No description available.

In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. This thesis concerns the construction of non-constant-dimension projective space codes for adversarial error-correction in random linear network coding. The metric used is the so-called injection distance introduced by Silva and Kschischang, which perfectly reflects the adversarial nature of the channel. A Gilbert-Varshamov-type bound for such codes is derived and its asymptotic behaviour is analysed. It is shown that in the limit as the ambient space dimension approaches infinity, the Gilbert-Varshamov bound on the size of non-constant-dimension codes behaves similar to the Gilbert-Varshamov bound on the size of constant-dimension codes contained within the largest Grassmannians in the projective space. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric. To our knowledge this work is the first to address the construction of non-constant-dimension codes designed for the injection metric.

In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. This thesis concerns the construction of non-constant-dimension projective space codes for adversarial error-correction in random linear network coding. The metric used is the so-called injection distance introduced by Silva and Kschischang, which perfectly reflects the adversarial nature of the channel. A Gilbert-Varshamov-type bound for such codes is derived and its asymptotic behaviour is analysed. It is shown that in the limit as the ambient space dimension approaches infinity, the Gilbert-Varshamov bound on the size of non-constant-dimension codes behaves similar to the Gilbert-Varshamov bound on the size of constant-dimension codes contained within the largest Grassmannians in the projective space. Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric. To our knowledge this work is the first to address the construction of non-constant-dimension codes designed for the injection metric.

Στην εργασία αυτή, μελετώνται διαφορετικοί αποκωδικοποιητές για κώδικες Reed-Solomon. Αφού γίνει μια εισαγωγή στο σύστημα επικοινωνίας, στα πεπερασμένα σώματα και στη θεωρία κωδίκων, παρουσιάζονται αλγόριθμοι που υλοποιούν αποκωδικοποιητές περιορισμένης απόστασης, λίστας και soft decoders. Συγκεκριμένα, μελετώνται κλασσικοί αποκωδικοποιητές, αποκωδικοποιητές βασισμένοι στον αλγόριθμο Guruswami-Sudan, και αποκωδικοποιητές βασισμένοι στον αλγόριθμο Koetter-Vardy. Η σύγκριση γίνεται ως προς τη διορθωτική ικανότητα και τη χρονική πολυπλοκότητα. Στα πλαίσια της εργασίας αυτής, σε συνέχεια της μελέτης υπαρχόντων αποκωδικοποιητών προτείνεται ένα είδος προσαρμοστικού αποκωδικοποιητή: φέρει την ίδια διορθωτική ικανότητα με έναν αποκωδικοποιητή λίστας, αλλά σε ορισμένες περιπτώσεις έχει ικανοποιητικά μικρότερη χρονική πολυπλοκότητα. Επίσης γίνεται μία ποιοτική διερεύνηση για το πότε πρέπει να προτιμάται ο προσαρμοστικός αποκωδικοποιητής. Προτείνονται δύο διαφορετικοί προσαρμοστικοί αποκωδικοποιητές. Η πρώτη εκδοχή, είναι μία διάταξη με δύο αποκωδικοποιητές. Αρχικά το ληφθέν διάνυσμα από το κανάλι, εισέρχεται ως είσοδος σε έναν κλασσικό αποκωδικοποιητή. Αν ο κλασσικός παρουσιάσει αδυναμία αποκωδικοποίησης, τότε επιχειρεί να διορθώσει το ίδιο διάνυσμα ένας αποκωδικοποιητής λίστας. Η δέυτερη εκδοχή, μοιάζει με την πρώτη, με τη διαφορά ότι ο δεύτερος αποκωδικοποιητής χρησιμοποιεί αποτελέσματα που έχουν ήδη υπολογιστεί από τον πρώτο, μειώνοντας έτσι την συνολική χρονική πολυπλοκότητα, σχετικά με την πρώτη εκδοχή. / In this thesis we study a family of linear block codes, the Reed-Solomon(RS) codes. RS codes are q-ary codes over some finite field GF(q). Therefore, they have strong burst-error correction capability, because they deal with groups of bits instead of single bits. Initially, we describe the employed communication system model, and introduce basic from finite field theory (construction and identities) and coding theory. After describing the RS encoding process, we describe different RS decoders (bounded distance decoder, list decoder and soft-input decoder). Specifically, in addition to traditional approaches, we focus on decoders based on Guruswami-Sudan and Koetter – Vardy algorithms. We compare them according to their complexity and performance, both in theory and experimentally. Furthermore, in this thesis, we propose an adaptive decoder, which has the same performance as a list decoder but in some cases it achieves much lower average time complexity. We present the experimental results, highlighting the cases where the adaptive decoder outperforms conventional decoders. The adaptive decoder comes in two different types. The first type is a system with two different decoders: the low complexity decoder attempts to decode a received vector and in case of decoding failure the subsequent decoder tries to decode the same received vector. The second type resembles the general organization of the above system; the second decoder re-uses intermediate results, previously computed by the first one.

