fidelity. Furthermore, to insure a transmission on wireless channels with a minimum BER at reception, some transmission, coding and advanced modulation techniques are used in the physical layer (MIMO-OFDM system, adaptive modulation, FEC, etc). First, we propose a robust transmission system of JPWL encoded images integrating a joint source-channel decoding scheme based on soft input decoding techniques. Next, the optimization of an image transmission scheme on a realistic MIMO-OFDM channel is considered. The optimized image transmission strategy is based on soft input decoding techniques and a link adaptation approach. The proposed transmission scheme offers the possibility of jointly implementing, UEP, UPA, adaptive modulation, adaptive source coding and joint decoding strategies, in order to improve the image visual quality at the reception. Then, we propose a robust transmission system for embedded bit streams based on concatenated block coding mechanism offering an unequal error protection strategy. Thus, the novelty of this study consists in proposing efficient solutions for the global optimization of wireless communication system to improve transmission quality.

Les codes source-canal conjoints sont des codes réalisant simultanément une compression de données et une protection du train binaire généré par rapport à d’éventuelles erreurs de transmission. Ces codes sont non-linéaires, comme la plupart des codes de source. Leur intérêt potentiel est d’offrir de bonnes performances en termes de compression et de correction d’erreur pour des longueurs de codes réduites.La performance d’un code de source se mesure par la différence entre l’entropie de la source à compresser et le nombre moyen de bits nécessaire pour coder un symbole de cette source. La performance d’un code de canal se mesure par la distance minimale entre mots de codes ou entre suite de mots de codes, et plus généralement à l’aide du spectre des distances. Les codes classiques disposent d’outils pour évaluer efficacement ces critères de performance. Par ailleurs, la synthèse de bons codes de source ou de bons codes de canal est un domaine largement exploré depuis les travaux de Shannon. Par contre des outils analogues pour des codes source-canal conjoints, tant pour l’évaluation de performance que pour la synthèse de bons codes restaient à développer, même si certaines propositions ont déjà été faites dans le passé.Cette thèse s’intéresse à la famille des codes source-canal conjoints pouvant être décrits par des automates possédant un nombre fini d’états. Les codes quasi-arithmétiques correcteurs d’erreurs et les codes à longueurs variables correcteurs d’erreurs font partie de cette famille. La manière dont un automate peut être obtenu pour un code donné est rappelée.A partir d’un automate, il est possible de construire un graphe produit permettant de décrire toutes les paires de chemins divergeant d'un même état et convergeant vers un autre état. Nous avons montré que grâce à l’algorithme de Dijkstra, il est alors possible d’évaluer la distance libre d’un code conjoint avec une complexité polynomiale.Pour les codes à longueurs variables correcteurs d’erreurs, nous avons proposé des bornes supplémentaires, faciles à évaluer. Ces bornes constituent des extensions des bornes de Plotkin et de Heller aux codes à longueurs variables. Des bornes peuvent également être déduites du graphe produit associé à un code dont seule une partie des mots de codes a été spécifiée.Ces outils pour borner ou évaluer exactement la distance libre d’un code conjoint permettent de réaliser la synthèse de codes ayant des bonnes propriétés de distance pour une redondance donnée ou minimisant la redondance pour une distance libre donnée.Notre approche consiste à organiser la recherche de bons codes source-canal conjoints à l’aide d’arbres. La racine de l’arbre correspond à un code dont aucun bit n’est spécifié, les feuilles à des codes dont tous les bits sont spécifiés, et les nœuds intermédiaires à des codes partiellement spécifiés. Lors d’un déplacement de la racine vers les feuilles de l’arbre, les bornes supérieures sur la distance libre décroissent, tandis que les bornes inférieures croissent. Ceci permet d’appliquer un algorithme de type branch-and-prune pour trouver le code avec la plus grande distance libre, sans avoir à explorer tout l’arbre contenant les codes. L'approche proposée a permis la construction de codes conjoints pour les lettres de l'alphabet. Comparé à un schéma tandem équivalent (code de source suivi d'un code convolutif), les codes obtenus ont des performances comparables (taux de codage, distance libre) tout en étant moins complexes en termes de nombre d’état du décodeur.Plusieurs extensions de ces travaux sont en cours : 1) synthèse de codes à longueurs variables correcteurs d’erreurs formalisé comme un problème de programmation linéaire mixte sur les entiers ; 2) exploration à l’aide d’un algorithme de type A* de l’espace des codes de à longueurs variables correcteur d’erreurs. / Joint source-channel codes are codes simultaneously providing data compression and protection of the generated bitstream from transmission errors. These codes are non-linear, as most source codes. Their potential is to offer good performance in terms of compression and error-correction for reduced code lengths.The performance of a source code is measured by the difference between the entropy of the source to be compressed and the average number of bits needed to encode a symbol of this source. The performance of a channel code is measured by the minimum distance between codewords or sequences of codewords, and more generally with the distance spectrum. The classic codes have tools to effectively evaluate these performance criteria. Furthermore, the design of good source codes or good channel codes is a largely explored since the work of Shannon. But, similar tools for joint source-channel codes, for performances evaluation or for design good codes remained to develop, although some proposals have been made in the past.This thesis focuses on the family of joint source-channel codes that can be described by automata with a finite number of states. Error-correcting quasi-arithmetic codes and error-correcting variable-length codes are part of this family. The way to construct an automaton for a given code is recalled.From an automaton, it is possible to construct a product graph for describing all pairs of paths diverging from some state and converging to the same or another state. We have shown that, using Dijkstra's algorithm, it is possible to evaluate the free distance of a joint code with polynomial complexity. For errors-correcting variable-length codes, we proposed additional bounds that are easy to evaluate. These bounds are extensions of Plotkin and Heller bounds to variable-length codes. Bounds can also be deduced from the product graph associated to a code, in which only a part of code words is specified.These tools to accurately assess or bound the free distance of a joint code allow the design of codes with good distance properties for a given redundancy or minimizing redundancy for a given free distance. Our approach is to organize the search for good joint source-channel codes with trees. The root of the tree corresponds to a code in which no bit is specified, the leaves of codes in which all bits are specified, and the intermediate nodes to partially specified codes. When moving from the root to the leaves of the tree, the upper bound on the free distance decreases, while the lower bound grows. This allows application of an algorithm such as branch-and-prune for finding the code with the largest free distance, without having to explore the whole tree containing the codes.The proposed approach has allowed the construction of joint codes for the letters of the alphabet. Compared to an equivalent tandem scheme (source code followed by a convolutional code), the codes obtained have comparable performance (rate coding, free distance) while being less complex in terms of the number of states of the decoder. Several extensions of this work are in progress: 1) synthesis of error-correcting variable-length codes formalized as a mixed linear programming problem on integers, 2) Explore the search space of error-correcting variable-length codes using an algorithm such as A* algorithm.