Abstract Wireless sensor networks (WSNs) consisting of battery-powered sensors are increasingly deployed for a myriad of Internet of Things applications, e.g., environmental, industrial, and healthcare monitoring. Since wireless access is typically the main contributor to battery usage, minimizing communications is crucial to prolong network lifetime and improve user experience. The objective of this thesis is to develop and analyze energy-efficient distributed compressed data acquisition techniques for WSNs. The thesis proposes four approaches to conserve sensors' energy by minimizing the amount of information each sensor has to transmit to meet given application requirements. The first part addresses a cross-layer design to minimize the sensors’ sum transmit power via joint optimization of resource allocation and multi-path routing. A distributed consensus optimization based algorithm is proposed to solve the problem. The algorithm is shown to have superior convergence compared to several baselines. The remaining parts deal with compressed sensing (CS) of sparse/compressible sources. The second part focuses on the distributed CS acquisition of spatially and temporally correlated sensor data streams. A CS algorithm based on sliding window and recursive decoding is developed. The method is shown to achieve higher reconstruction accuracy with fewer transmissions and less decoding delay and complexity compared to several baselines, and to progressively refine past estimates. The last two approaches incorporate the quantization of CS measurements and focus on lossy source coding. The third part addresses the distributed quantized CS (QCS) acquisition of correlated sparse sources. A distortion-rate optimized variable-rate QCS method is proposed. The method is shown to achieve higher distortion-rate performance than the baselines and to enable a trade-off between compression performance and encoding complexity via the pre-quantization of measurements. The fourth part investigates information-theoretic rate-distortion (RD) performance limits of single-sensor QCS. A lower bound to the best achievable compression — defined by the remote RD function (RDF) — is derived. A method to numerically approximate the remote RDF is proposed. The results compare practical QCS methods to the derived limits, and show a novel QCS method to approach the remote RDF. / Tiivistelmä Patterikäyttöisistä antureista koostuvat langattomat anturiverkot yleistyvät esineiden internetin myötä esim. ympäristö-, teollisuus-, ja terveydenhoitosovelluksissa. Koska langaton tiedonsiirto kuluttaa merkittävästi energiaa, kommunikoinnin minimointi on elintärkeää pidentämään verkon elinikää ja parantamaan käyttäjäkokemusta. Väitöskirjan tavoitteena on kehittää ja analysoida energiatehokkaita hajautettuja pakattuja datankeruumenetelmiä langattomiin anturiverkkoihin. Työssä ehdotetaan neljä lähestymistapaa, jotka säästävät anturien energiaa minimoimalla se tiedonsiirron määrä, mikä vaaditaan täyttämään sovelluksen asettamat kriteerit. Väitöskirjan ensimmäinen osa tarkastelee protokollakerrosten yhteissuunnittelua, jossa minimoidaan anturien yhteislähetysteho optimoimalla resurssiallokaatio ja monitiereititys. Ratkaisuksi ehdotetaan konsensukseen perustuva hajautettu algoritmi. Tulokset osoittavat algoritmin suppenemisominaisuuksien olevan verrokkejaan paremmat. Loppuosat keskittyvät harvojen lähteiden pakattuun havaintaan (compressed sensing, CS). Toinen osa keskittyy tila- ja aikatasossa korreloituneen anturidatan hajautettuun keräämiseen. Työssä kehitetään liukuvaan ikkunaan ja rekursiiviseen dekoodaukseen perustuva CS-algoritmi. Tulokset osoittavat menetelmän saavuttavan verrokkejaan korkeamman rekonstruktiotarkkuuden pienemmällä tiedonsiirrolla sekä dekoodausviiveellä ja -kompleksisuudella ja kykenevän asteittain parantamaan menneitä estimaatteja. Työn viimeiset osat sisällyttävät järjestelmämalliin CS-mittausten kvantisoinnin keskittyen häviölliseen lähdekoodaukseen. Kolmas osa käsittelee hajautettua korreloitujen harvojen signaalien kvantisoitua CS-havaintaa (quantized CS, QCS). Työssä ehdotetaan särön ja muuttuvan koodinopeuden välisen suhteen optimoiva QCS-menetelmä. Menetelmällä osoitetaan olevan verrokkejaan parempi pakkaustehokkuus sekä kyky painottaa suorituskyvyn ja enkooderin kompleksisuuden välillä mittausten esikvantisointia käyttäen. Neljäs osa tutkii informaatioteoreettisia, koodisuhde-särösuhteeseen perustuvia suorituskykyrajoja yhden anturin QCS-järjestelmässä. Parhaimmalle mahdolliselle pakkaustehokkuudelle johdetaan alaraja, sekä kehitetään menetelmä sen numeeriseen arviointiin. Tulokset vertaavat käytännön QCS-menetelmiä johdettuihin rajoihin, ja osoittavat ehdotetun QCS-menetelmän saavuttavan lähes optimaalinen suorituskyky.