abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

Orientador: Francisco Villarreal Alvarado / Resumo: Este trabalho apresenta um algoritmo de codificação para imagens comprimidas que representacada pixel de uma imagem e suas coordenadas por um único valor. Para cadapixel e suas coordenadas, esse valor único é armazenado em um vetor que é usado nareconstrução da imagem sem que sua qualidade seja comprometida. O método propostoapresenta melhorias em relação a dois outros algoritmos propostos anteriormente, sendoque um deles já é uma melhoria do primeiro. O algoritmo apresentado neste trabalho diferedos outros dois algoritmos estudados na diminuição significativa do espaço necessáriopara armazenamento das imagens, na determinação de uma taxa de compressão exata ena redução do tempo de processamento de decodificação. Um outro avanço apresentadofoi a compressão de imagens coloridas utilizando a ferramenta wavemenu em conjuntocom o algoritmo que determina a taxa de compressão. / Mestre

O Sistema Brasileiro de Televisão Digital estabeleceu como padrão de codificação de áudio o algoritmo MPEG-4 Advanced Audio Coding, mais precisamente nos perfis Low Complexity, High Efficiency versão 1 e High Efficiency versão 2. O trabalho apresenta um estudo detalhado sobre o padrão, contendo desde alguns conceitos da psicoacústica como o mascaramento até a metodologia de decodificação do stream codificado, sempre voltado para o mercado do SBTVD. É proposta uma arquitetura em hardware para um decodificador compatível com o padrão MPEG-4 AAC LC. O decodificador é separado em dois grandes blocos mantendo em um deles o banco de filtros, considerado a parte mais custosa em termos de processamento. No bloco restante é realizada a decodificação do espectro, onde ocorre a decodificação dos códigos de Huffman, o segundo ponto crítico do algoritmo em termos de demandas computacionais. Por fim é descrita a implementação da arquitetura proposta em VHDL para prototipação em um FPGA da família Cyclone II da Altera. / MPEG-4 Advanced Audio Coding is the chosen algorithm for the Brazilian Digital Television System (SBTVD), supporting the Low Complexity, High Efficiency version 1 and High Efficiency version 2 profiles. A detailed study of the algorithm is presented, ranging from psychoacoustics concepts like masking to a review of the AAC bitstream decoding process, always keeping in mind the SBTVD. A digital hardware architecture is proposed, in which the algorithm is split in two separate blocks, one of them containing the Filter Bank, considered the most demanding task. The other block is responsible for decoding the coded spectrum, which contains the second most demanding task of the system: the Huffman decoding. In the final part of this work the conversion of the proposed architecture into VHDL modules meant to be prototyped with an Altera Cyclone II FPGA is described.