La simulation de systèmes d'ingénierie non linéaire complexes tels que les écoulements de fluide compressibles peut être ciblée pour rendre plus efficace et précise l'approximation d'une quantité spécifique (scalaire) d'intérêt du système. En mettant de côté l'erreur de modélisation et l'incertitude paramétrique, on peut y parvenir en combinant des estimations d'erreurs axées sur des objectifs et des raffinements adaptatifs de maillage spatial anisotrope. A cette fin, un cadre élégant et efficace est celui de l'adaptation dite basé-métrique où une estimation d'erreur a priori est utilisée comme indicateur d’adaptation de maillage. Dans cette thèse on propose une nouvelle extension de cette approche au cas des approximations de système portant une composante stochastique. Dans ce cas, un problème d'optimisation est formulé et résolu pour un meilleur contrôle des sources d'erreurs. Ce problème est posé dans le cadre continu de l'espace de métrique riemannien. Des développements algorithmiques sont également proposés afin de déterminer les sources dominates d’erreur et effectuer l’adaptation dans les espaces physique ou des paramètres incertains. L’approche proposé est testée sur divers problèmes comprenant une entrée de scramjet supersonique soumise à des incertitudes paramétriques géométriques et opérationnelles. Il est démontré que cette approche est capable de bien capturé les singularités dans l’escape stochastique, tout en équilibrant le budget de calcul et les raffinements de maillage dans les deux espaces. / The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling error and parametric uncertainty, this may be achieved by combining goal-oriented error estimates and adaptive anisotropic spatial mesh refinements. To this end, an elegant and efficient framework is the one of (Riemannian) metric-based adaptation where a goal-based a priori error estimation is used as indicator for adaptivity. This thesis proposes a novel extension of this approach to the case of aforementioned system approximations bearing a stochastic component. In this case, an optimisation problem leading to the best control of the distinct sources of errors is formulated in the continuous framework of the Riemannian metric space. Algorithmic developments are also presented in order to quantify and adaptively adjust the error components in the deterministic and stochastic approximation spaces. The capability of the proposed method is tested on various problems including a supersonic scramjet inlet subject to geometrical and operational parametric uncertainties. It is demonstrated to accurately capture discontinuous features of stochastic compressible flows impacting pressure-related quantities of interest, while balancing computational budget and refinements in both spaces.

Orientadores: Paulo Roberto Brumatti, Fernando Eduardo Torres Orihuela / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T23:44:44Z (GMT). No. of bitstreams: 1 Melo_Nolmar_M.pdf: 705654 bytes, checksum: b8ecfe0cc3ffd2dd2f63bc813a9c4a8d (MD5) Previous issue date: 2006 / Resumo: O objetivo central desta dissertação foi o de apresentar os Códigos Geométricos de Goppa via métodos elementares que foram introduzidos por J. H. van Lint, R. Pellikaan e T. Hfhold por volta de 1998. Numa primeira parte da dissertação são apresentados os conceitos fundamentais sobre corpos de funções racionais de uma curva algébrica na direção de se definir os códigos de Goppa de maneira clássica, neste estudo nos baseamos principalmente no livro ¿Algebraic Function Fields and Codes¿ de H. Stichtenoth. A segunda parte inicia-se com a introdução dos conceitos de funções peso, grau e ordem que são fundamentais para o estudo dos Códigos de Goppa via métodos elementares de álgebra linear e de semigrupos, tal estudo foi baseado em ¿Algebraic geometry codes¿ de J. H. van Lint, R. Pellikaan e T. Hfhold.A dissertação termina com a apresentação de exemplos que ilustram os métodos elementares que nos referimos acima / Abstract: The central objective of this dissertation was to present the Goppa Geometry Codes via elementary methods which were introduced by J. H. van Lint, R. Pellikaan and T. Hfhold about 1998. On the first past of such dissertation are presented the fundamental concepts about fields of rational functions of an algebraic curve in the direction as to define the Goppa Codes on a classical manner. In this study we based ourselves mainly on the book ¿Algebraic Function Fields and Codes¿ of H. Stichtenoth. The second part is initiated with an introduction about the functions weight, degree and order which are fundamental for the study of the Goppa Codes throught elementary methods of linear algebra and of semigroups and such study was based on ¿Algebraic Geometry Codes¿ of J. h. van Lint, R. Pellikaan and T. Hfhold. The dissertation ends up with a presentation of examples which illustrate the elementary methods that we have referred to above / Mestrado / Algebra / Mestre em Matemática