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-12-22T13:25:11Z No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:20:21Z (GMT) No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) / Made available in DSpace on 2017-01-31T10:20:21Z (GMT). No. of bitstreams: 1 vahidnikoofard.pdf: 794368 bytes, checksum: 26feb8d15d2757f79f8d7dfb69b610c2 (MD5) Previous issue date: 2015-06-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese é composta por assuntos distintos entre si de teorias quânticas de campos onde alguns deles são descritos em espaços não-comutativos (NC). Em primeiro lugar, analisamos a dinâmica de uma partícula livre sobre uma 2-esfera e através da dinâmica das suas equações de movimento, obtivemos as perturbações NCs neste espaço de fase. Este modelo sugere uma origem para o Zitterbewegung do elétron. Depois disso, consideramos umaversãoNCdasegundaleideNewtonparaestemodelo, quefoiobtidocomestecenário geométrico aplicado a este modelo. Em seguida, discutimos um formalismo alternativo relacionado à não-comutatividade chamado DFR onde o parâmetro NC é considerado uma coordenada e demonstramos exatamente que ela tem obrigatoriamente um momento conjugado neste espaço de fase DFR, diferentemente do que alguns autores da atual literatura sobre DFR afirmam. No próximo assunto, usando o formalismo de solda que, em poucaspalavras,colocapartículascomquiralidadesopostasnomesmomultipleto,soldamos algumas versões NCs de modelos bem conhecidos como modelos de Schwinger quirais e modelos (anti) auto duais no espaço-tempo de Minkowski estendido. Em outro assunto estudado aqui, também construímos a versão NC do modelo de Jackiw-Pi com um grupo de calibre arbitrário e usamos o mapeamento bem conhecido de Seiberg-Witten para obter este modelo NC em termos de variáveis comutativos. Finalmente, utilizamos o formalismo de campos e anticampos (ou método BV) para construir a ação de Batalin-Vilkovisky (BV) do modelo Jackiw-Pi estendido e após o prEntendiocedimento de fixação de calibre chegamos a uma ação completa, pronta para quantização. / This thesis is composed of distinct aspects of quantum field theories where some of them are described in noncommutative (NC) spaces. Firstly, we have analyzed the dynamics of a free particle over a 2-sphere and through the dynamics of the equations of motion we have derived its NC perturbations in the phase-space. This model suggests an origin for Zitterbewegung feature of the electron. After that we have considered the NC version of Newton’s second law for this model, which was obtained with the geometricalscenarioappliedtothismodel. Thenwehavediscussedtheso-calledDoplicher– Fredenhagen–Roberts (DFR) alternative formalism concerning noncommutativity where the NC parameter has a coordinate role and we showed exactly that it has a conjugated momentum in the DFR phase-space, differently of what some authors of the current DFR-literature claims. In the next issue, using the soldering formalism which, in few words, put opposite chiral particles in the same multiplet, we have soldered some NC versions of well known models like the chiral Schwinger model and (anti)self dual models in the extended Minkowski spacetime. Changing the subject, we have constructed the NC spacetime version of Jackiw-Pi model with an arbitrary gauge group and we used the well known Seiberg-Witten map to obtain the NC model expressed in terms of commutative variables. Finally, we have used the field-antifield (or BV method) formalism to construct the Batalin-Vilkovisky (BV) action of the extended Jackiw-Pi model and after the gauge fixing procedure we have arrived at a quantized-ready action for this model.

This thesis provides the explicit expression of the star-exponential for the action of normal j-groups on their coadjoint orbits, and of the so-called modified star-exponential defined by Gayral et al. Using this modified star-exponential as the kernel of a functional transform between the group and its coadjoint orbits yields an adapted Fourier transform which is also detailed here. The normal j-groups arise in the work of Pytatetskii-Shapiro, who established the one-to-one correspondence with homogeneous bounded domains of the complex space; these groups are also the central element of the deformation formula recently developed by Bieliavsky & Gayral (a non abelian analog of the strict deformation quantization theory of Rieffel). Since these groups are exponential, the results given in this text illustrate the general work of Arnal & Cortet on the star-representations of exponential groups.<p> As this work is meant to be as self-contained as possible, the first chapter reproduces many definitions introduced by Bieliavsky & Gayral, in order to obtain the expression of the symplectic symmetric space structure on normal j-groups, and of their unitary irreducible representations. The Weyl-type quantizer associated to this symmetric structure is then computed, thus yielding the Weyl quantization map for which the composition of symbols is precisely the deformed product defined by Bieliavsky-Gayral on normal j-groups. A detailed proof of the structure theorem of normal j-groups is also provided.<p> The second chapter focuses on the expression and properties of the star-exponential itself, and exhibits a useful tool for the computation, namely the resolution of the identity associated to square integrable unitary irreducible representations of the groups. The result thus obtained satisfies the usual integro-differential equation defining the star-exponential. A criterion for the existence of a tempered pair underlying a given tempered structure on Lie groups is proven; the star-exponential functions are also shown to belong to the multiplier algebra of the Schwartz space associated to the tempered structure. Before that, it is shown that all Schwartz spaces that appear in this work are isomorphic as topological vector spaces.