O Sistema Brasileiro de Televisão Digital estabeleceu como padrão de codificação de áudio o algoritmo MPEG-4 Advanced Audio Coding, mais precisamente nos perfis Low Complexity, High Efficiency versão 1 e High Efficiency versão 2. O trabalho apresenta um estudo detalhado sobre o padrão, contendo desde alguns conceitos da psicoacústica como o mascaramento até a metodologia de decodificação do stream codificado, sempre voltado para o mercado do SBTVD. É proposta uma arquitetura em hardware para um decodificador compatível com o padrão MPEG-4 AAC LC. O decodificador é separado em dois grandes blocos mantendo em um deles o banco de filtros, considerado a parte mais custosa em termos de processamento. No bloco restante é realizada a decodificação do espectro, onde ocorre a decodificação dos códigos de Huffman, o segundo ponto crítico do algoritmo em termos de demandas computacionais. Por fim é descrita a implementação da arquitetura proposta em VHDL para prototipação em um FPGA da família Cyclone II da Altera. / MPEG-4 Advanced Audio Coding is the chosen algorithm for the Brazilian Digital Television System (SBTVD), supporting the Low Complexity, High Efficiency version 1 and High Efficiency version 2 profiles. A detailed study of the algorithm is presented, ranging from psychoacoustics concepts like masking to a review of the AAC bitstream decoding process, always keeping in mind the SBTVD. A digital hardware architecture is proposed, in which the algorithm is split in two separate blocks, one of them containing the Filter Bank, considered the most demanding task. The other block is responsible for decoding the coded spectrum, which contains the second most demanding task of the system: the Huffman decoding. In the final part of this work the conversion of the proposed architecture into VHDL modules meant to be prototyped with an Altera Cyclone II FPGA is described.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-28T13:09:56Z No. of bitstreams: 2 Dissertação - Tulio Fernando da Mata - 2015.pdf: 1121756 bytes, checksum: 845f7de938a5d68c11d5b1bcd6fdf5ca (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-28T13:12:01Z (GMT) No. of bitstreams: 2 Dissertação - Tulio Fernando da Mata - 2015.pdf: 1121756 bytes, checksum: 845f7de938a5d68c11d5b1bcd6fdf5ca (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-28T13:12:01Z (GMT). No. of bitstreams: 2 Dissertação - Tulio Fernando da Mata - 2015.pdf: 1121756 bytes, checksum: 845f7de938a5d68c11d5b1bcd6fdf5ca (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper makes a brief reading on the crisis experienced by the mathematics education in Brazilian public schools in recent years, analyzing some of the reasons and motives of this crisis and trying to point out ways that this teaching will become better, more e cient and above all presenting mathematics as a fundamental importance for today's world science, pointing their applicability in everyday situations that may arouse the interest of students and present themselves as challenges to their ability to think and learn. In order to show the applicability and the importance of mathematics shows the encryption, if elected as a basis for analysis the cryptographic method RSA, one of the most widespread throughout the world, to present it as a tool that uses mathematical algorithms to encoding and/or decoding of data, enabling the protection and con dentiality of sensitive information transmitted via satellite in commercial and banking transactions. The paper presents the general importance of cryptography in the context of a globalized and technological world of today, as well as within the story, noting even its decisive contribution to the Allied victory against the Germans in the 2nd World War. It presents also the mathematical basis for encryption, prior knowledge of mathematics that are used to encrypt messages and or data, and presents examples of encoding and decoding simple messages. Finally, a general approach on the encryption is done, since its concept and common de nitions, pointing secured requirements for its use and the main types of algorithms for encryption and decryption codes, also called cryptographic keys. / O presente trabalho faz uma breve leitura sobre a situação de crise vivida pelo ensino de matemática na escola pública brasileira nos últimos anos, analisando algumas das razões e motivos dessa crise e tentando apontar caminhos para que esse ensino se torne melhor e mais e ciente e acima de tudo apresentando a matemática como uma ciência de fundamental importância para o mundo atual, apontando sua aplicabilidade em situações cotidianas que podem despertar o interesse dos alunos e se apresentam como desa os para suas capacidades de raciocinar e de aprender. Na perspectiva de mostrar a aplicabilidade e a importância da matemática apresenta-se a criptogra a, elegendo-se como base de análise o método criptográ co RSA, um dos mais difundidos em todo o mundo, para apresentá-lo como uma ferramenta que usa algoritmos matemá- ticos para a codi cação e/ou decodi cação de dados, permitindo a proteção e o sigilo de informações con denciais transmitidas via satélite em transações comerciais e banc árias. O trabalho apresenta a importância geral da criptogra a no contexto do mundo globalizado e tecnológico da atualidade, assim como dentro da história, ressaltando, inclusive, sua contribuição decisiva para a vitória dos Aliados contra os alemães na 2.a Guerra Mundial. Apresenta-se ainda a base matemática necessária para criptogra- a, ou seja, os conhecimentos prévios de matemática que são usados para criptografar mensagens e dados, bem como se apresenta exemplos de codi cação e decodi cação de mensagens simples. Por m, faz-se uma abordagem geral sobre a criptogra a, desde seu conceito e de nições mais comuns, apontando os requisitos garantidos pelo seu uso e os principais tipos de algoritmos para cifragem e decifragem de códigos, também chamadas de chaves criptográ cas.

Reed-Solomon code is nowadays broadly used in many fields of data transmission. Using of error correction codes is divided into two main operations: information coding before sending information into communication channel and decoding received information at the other side. There are vast of decoding algorithms of Reed-Solomon codes, which have specific features. There is needed knowledge of features of algorithms to choose correct algorithm which satisfies requirements of system. There are evaluated cyclic decoding algorithm, Peterson-Gorenstein-Zierler algorithm, Berlekamp-Massey algorithm, Sugiyama algorithm with erasures and without erasures and Guruswami-Sudan algorithm. There was done implementation of algorithms in software and in hardware. Simulation of implemented algorithms was performed. Algorithms were evaluated and there were proposed methods to improve their work.

This thesis focuses on the re-generation of sound from a spike based coding system. Three different types of spike based coding system have been analyzed. Two of them are biologically inspired spike based coding systems i.e. the spikes are generated in a similar way to how our auditory nerves generate spikes. They have been called AN (Auditory Nerve) spikes and AN Onset (Amplitude Modulated Onset) spikes. Sounds have been re-generated from spikes generated by both of those spike coding technique. A related event based coding technique has been developed by Koickal and the sounds have been re-generated from spikes generated by Koickal's spike coding technique and the results are compared. Our brain does not reconstruct sound from the spikes received from auditory nerves, it interprets it. But by reconstructing sounds from these spike coding techniques, we will be able to identify which spike based technique is better and more efficient for coding different types of sounds. Many issues and challenges arise in reconstructing sound from spikes and they are discussed. The AN spike technique generates the most spikes of the techniques tested, followed by Koickal's technique (54.4% lower) and the AN Onset technique (85.6% lower). Both subjective and objective types of testing have been carried out to assess the quality of reconstructed sounds from these three spike coding techniques. Four types of sounds have been used in the subjective test: string, percussion, male voice and female voice. In the objective test, these four types and many other types of sounds have been included. From the results, it has been established that AN spikes generates the best quality of decoded sounds but it produces many more spikes than the others. AN Onset spikes generates better quality of decoded sounds than Koickal's technique for most of sounds except choir type of sounds and noises, however AN Onset spikes produces 68.5% fewer spikes than Koickal's spikes. This provides evidences that AN Onset spikes can outperform Koickal's spikes for most of the sound types.

