Contributos para a análise estatística de séries de contagem

A análise das séries temporais de valores inteiros tornou-se, nos últimos anos, uma área de investigação importante, não só devido à sua aplicação a dados de contagem provenientes de diversos campos da ciência, mas também pelo facto de ser uma área pouco explorada, em contraste com a análise séries temporais de valores contínuos. Uma classe que tem obtido especial relevo é a dos modelos baseados no operador binomial thinning, da qual se destaca o modelo auto-regressivo de valores inteiros de ordem p. Esta classe é muito vasta, pelo que este trabalho tem como objectivo dar um contributo para a análise estatística de processos de contagem que lhe pertencem. Esta análise é realizada do ponto de vista da predição de acontecimentos, aos quais estão associados mecanismos de alarme, e também da introdução de novos modelos que se baseiam no referido operador. Em muitos fenómenos descritos por processos estocásticos a implementação de um sistema de alarmes pode ser fundamental para prever a ocorrência de um acontecimento futuro. Neste trabalho abordam-se, nas perspectivas clássica e bayesiana, os sistemas de alarme óptimos para processos de contagem, cujos parâmetros dependem de covariáveis de interesse e que variam no tempo, mais concretamente para o modelo auto-regressivo de valores inteiros não negativos com coeficientes estocásticos, DSINAR(1). A introdução de novos modelos que pertencem à classe dos modelos baseados no operador binomial thinning é feita quando se propõem os modelos PINAR(1)T e o modelo SETINAR(2;1). O modelo PINAR(1)T tem estrutura periódica, cujas inovações são uma sucessão periódica de variáveis aleatórias independentes com distribuição de Poisson, o qual foi estudado com detalhe ao nível das suas propriedades probabilísticas, métodos de estimação e previsão. O modelo SETINAR(2;1) é um processo auto-regressivo de valores inteiros, definido por limiares auto-induzidos e cujas inovações formam uma sucessão de variáveis independentes e identicamente distribuídas com distribuição de Poisson. Para este modelo estudam-se as suas propriedades probabilísticas e métodos para estimar os seus parâmetros. Para cada modelo introduzido, foram realizados estudos de simulação para comparar os métodos de estimação que foram usados.

Implicit optimality criterion for convex SIP problem with box constrained index set

We consider a convex problem of Semi-Infinite Programming (SIP) with multidimensional index set. In study of this problem we apply the approach suggested in [20] for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.

Visible light communication systems for road safety applications

Esta tese apresenta um estudo exploratório sobre sistemas de comunicação por luz visível e as suas aplicações em sistemas de transporte inteligentes como forma a melhorar a segurança nas estradas. Foram desenvolvidos neste trabalho, modelos conceptuais e analíticos adequados à caracterização deste tipo de sistemas. Foi desenvolvido um protótipo de baixo custo, capaz de suportar a disseminação de informação utilizando semáforos. A sua realização carece de um estudo detalhado, nomeadamente: i) foi necessário obter modelos capazes de descrever os padrões de radiação numa área de serviço pré-definida; ii) foi necessário caracterizar o meio de comunicações; iii) foi necessário estudar o comportamento de vários esquemas de modulação de forma a optar pelo mais robusto; finalmente, iv) obter a implementação do sistema baseado em FPGA e componentes discretos. O protótipo implementado foi testado em condições reais. Os resultados alcançados mostram os méritos desta solução, chegando mesmo a encorajar a utilização desta tecnologia em outros cenários de aplicação.

Cimentos de fosfato de magnésio: consolidação e caracterização

A reação entre o óxido de magnésio (MgO) e o fosfato de monoamónio (MAP), à temperatura ambiente, origina os cimentos de fosfato de magnésio, materiais caracterizados pela sua presa rápida e pelas excelentes propriedades mecânicas adquiridas precocemente. As propriedades finais são dependentes, essencialmente, da composição do cimento (razão molar magnésia:fosfato e utilização de retardantes de presa) mas também são influenciadas pela reatividade da magnésia utilizada. Neste trabalho, a reação foi caracterizada através do estudo da influência da razão molar MgO:MAP (variando de 1:1 até 8:1), da presença e teor de aditivos retardantes (ácido bórico, ácido cítrico e tripolifosfato de sódio) e da variação da área superficial específica da magnésia (conseguida por calcinação do óxido), no tempo de presa, na temperatura máxima atingida e nas fases cristalinas finais formadas. A reação de presa pode ser comparada à hidratação do cimento Portland, com a existência de 4 estágios (reação inicial, indução, aceleração e desaceleração), com a diferença que estes estágios ocorrem a velocidade muito mais alta nos cimentos de fosfato de magnésio. Este estudo foi realizado utilizando a espetroscopia de impedâncias, acompanhada pela monitorização da evolução de temperatura ao longo do tempo de reação e, por paragem de reação, identificando as fases cristalinas formadas. A investigação do mecanismo de reação foi complementada com a observação da microestrutura dos cimentos formados e permitiu concluir que a origem da magnésia usada não afeta a reação nem as propriedades do cimento final. A metodologia de superfície de resposta foi utilizada para o estudo e otimização das características finais do produto, tendo-se mostrado um método muito eficaz. Para o estudo da variação da área superficial específica da magnésia com as condições de calcinação (temperatura e tempo de patamar) usou-se o planeamento fatorial de experiências tendo sido obtido um modelo matemático que relaciona a resposta da área superficial específica da magnésia com as condições de calcinação. As propriedades finais dos cimentos (resistência mecânica à compressão e absorção de água) foram estudadas utilizando o planeamento simplex de experiências, que permitiu encontrar modelos que relacionam a propriedade em estudo com os valores das variáveis (razão molar MgO:MAP, área superficial específica da magnésia e quantidade de ácido bórico). Estes modelos podem ser usados para formular composições e produzir cimentos com propriedades finais específicas.