Orientador: Jaime Portugheis / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-25T19:09:11Z (GMT). No. of bitstreams: 1 PujaicoRivera_Fernando_D.pdf: 1689945 bytes, checksum: b226b1d9cf87f31fc3d470ac895b0e33 (MD5) Previous issue date: 2014 / Resumo: Esta tese propõe um sistema de transmissão de informação de várias fontes correlacionadas sobre canais ruidosos. Inicialmente se aborda o problema da codificação fonte-canal conjunta. Para este problema se definirá conceitos de taxas ótimas e se apresentará a maneira de obtê-las. Posteriormente, será proposto um algoritmo de decodificação conjunta com complexidade tratável. Diversos resultados de desempenho do algoritmo proposto serão apresentados. Estes resultados mostram um bom compromisso entre desempenho e complexidade quando comparados com a decodificação independente. Finalmente, o algoritmo de decodificação conjunta seguido de uma proposta de regra de fusão é usado no problema CEO e o desempenho deste novo algoritmo é apresentado / Abstract: This thesis proposes a system that transmits information from various correlated sources over noisy channels. Initially, it addresses the problem of joint source-channel coding. To solve this problem, concepts of optimal rates will be defined and the way to obtain them will be presented. Subsequently, a joint decoding algorithm with a tractable complexity is proposed. Several performance results of the proposed algorithm will be presented. These results show a good compromise between performance and complexity when compared to the non-joint decoding. Finally, the joint decoding algorithm, followed by a proposal for a fusion rule is used in the CEO problem and the performance of this new algorithm is presented / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Low earth orbit (LEO) satellite communication presents a unique environment which inherently di ers from most other communication channels. Due to the varying orbital patterns of LEO satellites the link exhibits varying link margins. Limited communication time windows need to be optimised to maximise the volumetric data throughput. Large coding gains can be obtained by the implementation of forward error correction codes. This thesis presents a means for optimising the data throughput of LEO satellite communication through the implementation of a mission speci c error control strategy. Low density parity check (LDPC) codes are versatile and present good error performances at many di erent code rates and block lengths. With power limitations on the space segment and remote ground stations, hardware utilisation e ciency must be optimised to reduce power consumption. In response to this requirement, this thesis evaluates various algorithms for LDPC decoders. An iterative LDPC decoder, implementing an approximation algorithm, is presented as a low complexity solution with good error performance. The proposed solution provides a very good balance between required hardware complexity and coding performance. It was found that many parameters of the decoders and codes can be altered to allow the implementation of these codes in systems with varying memory and processing capabilities. / AFRIKAANSE OPSOMMING: Kommunikasiekanale van satelliete met lae wentelbane, bied 'n unieke omgewing wat inherent verskil van meeste ander kommunikasiekanale. As gevolg van veranderende wentelbaanpatrone, vertoon die kanaal 'n wisselende foutgedrag. Kommunikasievensters is beperk en moet geoptimeer word om die totale deurset van die stelsel te maksimeer. Groot koderingswinste kan verkry word deur die implementering van foutkorreksie kodes. Hierdie tesis voorsien 'n metode om die datadeurset van satelliete met lae wentelbaan te optimeer, deur middel van implementering van 'n missie-spesi eke foutbeheer strategie. Lae digtheid pariteit toetskodes (LDPC) is veelsydige kodes, bied goeie foutbeheer en is doeltre end vir verskillende kodekoerse en bloklengtes. Met drywingsbeperkinge op die ruimtesegment en afgesonderde grondstasies, moet hardeware komponente doeltreffend gebruik word om drywingsverbruik te verminder. Ten einde aan hierdie ontwerpsvereiste te voldoen, evalueer hierdie tesis verskeie LDPC dekodeerderalgoritmes. Deur 'n iteratiewe LDPC dekodeerder met 'n benaderingsalgoritme te implementeer, word 'n oplossing van lae kompleksiteit aangebied, maar wat steeds goeie foutkorreksie eienskappe toon. Die voorgestelde oplossing bied 'n baie goeie balans tussen benodigde hardeware kompleksiteit en koderingsprestasie. Daar is gevind dat heelwat parameters van die dekodeerders en kodes aangepas kan word, ten einde implementering in stelsels met 'n wye verskeidenheid van geheuespasie en verwerkingsvermoëns moontlik te maak.