Masters of Science / Codes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph 􀀀k n has vertices the 2n vectors of Fn2 and adjacency de ned by two vectors being adjacent if they di er in k coordinate positions. In particular, 􀀀1 n is the classical n-cube, usually denoted by H1(n; 2): This study examines the codes (both binary and p-ary for p an odd prime) of the row span of adjacency and incidence matrices of these graphs. We rst examine codes of the adjacency matrices of the n-cube. These have been considered in [14]. We then consider codes generated by both incidence and adjacency matrices of the Hamming graphs H1(n; 3) [12]. We will also consider codes of the line graphs of the n-cube as in [13]. Further, the automorphism groups of the codes, designs and graphs will be examined, highlighting where there is an interplay. Where possible, suitable permutation decoding sets will be given.

This study examined a Pseudoword Phonics Curriculum to determine if this form of instruction would increase students’ decoding skills compared to typical real-word phonics instruction. In typical phonics instruction, children learn to decode familiar words which allow them to draw on their prior knowledge of how to pronounce the word and may detract from learning decoding skills. By using pseudowords during phonics instruction, students may learn more decoding skills because they are unfamiliar with the “words” and therefore cannot draw on memory for how to pronounce the word. It was hypothesized that students who learn phonics with pseudowords will learn more decoding skills and perform higher on a real-word assessment compared to students who learn phonics with real words. Students from two kindergarten classes participated in this study. An author-created word decoding assessment was used to determine the students’ ability to decode words. The study was broken into three phases, each lasting one month. During Phase 1, both groups received phonics instruction using real words, which allowed for the exploration of baseline student growth trajectories and potential teacher effects. During Phase 2, the experimental group received pseudoword phonics instruction while the control group continued real-word phonics instruction. During Phase 3, both groups were taught with real-word phonics instruction. Students were assessed on their decoding skills before and after each phase. Results from multiple regression and multi-level model analyses revealed a greater increase in decoding skills during the second and third phases of the study for students who received the pseudoword phonics instruction compared to students who received the real-word phonics instruction. This suggests that pseudoword phonics instruction improves decoding skills quicker than real-word phonics instruction. This also suggests that teaching decoding with pseudowords for one month can continue to improve decoding skills when children return to real-word phonics instruction. Teacher feedback suggests that confidence with reading increased for students who learned with pseudowords because they were less intimidated by the approach and viewed pseudoword phonics as a game that involved reading “silly” words. Implications of these results, limitations of this study, and areas for future research are discussed.

One of the most popular ways to exploit the advantages of a multiple-input multiple-output (MIMO) system is using space time block coding. A space time block code (STBC) is a finite set of complex matrices whose entries consist of the information symbols to be transmitted. A linear STBC is one in which the information symbols are linearly combined to form a two-dimensional code matrix. A well known method of maximum-likelihood (ML) decoding of such STBCs is using the sphere decoder (SD). In this thesis, new constructions of STBCs with low sphere decoding complexity are presented and various ways of characterizing and reducing the sphere decoding complexity of an STBC are addressed. The construction of low sphere decoding complexity STBCs is tackled using irreducible matrix representations of Clifford algebras, cyclic division algebras and crossed-product algebras. The complexity reduction algorithms for the STBCs constructed are explored using tree based search algorithms. Considering an STBC as a vector space over the set of weight matrices, the problem of characterizing the sphere decoding complexity is addressed using quadratic form representations. The main results are as follows. A sub-class of fast decodable STBCs known as Block Orthogonal STBCs (BOSTBCs) are explored. A set of sufficient conditions to obtain BOSTBCs are explained. How the block orthogonal structure of these codes can be exploited to reduce the SD complexity of the STBC is then explained using a depth first tree search algorithm. Bounds on the SD complexity reduction and its relationship with the block orthogonal structure are then addressed. A set of constructions to obtain BOSTBCs are presented next using Clifford unitary weight designs (CUWDs), Coordinate-interleaved orthogonal designs (CIODs), cyclic division algebras and crossed product algebras which show that a lot of codes existing in literature exhibit the block orthogonal property. Next, the dependency of the ordering of information symbols on the SD complexity is discussed following which a quadratic form representation known as the Hurwitz-Radon quadratic form (HRQF) of an STBC is presented which is solely dependent on the weight matrices of the STBC and their ordering. It is then shown that the SD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization). It is also shown that the SD complexity is completely captured into a single matrix obtained from the HRQF. Also, for a given set of weight matrices, an algorithm to obtain a best ordering of them leading to the least SD complexity is presented using the HRQF matrix.