<p> The modified version of this star-exponential is computed in chapter three, first for elementary normal j-groups and then for normal j-groups. It is then used to define an adapted Fourier transform between the group and the dual of its Lie algebra. This transform generalizes (to all normal j-groups) a Fourier transform that was already studied in the “ax+b” case by Gayral et al. (2008), as well as by Ali et al. (2003) in the context of wavelet transforms. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Dans cette thèse nous étudions un système quantique, obtenu comme un analogue d'un système classique superintégrable perturbé au moyen de la quantification géométrique. Notre objectif est de mettre en évidence la présence des phénomènes analogues à ceux qui caractérisent la superintégrabilité classique, notamment la coexistence des mouvements réguliers et chaotiques liés aux effets des résonances ainsi que la régularité du régime non-résonant. L'analyse est effectuée par l'étude des distributions du Husimi des états quantiques sélectionnés, avec une attention particulière aux états stationnaires et à l'évolution des états cohérents. Les calculs sont effectués en utilisant les méthodes numériques et les méthodes perturbatives. Les calculs sont effectués en utilisant les méthodes numériques et les méthodes perturbatives. Bien que cette thèse devrait être considérée comme une étude préliminaire, dont l'objectif est de créer le socle des études futures, nos résultats donnent des indications intéressantes sur la dynamique quantique. Par exemple, il est démontré comment les résonancees classiques exercent une influence considérable sur le spectre du système quantique et comment il est possible, dans le comportement quantique, de trouver une trace de l'invariant adiabatique dans le régime de résonance. / The abundance, among physical models, of perturbations of superintegrable Hamiltonian systems makes the understanding of their long-term dynamics an important research topic. While from the classical standpoint the situation, at least in many important cases, is well understood through the use of Nekhoroshev stability theorem and of the adiabatic invariants theory, in the quantum framework there is, on the contrary, a lack of precise results. The purpose of this thesis is to study a perturbed superintegrable quantum system, obtained from a classical counterpart by means of geometric quantization, in order to highlight the presence of indicators of superintegrability analogues to the ones that characterize the classical system, such as the coexistence of regular motions with chaotic one, due to the effects of resonances, opposed to the regularity in the non resonant regime. The analysis is carried out by studying the Husimi distributions of chosen quantum states, with particular emphasis on stationary states and evolved coherent states. The computation are performed using both numerical methods and perturbative schemes. Although this should be considered a preliminary work, the purpose of which is to lay the fundations for future investigations, the results obtained here give interesting insights into quantum dynamics. For instance, it is shown how classical resonances exert a considerable influence on the spectrum of the quantum system and how it is possible, in the quantum behaviour, to find a trace of the classical adiabatic invariance in the resonance regime. / L'abbondanza, fra i modelli fisici, di perturbazioni di sistemi Hamiltoniani superintegrabili rende la comprensione della loro dinamica per tempi lunghi un importante argomento diricerca. Mentre dal punto di vista classico la situazione, perlomeno in molti case importanti, è ben compresa grazie all'uso del teorema di stabilità di Nekhoroshev e della teoria degli invariantiadiabatici, nel caso quantistico vi è, al contrario, una mancanza di risultati precisi. L'obiettivo di questa tesi è di studiare un sistema superintegrabile quantistico, ottenuto partendo da un corrispettivo classico tramite quantizzazione geometrica, al fine di evidenziare la presenza di indicatori di supertintegrabilità analoghi a quelliche caratterizzano il sistema classico, come la coesistenza di moti regolari e caotici, dovuta all'effetto delle risonanze, in contrapposizione con la regolarità nel regime non risonante. L'analisi è condotta studiando le distribuzioni di Husimi di stati quantistici scelti, con particolare enfasi posta sugli stati stazionari e sugli stati coerenti evoluti. I calcoli sono effettuati sia utilizzando tecniche numeriche che schemi perturbativi. Pur essendo da considerardi questo un lavoro preliminare, il cui compito è di porre le fondamenta per analisi future, i risultati qui ottenuti offrono interessanti spunti sulla dinamica quantistica. Per esempio è mostrato come le risonanze classiche abbiano un chiaro effeto sullo spettro del sistema quantistico, ed inoltre comesia possibile trovare una traccia, nel comportamento quantistico, dell'invarianza adiabatica classica nel regime risonante.