Neste trabalho, uma combinação do Método dos Elementos de Contorno (MEC) com o Método dos Elementos Finitos (MEF) é apresentada para análise bidimensional de sólidos elastostáticos reforçados, sendo considerados modelos de aderência no acoplamento. O elemento de contorno é adotado para modelar o comportamento do domínio, enquanto que o modelo por elementos finitos é utilizado para modelar o enrijecedor. Devido às singularidades nas equações integrais do MEC, estudou-se o erro ocasionado pelos integrandos de ordem e e como conseqüência sugerem-se, neste trabalho, equações mais simples para representar o erro das integrações. Para a formulação do acoplamento, um polinômio do terceiro grau é adotado para aproximar tanto o campo de deslocamento quanto a rotação do enrijecedor, enquanto aproximações lineares são usadas para representar a força de contato entre o domínio e o enrijecedor. Modelos de escorregamento, apresentados, são lineares e governados em função do carregamento escrito em termos das forças de contato e o deslocamento relativo. A partir da combinação entre o MEC e o MEF obtém-se uma matriz retangular contendo duas equações para o MEC e uma para o MEF. O resultado das equações algébricas redundantes é eliminado pela aplicação do procedimento dos mínimos quadrados. Exemplos ilustram o bom ajuste e os melhores resultados proporcionados pelo controle do erro das equações integrais, mostrando ainda através de exemplos, a potencialidade e as limitações no acoplamento entre os dois materiais, considerando modelos de aderência ou não. / In this work it is presented a coupling between the Boundary Element Method and the Finite Element Method for two-dimensional elastostatic analysis of reinforced bodies considering adherence. The Boundary Element is used to model the matrix while the reinforcement is modeled by the Finite Element. Due to the inherent singularities present in Boundary Element formulations the quadrature rules, used to develop the necessary integrals may present undesired errors. In this sense the behavior of this integration error is studied and a simple way to control it is proposed along the work. Regarding the coupling formulation a third degree polynomial is adopted to describe the displacements and rotations of the reinforcement, while a linear polynomial is used to describe the contact forces among the continuum and the reinforcement. Adherence (or sliding) models are presented and implemented in the computer code. A linear relation between relative displacement and transmitted force is adopted. From difference of approximation regarding contact forces and displacements a rectangular matrix arrises from the BEM/FEM coupling. The additional equations are eliminated by the use of a least square method based on the multiplication of transpose matrices. Examples are shown to demonstrate the good behavior of error control applied on gaussian quadratures regarding Boundary Element simulations for coupled or not situations, considering or not adherence models.

Recent designs for low-density parity-check (LDPC) codes have exhibited capacity approaching performance for large block length, overtaking the performance of turbo codes. While theoretically impressive, LDPC codes present some challenges for practical implementation. In general, LDPC codes have higher encoding complexity than turbo codes both in terms of computational latency and architecture size. Decoder circuits for LDPC codes have a high routing complexity and thus demand large amounts of circuit area. There has been recent interest in developing analog circuit architectures suitable for decoding. These circuits offer a fast, low-power alternative to the digital approach. Analog decoders also have the potential to be significantly smaller than digital decoders. In this thesis we present a novel and efficient approach to LDPC encoder / decoder (codec) design. We propose a new algorithm which allows the parallel decoder architecture to be reused for iterative encoding. We present a new class of LDPC codes which are iteratively encodable, exhibit good empirical performance, and provide a flexible choice of code length and rate. Combining the analog decoding approach with this new encoding technique, we design a novel time-multiplexed LDPC codec, which switches between analog decode and digital encode modes. In order to achieve this behaviour from a single circuit we have developed mode-switching gates. These logic gates are able to switch between analog (soft) and digital (hard) computation, and represent a fundamental circuit design contribution. Mode-switching gates may also be applied to built-in self-test circuits for analog decoders. Only a small overhead in circuit area is required to transform the analog decoder into a full codec. The encode operation can be performed two orders of magnitude faster than the decode operation, making the circuit suitable for full-duplex applications. Throughput of the codec scales linearly with block size, for both encode and decode operations. The low power and small area requirements of the circuit make it an attractive option for small portable devices.