Communication middleware for the future mobile internet

A evolução constante em novas tecnologias que providenciam suporte à forma como os nossos dispositivos se ligam, bem como a forma como utilizamos diferentes capacidades e serviços on-line, criou um conjunto sem precedentes de novos desafios que motivam o desenvolvimento de uma recente área de investigação, denominada de Internet Futura. Nesta nova área de investigação, novos aspectos arquiteturais estão ser desenvolvidos, os quais, através da re-estruturação de componentes nucleares subjacentesa que compõem a Internet, progride-a de uma forma capaz de não são fazer face a estes novos desafios, mas também de a preparar para os desafios de amanhã. Aspectos chave pertencendo a este conjunto de desafios são os ambientes de rede heterogéneos compostos por diferentes tipos de redes de acesso, a cada vez maior mudança do tráfego peer-to-peer (P2P) como o tipo de tráfego mais utilizado na Internet, a orquestração de cenários da Internet das Coisas (IoT) que exploram mecanismos de interação Maquinaa-Maquina (M2M), e a utilização de mechanismos centrados na informação (ICN). Esta tese apresenta uma nova arquitetura capaz de simultaneamente fazer face a estes desafios, evoluindo os procedimentos de conectividade e entidades envolvidas, através da adição de uma camada de middleware, que age como um mecanismo de gestão de controlo avançado. Este mecanismo de gestão de controlo aproxima as entidades de alto nível (tais como serviços, aplicações, entidades de gestão de mobilidade, operações de encaminhamento, etc.) com as componentes das camadas de baixo nível (por exemplo, camadas de ligação, sensores e atuadores), permitindo uma otimização conjunta dos procedimentos de ligação subjacentes. Os resultados obtidos não só sublinham a flexibilidade dos mecanismos que compoem a arquitetura, mas também a sua capacidade de providenciar aumentos de performance quando comparados com outras soluÇÕes de funcionamento especÍfico, enquanto permite um maior leque de cenáios e aplicações.

Social-aware opportunistic routing

The increased capabilities (e.g., processing, storage) of portable devices along with the constant need of users to retrieve and send information have introduced a new form of communication. Users can seamlessly exchange data by means of opportunistic contacts among them and this is what characterizes the opportunistic networks (OppNets). OppNets allow users to communicate even when an end-to-end path may not exist between them. Since 2007, there has been a trend to improve the exchange of data by considering social similarity metrics. Social relationships, shared interests, and popularity are examples of such metrics that have been employed successfully: as users interact based on relationships and interests, this information can be used to decide on the best next forwarders of information. This Thesis work combines the features of today's devices found in the regular urban environment with the current social-awareness trend in the context of opportunistic routing. To achieve this goal, this work was divided into di erent tasks that map to a set of speci c objectives, leading to the following contributions: i) an up-to-date opportunistic routing taxonomy; ii) a universal evaluation framework that aids in devising and testing new routing proposals; iii) three social-aware utility functions that consider the dynamic user behavior and can be easily incorporated to other routing proposals; iv) two opportunistic routing proposals based on the users' daily routines and on the content traversing the network and interest of users in such content; and v) a structure analysis of the social-based network formed based on the approaches devised in this work.