Nowadays, the digital terrestrial television (DTT) market is characterized by the high capacity needed for high definition TV services. There is a need for an efficient use of the broadcast spectrum, which requires new technologies to guarantee increased capacities. Non-Uniform Constellations (NUC) arise as one of the most innovative techniques to approach those requirements. NUCs reduce the gap between uniform Gray-labelled Quadrature Amplitude Modulation (QAM) constellations and the theoretical unconstrained Shannon limit. With these constellations, symbols are optimized in both in-phase (I) and quadrature (Q) components by means of signal geometrical shaping, considering a certain signal-to-noise ratio (SNR) and channel model. There are two types of NUC, one-dimensional and two-dimensional NUCs (1D-NUC and 2D-NUC, respectively). 1D-NUCs maintain the squared shape from QAM, but relaxing the distribution between constellation symbols in a single component, with non-uniform distance between them. These constellations provide better SNR performance than QAM, without any demapping complexity increase. 2D-NUCs also relax the square shape constraint, allowing to optimize the symbol positions in both dimensions, thus achieving higher capacity gains and lower SNR requirements. However, the use of 2D-NUCs implies a higher demapping complexity, since a 2D-demapper is needed, i.e. I and Q components cannot be separated. In this dissertation, NUCs are analyzed from both transmit and receive point of views, using either single-input single-output (SISO) or multiple-input multiple-output (MIMO) antenna configurations. In SISO transmissions, 1D-NUCs and 2D-NUCs are optimized for a wide range of SNRs and different constellation orders. The optimization of rotated 2D-NUCs is also investigated. Even though the demapping complexity is not increased, the SNR gain of these constellations is not significant. The highest rotation gain is obtained for low-order constellations and high SNRs. However, with multi-RF techniques, the SNR gain is drastically increased, since I and Q components are transmitted in different RF channels. In this thesis, multi-RF gains of NUCs with and without rotation are provided for some representative scenarios. At the receiver, two different implementation bottlenecks are explored. First, the demapping complexity of all considered constellations is analyzed. Afterwards, two complexity reduction algorithms for 2D-NUCs are proposed. Both algorithms drastically reduce the number of distances to compute. Moreover, both are finally combined in a single demapper. Quantization of NUCs is also explored in this dissertation, since LLR values and I/Q components are modified when using these constellations, compared to traditional QAM constellations. A new algorithm that is based on the optimization of the quantizer levels for a particular constellation is proposed. The use of NUCs in multi-antenna communications is also investigated. It includes the optimization in one or two antennas, the use of power imbalance, the cross-polar discrimination (XPD) between receive antennas, or the use of different demappers. Assuming different values for the parameters evaluated, new Multi-Antenna Non-Uniform Constellations (MA-NUC) are obtained by means of a particularized re-optimization process, specific for MIMO. At the receiver, an extended demapping complexity analysis is performed, where it is shown that the use of 2D-NUCs in MIMO extremely increases the demapping complexity. As an alternative, an efficient solution for 2D-NUCs and MIMO systems based on Soft-Fixed Sphere Decoding (SFSD) is proposed. The main drawback is that SFSD demappers do not work with 2D-NUCs, since they perform a Successive Interference Cancellation (SIC) step that needs to be performed in separated I and Q components. The proposed method quantifies the closest symbol using Voronoi regions and allows SFSD demappers to work. / Hoy en día, el mercado de la televisión digital terrestre (TDT) está caracterizado por la alta capacidad requerida para transmitir servicios de televisión de alta definición y el espectro disponible. Es necesario por tanto un uso eficiente del espectro radioeléctrico, el cual requiere nuevas tecnologías para garantizar mayores capacidades. Las constelaciones no-uniformes (NUC) emergen como una de las técnicas más innovadoras para abordar tales requerimientos. Las NUC reducen el espacio existente entre las constelaciones uniformes QAM y el límite teórico de Shannon. Con estas constelaciones, los símbolos se optimizan en ambas componentes fase (I) y cuadratura (Q) mediante técnicas geométricas de modelado de la señal, considerando un nivel señal a ruido (SNR) concreto y un modelo de canal específico. Hay dos tipos de NUC, unidimensionales y bidimensionales (1D-NUC y 2D-NUC, respectivamente). Las 1D-NUC mantienen la forma cuadrada de las QAM, pero permiten cambiar la distribución entre los símbolos en una componente concreta, teniendo una distancia no uniforme entre ellos. Estas constelaciones proporcionan un mejor rendimiento SNR que QAM, sin ningún incremento en la complejidad en el demapper. Las 2D-NUC también permiten cambiar la forma cuadrada de la constelación, permitiendo optimizar los símbolos en ambas dimensiones y por tanto obteniendo mayores ganancias en capacidad y menores requerimientos en SNR. Sin embargo, el uso de 2D-NUCs implica una mayor complejidad en el receptor. En esta tesis se analizan las NUC desde