Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 109-114).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Η διπλωματική εργασία επικεντρώνεται στη μελέτη της κωδικοποίησης για κώδικες LDPC. Στα πλαίσιά της, θα μελετηθούν τα προβλήματα και η πολυπλοκότητα κωδικοποίησης συναρτήσει του μήκους της κωδικής λέξης. Έμφαση θα δοθεί σε εφαρμογές με μεγάλο μήκος κωδικής λέξης όπως εκείνες που χρησιμοποιούνται σε νέες τηλεπικοινωνιακές εφαρμογές, όπως δορυφορικό Digital Video Broadcast (DVB) DVB-S2, IEEE 802.3an (10GBASE-T) και IEEE 802.16(WiMAX). Σε τέτοιες εφαρμογές όπου η κωδική λέξη μπορεί να έχει μήκος αρκετά μεγαλύτερο των 1000 bits, η πολυπλοκότητα κωδικοποίησης είναι σημαντική. Αυτό συμβαίνει διότι απαιτούνται μεγάλες σε μέγεθος μνήμες για την αποθήκευση του Πίνακα Έλεγχου Ισοτιμίας (Parity-check Matrix H), πολύ μεγάλη χρονική επεξεργαστική πολυπλοκότητα O(n^2) αλλά και πολλά επεξεργαστικά στοιχεία τάξης Ο(n^2). Ο σκοπός λοιπόν είναι να μελετηθούν οι αλγόριθμοι κωδικοποίησης και να μελετηθεί πώς μπορεί να αξιοποιηθεί η αραιότητα του Πίνακα Έλεγχου Ισοτιμίας έτσι ώστε να επιτευχθεί κατά το δυνατόν γραμμική πολυπλοκότητα O(n) κωδικοποίησης. Στη συνέχεια, αφού αναπτυχθεί η κατάλληλη μέθοδος κωδικοποίησης, θα ακολουθήσει η μελέτη και ο σχεδιασμός μίας βέλτιστης VLSI αρχιτεκτονικής για την υλοποίηση σε υλικό του LDPC κωδικοποιητή, ώστε να ικανοποιεί και άλλα πρακτικά κριτήρια, με έμφαση στη μείωση της καθυστέρησης και της απαιτούμενης επιφάνειας. Θα αναπτυχθεί επίσης μια κατάλληλη αρχιτεκτονική για διάφορους βαθμούς παραλληλίας του κωδικοποιητή. / An LDPC code is a linear block code specified by a very sparse parity check matrix (PCM). LDPC codes are usually represented by a bi-partite graph in which a variable node corresponds to a ’coded bit’ or a PCM column, and a check node corresponds to a parity check equation or a PCM row. There is an edge between each pair of nodes if there is a ’one’ in the corresponding PCM entry. In a general analysis an (n, k) LDPC code has k information bits and n coded bits with code rate r = k/n. An important issue in the implementation of LDPC-code based forward error correction systems is the encoding of LDPC codes. Generally, LDPC codes cannot have the simple encoding structures based on of shift registers as in the case of convolutional, turbo codes, or cyclic block codes. However, general LDPC codes do not fall in this category. Except QC-cyclic LDPC codes, most efficient LDPC codes, especially irregular LDPC codes are hard to encode with the idea of shift registers. A straightforward way is to derive a systematic generator matrix from a PCM, and then to encode LDPC code systematically with the generator matrix. This can work for every LDPC code in theory, but practically it is a very bad idea because it has high complexity, as the generator matrix derived from parity-check matrix is not sparse contrasted to the PCM. Generator matrix can be very dense matrix. The objective is to utilize the sparseness to achieve LDPC encoding in linear time. This Master’s thesis presents a flexible encoder architecture using QC-cyclic LDPC codes and efficient two-step encoding algorithm in order to achieve linear time encoding. The particular approach considers several VLSI design issues of LDPC encoder. In particular efficient approaches are presented for reducing memory requirements, for reducing hardware complexity, and increasing the speed and throughput of LDPC encoding. The proposed structure is also generic and scalable, supporting multiple configurations, in terms of bits per symbol and code rate. A generic scalable processing unit is also presented. It supports LDPC codes that define parity check matrix as a combination of identity matrix, shifted identity matrix and all-zero matrix (QC-cyclic LDPC codes). The particular LDPC encoder architecture is synthesized and experimental results are reported.

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Made available in DSpace on 2014-10-09T12:28:22Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:28Z (GMT). No. of bitstreams: 0 / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

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abstract: Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles and overlap sequences. Universal cycles are Gray codes on a set of strings of length n in which the first n-1 letters of one object are the same as the last n-1 letters of its predecessor in the listing. Overlap sequences allow this overlap to vary between 1 and n-1. Some of our main contributions to the areas of Gray codes and universal cycles include a new Gray code algorithm for fixed weight m-ary words, and results on the existence of universal cycles for weak orders on [n]. Overlap cycles are a relatively new structure with very few published results. We prove the existence of s-overlap cycles for k-permutations of [n], which has been an open research problem for several years, as well as constructing 1- overlap cycles for Steiner triple and quadruple systems of every order. Also included are various other results of a similar nature covering other structures such as binary strings, m-ary strings, subsets, permutations, weak orders, partitions, and designs. These listing structures lend themselves readily to some classes of combinatorial objects, such as binary n-tuples and m-ary n-tuples. Others require more work to find an appropriate structure, such as k-subsets of an n-set, weak orders, and designs. Still more require a modification in the representation of the objects to fit these structures, such as partitions. Determining when and how we can fit these sets of objects into our three listing structures is the focus of this dissertation. / Dissertation/Thesis / Ph.D. Mathematics 2012

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Made available in DSpace on 2014-10-09T12:28:22Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:28Z (GMT). No. of bitstreams: 0 / O presente trabalho tem o objetivo de avaliar os riscos potenciais apresentados pelos incidentes em reatores nucleares de pesquisa. Para o desenvolvimento do trabalho, duas bases de dados do Organismo Internacional de Energia Atômica, OIEA, foram usadas, o Incident Report System for Research Reactor e Research Reactor Data Base. Para este tipo de avaliação fez-se uso de Análise Probabilística de Segurança (APS), dentro de um limite de confiança de 90% e, Análise de Probabilidades determinística (APD). Para obtenção dos resultados dos cálculos de probabilidades por APS, utilizou-se a teoria e as equações sugeridas em documento da IAEA TECDOC - 636. O desenvolvimento dos cálculos das probabilidades por APS utilizou-se o Programa Scilab versão 5.1.1, de livre acesso, executável nas plataformas do Windows, Linux. Um programa específico para obter os resultados das probabilidades foi desenvolvido dentro do programa principal Scilab 5.1.1., para duas distribuições Fischer e Chi-quadrado, ambas no limite de confiança de 90%. Fazendo uso das equações de Sordi e do programa Origin 6.0, foram obtidas as doses máximas admissíveis relacionadas às probabilidades que satisfazem os limites de riscos estabelecidos pela Comissão Internacional de Proteção Radiológica, CIPR e, pode-se também obter estas doses máximas graficamente com a figura 1 resultante dos cálculos de probabilidades x doses máximas admissíveis. Verificou-se que a confiabilidade nos resultados das probabilidades está relacionada com a experiência operacional (reator x ano e fração) e, que quanto maior ela for, maior é a confiabilidade no resultado. Finalizando, sugere-se uma lista de futuros trabalhos que complementam este. / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP