Codes can be represented by edge-labeled directed graphs called trellises, which are used in decoding with the Viterbi algorithm. We will first examine the well-known product construction for trellises and present an algorithm for recovering the factors of a given trellis. To maximize efficiency, trellises that are minimal in a certain sense are desired. It was shown by Koetter and Vardy that one can produce all minimal tail-biting trellises for a code by looking at a special set of generators for a code. These generators along with a set of spans comprise what is called a characteristic pair, and we will discuss how to determine the number of these pairs for a given code. Finally, we will look at trellis dualization, in which a trellis for a code is used to produce a trellis representing the dual code. The first method we discuss comes naturally with the known BCJR construction. The second, introduced by Forney, is a very general procedure that works for many different types of graphs and is based on dualizing the edge set in a natural way. We call this construction the local dual, and we show the necessary conditions needed for these two different procedures to result in the same dual trellis.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-28T14:31:27Z No. of bitstreams: 1 lucianamirandavieiraxavier.pdf: 351536 bytes, checksum: f476ea35c3ced7fc7f8315f85d076f6e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-07T21:18:56Z (GMT) No. of bitstreams: 1 lucianamirandavieiraxavier.pdf: 351536 bytes, checksum: f476ea35c3ced7fc7f8315f85d076f6e (MD5) / Made available in DSpace on 2017-08-07T21:18:56Z (GMT). No. of bitstreams: 1 lucianamirandavieiraxavier.pdf: 351536 bytes, checksum: f476ea35c3ced7fc7f8315f85d076f6e (MD5) Previous issue date: 2009-02-27 / FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas Gerais / Nesta tese, revisa-se os principais métodos de quantização de sistemas vinculados a partir das técnicas Hamiltoniana de Dirac e Lagrangeana de Faddev-Jackiw ( sem vínculos) e sua extenção a de Barcelos Neto- Wotzasek (com vínculos), estes denominados simplesmente por Formalismo Simplético (FS). Em vista da correspondência entre os formalismos, eles serão aplicados ao Modelo de Skyrme SU(2) e ao Eletromagnetimo de Maxwell. Apresenta-se uma técnica contemporânea, que mergulha uma teoria de segunda classe em uma dual com invariância de calibre, a saber, o Formalismo Simplético de Imersão (FSI). Esse método baseia-se no FS e estende-se o espaço de configuração por meio das variáveis de Wess-Zumino. Para ilustrar esse FSI, constroi-se a eletrodinâmica de Maxwell como uma teoria de calibre, na qual as divergências clássicas não estejam presentes. Uma generalização relativística é a eletrodinâmica de Proca e de Chern-Simons, que consideram a possibilidade de existência de um fóton massivo e de um campo com alcance finito. A descrição dual reproduz o mesmo resultado encontrado na literatura através de outros métodos. Apesar da arbitrariedade dos geradores da simetria de calibre, os modos-zeros, mostram uma família de representações dinâmicas duais para o sistema em questão. / In this thesis, it will be revised the main quantization methods of constrained systems using the Dirac Hamiltonian method and Faddev-Jackiw Lagrangian techniques (without constrained), and its extension to the Barcelos Neto- Wotzasek Lagrangian method (with constrained), these known as Symplectic Formalism. Because of the correspondence among the formalisms, they will be applied of the Skyrme SU(2) model and Electromagnetism of Maxwell. It will be presented a contemporary technique that it embed a second class theory in a dual with gauge invariance, the Embedding Symplectic Formalism . This method is based on the Symplectic Formalism, it is extended the configuration space through Wess-Zumino variables. In order to illustrate this Embedding Symplectic Formalism, the Maxwell electrodynamics is built as a gauge theory, without the classic differences. A relativistic generalization is the Proca and Chern-Simons electrodynamics that consider the possibility of existence of a massive photon and a field with finite reach. The dual description reproduce the identic result reported in the literature using other methods. Although, the arbitrariness of the gauge symmetry generator, zero-mode, it reveals a family of dynamic dual representations to this system.