el punto de vista tanto de transmisión como de recepción, utilizando bien configuraciones con una antena (SISO) o con múltiples antenas (MIMO). En transmisiones SISO, se han optimizado 1D-NUCs para un rango amplio de distintas SNR y varios órdenes de constelación. También se ha investigado la optimización de 2D-NUCs rotadas. Aunque la complejidad no aumenta, la ganancia SNR de estas constelaciones no es significativa. La mayor ganancia por rotación se obtiene para bajos órdenes de constelación y altas SNR. Sin embargo, utilizando técnicas multi-RF, la ganancia aumenta drásticamente puesto que las componentes I y Q se transmiten en distintos canales RF. En esta tesis, se han estudiado varias ganancias multi-RF representativas de las NUC, con o sin rotación. En el receptor, se han identificado dos cuellos de botella diferentes en la implementación. Primero, se ha analizado la complejidad en el receptor para todas las constelaciones consideradas y, posteriormente, se proponen dos algoritmos para reducir la complejidad con 2D-NUCs. Además, los dos pueden combinarse en un único demapper. También se ha explorado la cuantización de estas constelaciones, ya que tanto los valores LLR como las componentes I/Q se ven modificados, comparando con constelaciones QAM tradicionales. Además, se ha propuesto un algoritmo que se basa en la optimización para diferentes niveles de cuantización, para una NUC concreta. Igualmente, se ha investigado en detalle el uso de NUCs en MIMO. Se ha incluido la optimización en una sola o en dos antenas, el uso de un desbalance de potencia, factores de discriminación entre antenas receptoras (XPD), o el uso de distintos demappers. Asumiendo distintos valores, se han obtenido nuevas constelaciones multi-antena (MA-NUC) gracias a un nuevo proceso de re-optimización específico para MIMO. En el receptor, se ha extendido el análisis de complejidad en el demapper, la cual se incrementa enormemente con el uso de 2D-NUCs y sistemas MIMO. Como alternativa, se propone una solución basada en el algoritmo Soft-Fixed Sphere Decoding (SFSD). El principal problema es que estos demappers no funcionan con 2D-NUCs, puesto que necesitan de un paso adicional en el que las componentes I y Q necesitan separarse. El método propuesto cuantifica el símbolo más cercano utilizando las regiones de Voronoi, permitiendo el uso de este tipo de receptor. / Actualment, el mercat de la televisió digital terrestre (TDT) està caracteritzat per l'alta capacitat requerida per a transmetre servicis de televisió d'alta definició i l'espectre disponible. És necessari per tant un ús eficient de l'espectre radioelèctric, el qual requereix noves tecnologies per a garantir majors capacitats i millors servicis. Les constel·lacions no-uniformes (NUC) emergeixen com una de les tècniques més innovadores en els sistemes de televisió de següent generació per a abordar tals requeriments. Les NUC redueixen l'espai existent entre les constel·lacions uniformes QAM i el límit teòric de Shannon. Amb estes constel·lacions, els símbols s'optimitzen en ambdós components fase (I) i quadratura (Q) per mitjà de tècniques geomètriques de modelatge del senyal, considerant un nivell senyal a soroll (SNR) concret i un model de canal específic. Hi ha dos tipus de NUC, unidimensionals i bidimensionals (1D-NUC i 2D-NUC, respectivament). 1D-NUCs mantenen la forma quadrada de les QAM, però permet canviar la distribució entre els símbols en una component concreta, tenint una distància no uniforme entre ells. Estes constel·lacions proporcionen un millor rendiment SNR que QAM, sense cap increment en la complexitat al demapper. 2D-NUC també canvien la forma quadrada de la constel·lació, permetent optimitzar els símbols en ambdós dimensions i per tant obtenint majors guanys en capacitat i menors requeriments en SNR. No obstant això, l'ús de 2D-NUCs implica una major complexitat en el receptor, ja que es necessita un demapper 2D, on les components I i Q no poden ser separades. En esta tesi s'analitzen les NUC des del punt de vista tant de transmissió com de recepció, utilitzant bé configuracions amb una antena (SISO) o amb múltiples antenes (MIMO). En transmissions SISO, s'han optimitzat 1D-NUCs, per a un rang ampli de distintes SNR i diferents ordes de constel·lació. També s'ha investigat l'optimització de 2D-NUCs rotades. Encara que la complexitat no augmenta, el guany SNR d'estes constel·lacions no és significativa. El major guany per rotació s'obté per a baixos ordes de constel·lació i altes SNR. No obstant això, utilitzant tècniques multi-RF, el guany augmenta dràsticament ja que les components I i Q es transmeten en distints canals RF. En esta tesi, s'ha estudiat el guany multi-RF de les NUC, amb o sense rotació. En el receptor, s'han identificat dos colls de botella diferents en la implementació. Primer, s'ha analitzat la complexitat en el receptor per a totes les constel·lacions considerades i, posteriorment, es proposen dos algoritmes per a reduir la complexitat amb 2D-NUCs. Ambdós algoritmes redueixen dràsticament el nombre de distàncies. A més, els dos poden combinar-se en un únic demapper. També s'ha explorat la quantització d'estes constel·lacions, ja que tant els valors LLR com les components I/Q es veuen modificats, comparant amb constel·lacions QAM tradicionals. A més, s'ha proposat un algoritme que es basa en l'optimització per a diferents nivells de quantització, per a una NUC concreta. Igualment, s'ha investigat en detall l'ús de NUCs en MIMO. S'ha inclòs l'optimització en una sola o en dos antenes, l'ús d'un desbalanç de potència, factors de discriminació entre antenes receptores (XPD), o l'ús de distints demappers. Assumint distints valors, s'han obtingut noves constel·lacions multi-antena (MA-NUC) gràcies a un nou procés de re-optimització específic per a MIMO. En el receptor, s'ha modificat l'anàlisi de complexitat al demapper, la qual s'incrementa enormement amb l'ús de 2D-NUCs i sistemes MIMO. Com a alternativa, es proposa una solució basada en l'algoritme Soft-Fixed Sphere Decoding (SFSD) . El principal problema és que estos demappers no funcionen amb 2D-NUCs, ja que necessiten d'un pas addicional en què les components I i Q necessiten separar-se. El mètode proposat quantifica el símbol més pròxim utilitzan / Fuentes Muela, M. (2017). Non-Uniform Constellations for Next-Generation Digital Terrestrial Broadcast Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/84743 / TESIS

The subject of this thesis is neural network acceleration with the goal of reducing the number of floating point multiplications. The theoretical part of the thesis surveys current trends and methods used in the field of neural network acceleration. However, the focus is on the binarization techniques which allow replacing multiplications with logical operators. The theoretical base is put into practice in two ways. First is the GPU implementation of crucial binary operators in the Tensorflow framework with a performance benchmark. Second is an application of these operators in simple image classifier. Results are certainly encouraging. Implemented operators achieve speed-up by a factor of 2.5 when compared to highly optimized cuBLAS operators. The last chapter compares accuracies achieved by binarized models and their full-precision counterparts on various architectures.

With the increasing demand for faster communication systems, soon data rates in the terabit regime (100 Gbit/s and beyond) are required, which yields new challenges for the design of analog-to-digital converters (ADCs) since high bandwidths imply high sampling rates. For sampling rates larger than 300MHz, which we now achieve with 5G, the ADC power consumption per conversion step scales quadratically with the sampling rate. Thus, ADCs become a major energy consumption bottleneck. To circumvent this problem, we consider digital receivers based on 1-bit quantization and oversampling. We motivate this concept by a brief comparison of the energy efficiency of a recently proposed system employing 1-bit quantization and oversampling to the conventional approach using high resolution quantization and Nyquist rate sampling. Our numerical results show that the energy efficiency can be improved significantly by employing 1-bit quantization and oversampling at the receiver at the cost of increased bandwidth. The main part of this work is concerned with the synchronization of fully digital receivers using 1-bit quantization and oversampling. As a first step, we derive performance bounds for phase, timing, and frequency estimation in order to gain a deeper insight into the impact of 1-bit quantization and oversampling. We identify uniform phase and sample dithering as crucial to combat the non-linear behavior introduced by 1-bit quantization. This dithering can be implemented by sampling at an irrational intermediate frequency and with an oversampling factor with respect to the symbol rate that is irrational, respectively. Since oversampling results in noise correlation, a closed form expression of the likelihood function is not available. To enable an analytical treatment we thus study a system model with white noise by adapting the receive filter bandwidth to the sampling rate. Considering the aforementioned dithering, we obtain very tight closed form lower bounds on the Cramér-Rao lower bound (CRLB) in the large sample regime. We show that with uniform phase and sample dithering, all large sample properties of the CRLB of the unquantized receiver are preserved under 1-bit quantization, except for a signal-to-noise ratio (SNR) dependent performance loss that can be decreased by oversampling. For the more realistic colored noise case, we discuss a numerically computable upper bound of the CRLB and show that the properties of the CRLB for white noise still hold for colored noise except that the performance loss due to 1-bit quantization is reduced. Assuming a neglectable frequency offset, we use the least squares objective function to derive a typical digital matched filter receiver with a data-and timing-aided phase estimator and a timing estimator that is based on square time recovery. We show that both estimators are consistent under very general assumptions, e.g., arbitrary colored noise and stationary ergodic transmit symbols. Performance evaluations are done via simulations and are compared against the numerically computable upper bound of the CRLB. For low SNR the estimators perform well but for high SNR they converge to an error floor. The performance loss of the phase estimator due to decision-directed operation or estimated timing information is marginal. In summary, we have derived practical solutions for the design of fully digital receivers using 1-bit quantization and oversampling and presented a mathematical analysis of the proposed receiver structure. This is an important step towards enabling energy efficient future wireless communication systems with data rates of 100 Gbit/s and beyond.

Cette thèse s’intéresse à différents problèmes de contrôle et d’optimisation dont il n’existe à ce jour que des solutions approchées. D’une part nous nous intéressons à des techniques visant à réduire ou supprimer les approximations pour obtenir des solutions plus précises voire exactes. D’autre part nous développons de nouvelles méthodes d’approximation pour traiter plus rapidement des problèmes à plus grande échelle. Nous étudions des méthodes numériques de simulation d’équation différentielle stochastique et d’amélioration de calculs d’espérance. Nous mettons en œuvre des techniques de type quantification pour la construction de variables de contrôle ainsi que la méthode de gradient stochastique pour la résolution de problèmes de contrôle stochastique. Nous nous intéressons aussi aux méthodes de clustering liées à la quantification, ainsi qu’à la compression d’information par réseaux neuronaux. Les problèmes étudiés sont issus non seulement de motivations financières, comme le contrôle stochastique pour la couverture d’option en marché incomplet mais aussi du traitement des grandes bases de données de médias communément appelé Big data dans le chapitre 5. Théoriquement, nous proposons différentes majorations de la convergence des méthodes numériques d’une part pour la recherche d’une stratégie optimale de couverture en marché incomplet dans le chapitre 3, d’autre part pour l’extension la technique de Beskos-Roberts de simulation d’équation différentielle dans le chapitre 4. Nous présentons une utilisation originale de la décomposition de Karhunen-Loève pour une réduction de variance de l’estimateur d’espérance dans le chapitre 2. / This thesis proposes different problems of stochastic control and optimization that can be solved only thanks approximation. On one hand, we develop methodology aiming to reduce or suppress approximations to obtain more accurate solutions or something exact ones. On another hand we develop new approximation methodology in order to solve quicker larger scale problems. We study numerical methodology to simulated differential equations and enhancement of computation of expectations. We develop quantization methodology to build control variate and gradient stochastic methods to solve stochastic control problems. We are also interested in clustering methods linked to quantization, and principal composant analysis or compression of data thanks neural networks. We study problems motivated by mathematical finance, like stochastic control for the hedging of derivatives in incomplete market but also to manage huge databases of media commonly known as big Data in chapter 5. Theoretically we propose some upper bound for convergence of the numerical method used. This is the case of optimal hedging in incomplete market in chapter 3 but also an extension of Beskos-Roberts methods of exact simulation of stochastic differential equations in chapter 4. We present an original application of karhunen-Loève decomposition for a control variate of computation of expectation in chapter 2.

This thesis deals with the integration of auxiliary data knowledge into machine learning methods especially prototype based classification models. The problem of classification is diverse and evaluation of the result by using only the accuracy is not adequate in many applications. Therefore, the classification tasks are analyzed more deeply. Possibilities to extend prototype based methods to integrate extra knowledge about the data or the classification goal is presented to obtain problem adequate models. One of the proposed extensions is Generalized Learning Vector Quantization for direct optimization of statistical measurements besides the classification accuracy. But also modifying the metric adaptation of the Generalized Learning Vector Quantization for functional data, i. e. data with lateral dependencies in the features, is considered.:Symbols and Abbreviations 1 Introduction 1.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . 1 1.2 Utilized Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Prototype Based Methods 19 2.1 Unsupervised Vector Quantization . . . . . . . . . . . . . . . . . . 22 2.1.1 C-means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.2 Self-Organizing Map . . . . . . . . . . . . . . . . . . . . . . 25 2.1.3 Neural Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.4 Common Generalizations . . . . . . . . . . . . . . . . . . . 30 2.2 Supervised Vector Quantization . . . . . . . . . . . . . . . . . . . . 35 2.2.1 The Family of Learning Vector Quantizers - LVQ . . . . . . 36 2.2.2 Generalized Learning Vector Quantization . . . . . . . . . 38 2.3 Semi-Supervised Vector Quantization . . . . . . . . . . . . . . . . 42 2.3.1 Learning Associations by Self-Organization . . . . . . . . . 42 2.3.2 Fuzzy Labeled Self-Organizing Map . . . . . . . . . . . . . 43 2.3.3 Fuzzy Labeled Neural Gas . . . . . . . . . . . . . . . . . . 45 2.4 Dissimilarity Measures . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.1 Differentiable Kernels in Generalized LVQ . . . . . . . . . 52 2.4.2 Dissimilarity Adaptation for Performance Improvement . 56 3 Deeper Insights into Classification Problems - From the Perspective of Generalized LVQ- 81 3.1 Classification Models . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2 The Classification Task . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.3 Evaluation of Classification Results . . . . . . . . . . . . . . . . . . 88 3.4 The Classification Task as an Ill-Posed Problem . . . . . . . . . . . 92 4 Auxiliary Structure Information and Appropriate Dissimilarity Adaptation in Prototype Based Methods 93 4.1 Supervised Vector Quantization for Functional Data . . . . . . . . 93 4.1.1 Functional Relevance/Matrix LVQ . . . . . . . . . . . . . . 95 4.1.2 Enhancement Generalized Relevance/Matrix LVQ . . . . 109 4.2 Fuzzy Information About the Labels . . . . . . . . . . . . . . . . . 121 4.2.1 Fuzzy Semi-Supervised Self-Organizing Maps . . . . . . . 122 4.2.2 Fuzzy Semi-Supervised Neural Gas . . . . . . . . . . . . . 123 5 Variants of Classification Costs and Class Sensitive Learning 137 5.1 Border Sensitive Learning in Generalized LVQ . . . . . . . . . . . 137 5.1.1 Border Sensitivity by Additive Penalty Function . . . . . . 138 5.1.2 Border Sensitivity by Parameterized Transfer Function . . 139 5.2 Optimizing Different Validation Measures by the Generalized LVQ 147 5.2.1 Attention Based Learning Strategy . . . . . . . . . . . . . . 148 5.2.2 Optimizing Statistical Validation Measurements for Binary Class Problems in the GLVQ . . . . . . . . . . . . . 155 5.3 Integration of Structural Knowledge about the Labeling in Fuzzy Supervised Neural Gas . . . . . . . . . . . . . . . . . . . . . . . . . 160 6 Conclusion and Future Work 165 My Publications 168 A Appendix 173 A.1 Stochastic Gradient Descent (SGD) . . . . . . . . . . . . . . . . . . 173 A.2 Support Vector Machine . . . . . . . . . . . . . . . . . . . . . . . . 175 A.3 Fuzzy Supervised Neural Gas Algorithm Solved by SGD . . . . . 179 Bibliography 182 Acknowledgements 201

Le but est d’explorer l’interaction entre les particules quantiques et la gravitation. On utilisera la quantification de Landau, l’effet Hall quantique et on examinera la relation entre la gravitation et l’effet Josephson. On propose une version de l’expérience "COW" (Colella-Overhauser-Werner) pour examiner les déviations de la loi du carré inverse de type Yukawa et de puissance inverse. Il est question de montages permettant d’investiguer la possibilité de mesurer le gravitomagnétisme et la constante de la gravitation G. On a examiné les transitions quantiques pour des neutrons ultra-froids (Ultra-Cold Neutron : UCN). Les résultats étaient satisfaisants pour 105 UCN. On a imaginé un effet laser avec ces neutrons émetteurs de gravitons : le phénomène est cependant très faible. Pour les corrections des niveaux de Landau : on a utilisé trois types d’espace-temps. Pour Schwarzschild, en utilisant une masse perturbatrice, les corrections d’ordres 1 et 2 dépendent du niveau n et du nombre quantique `. Cela enlève la dégénérescence des niveaux conventionnels. On obtient des résultats similaires pour les espaces-temps de Kerr et de Levi-Civita. On a proposé une expérience analogue à l’expérience COW. On a des déphasages malgré de faibles valeurs anticipées : de 10^−18 rad à 10^−4 rad pour le type Yukawa et de 10^−3 rad à 10^−9 rad pour puissance inverse. On a proposé des mesures possibles pour le gravitomagnétisme. On a aussi repris l’étude de l’influence de la gravitation sur l’effet Hall quantique. On obtient de faibles corrections pour un champ gravitationnel. On ne peut toutefois pas conclure à des quantités mesurables pour les déviations de type Yukawa et de puissance inverse. Par contre, on peut utiliser l’effet pour mesurer G avec grande précision. On a examiné l’effet Josephson sous l’effet de la gravitation en imaginant un montage simple. On a d’excellents résultats : des corrections de 10^−7 à 10^−9 Hz pour des déviations de type Yukawa et 10^−6 Hz pour des déviations en puissance inverse. Surtout, le lien entre la gravitation et la fréquence du courant de Josephson est clairement établit et mesurable. / The goal is to explore the interaction between quantum particles and gravitation. We will use Landau quantization, the quantum Hall effect and we will examine the relationship between gravity and Josephson’s effect. We propose a version of "COW" experience (Colella-Overhauser-Werner) to examine the Yukawa and inverse power deviations. We propose setups to investigate the possibility to measure gravitomagnetism and the gravitational constant G. Quantum transitions for ultra-cold neutrons (UCN) have been examined. The results were satisfactory for 105 UCN. We imagined a laser effect with these graviton emitting neutrons: the phenomenon is however very weak. For Landau level corrections: we proceeded with three types of space-times. For Schwarzschild, using a disturbing mass, the corrections of orders 1 and 2 depend on the level n and the quantum number "`". This removes the degeneracy of conventional levels. Similar results are obtained for the Kerr and the Levi-Civita spacetimes. We took over an analog of the COW experiment. We have phase shifts despite low expected values: from 10^−18 rad to 10^−4 rad for Yukawa and from 10^−3 rad to 10^−9 rad for inverse power laws. The same setup has been proposed for testing gravitomagnetism. We have also resumed the study of the influence of gravity on the quantum Hall effect. Small corrections are obtained for a gravitational field. We cannot however conclude with measurable quantities for Yukawa and inverse power laws. On the other hand, one can use the effect to measure G with great precision. We examined the Josephson effect under the effect of gravity by imagining a simple setup. We have excellent results: corrections from 10^−7 to 10^−9 Hz for Yukawa and 10^−6 Hz for inverse power law. Above all, the link between gravity and the frequency of Josephson’s current is clearly established and measurable.