Characterization of water-soluble organic matter from urban aerosols

Water-soluble organic matter (WSOM) from atmospheric particles comprises a complex array of molecular structures that play an important role on the physic-chemical properties of atmospheric particles and, therefore, are linked to several global-relevant atmospheric processes which impact the climate and public health. Due to the large variety of sources and formation processes, adequate knowledge on WSOM composition and its effects on the properties of atmospheric aerosol are still limited. Therefore, this thesis aims at providing new insights on the molecular composition of WSOM from fine atmospheric aerosols typical of an urban area (Aveiro, Portugal). In a first step, adsorption phenomena of semivolatile organic compounds on quartz fibre filters employed in the collection of atmospheric aerosols were assessed. Afterwards, atmospheric aerosol samples were collected during fifteen months, on a weekly basis. A mass balance of aerosol samples was performed in order to set the relative contribution of elemental carbon, WSOM and water-insoluble organic matter to the aerosol mass collected at the urban area of Aveiro, with a special focus on the assessment of the influence of different meteorological conditions. In order to assess the chemical complexity of the WSOM from urban aerosols, their structural characteristics were studied by means of Fourier transform infrared infrared - Attenuated Total Reflectance (FTIR-ATR) and solid-state cross polarization with magic angle spinning 13C nuclear magnetic resonance (CPMAS 13C NMR) spectroscopies, as well as their elemental composition. The structural characterization of aerosol WSOM samples collected in the urban area highlighted a highly complex mixture of functional groups. It was concluded that aliphatic and aromatic structures, hydroxyl groups and carboxyl groups are characteristic to all samples. The semi-quantitative assessment of the CPMAS 13C NMR data showed different distributions of the various functional groups between the aerosol samples collected at different seasons. Moreover, the presence of signals typical of lignin-derived structures in both CPMAS 13C NMR and FTIR-ATR spectra of the WSOM samples from the colder seasons, highlights the major contribution of biomass burning processes in domestic fireplaces, during low temperature conditions, into the bulk chemical properties of WSOM from urban aerosols. A comprehensive two-dimensional liquid chromatography (LC x LC) method, on-line coupled to a diode array, fluorescence, and evaporative light scattering detectors, was employed for resolving the chemical heterogeneity of the aerosol WSOM samples and, simultaneously, to map the hydrophobicity versus the molecular weight distribution of the samples. The LC x LC method employed a mixed-mode hydrophilic interaction column operating under aqueous reversed phase mode in the first dimension, and a size-exclusion column in the second dimension, which was found to be useful for separating the aerosol WSOM samples into various fractions with distinct molecular weight and hydrophobic features. The estimative of the average molecular weight (Mw) distribution of the urban aerosol WSOM samples ranged from 48 to 942 Da and from 45 to 1241 Da in terms of UV absorption and fluorescence detection, respectively. Findings suggest that smaller Mw group fractions seem to be related to a more hydrophobic nature.

Ferroelectric : CNTs structures fabrication for advanced functional nano devices

This work is about the combination of functional ferroelectric oxides with Multiwall Carbon Nanotubes for microelectronic applications, as for example potential 3 Dimensional (3D) Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Miniaturized electronics are ubiquitous now. The drive to downsize electronics has been spurred by needs of more performance into smaller packages at lower costs. But the trend of electronics miniaturization challenges board assembly materials, processes, and reliability. Semiconductor device and integrated circuit technology, coupled with its associated electronic packaging, forms the backbone of high-performance miniaturized electronic systems. However, as size decreases and functionalization increases in the modern electronics further size reduction is getting difficult; below a size limit the signal reliability and device performance deteriorate. Hence miniaturization of siliconbased electronics has limitations. On this background the Road Map for Semiconductor Industry (ITRS) suggests since 2011 alternative technologies, designated as More than Moore; being one of them based on carbon (carbon nanotubes (CNTs) and graphene) [1]. CNTs with their unique performance and three dimensionality at the nano-scale have been regarded as promising elements for miniaturized electronics [2]. CNTs are tubular in geometry and possess a unique set of properties, including ballistic electron transportation and a huge current caring capacity, which make them of great interest for future microelectronics [2]. Indeed CNTs might have a key role in the miniaturization of Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Moving from a traditional two dimensional (2D) design (as is the case of thin films) to a 3D structure (based on a tridimensional arrangement of unidimensional structures) will result in the high reliability and sensing of the signals due to the large contribution from the bottom electrode. One way to achieve this 3D design is by using CNTs. Ferroelectrics (FE) are spontaneously polarized and can have high dielectric constants and interesting pyroelectric, piezoelectric, and electrooptic properties, being a key application of FE electronic memories. However, combining CNTs with FE functional oxides is challenging. It starts with materials compatibility, since crystallization temperature of FE and oxidation temperature of CNTs may overlap. In this case low temperature processing of FE is fundamental. Within this context in this work a systematic study on the fabrication of CNTs - FE structures using low cost low temperature methods was carried out. The FE under study are comprised of lead zirconate titanate (Pb1-xZrxTiO3, PZT), barium titanate (BaTiO3, BT) and bismuth ferrite (BiFeO3, BFO). The various aspects related to the fabrication, such as effect on thermal stability of MWCNTs, FE phase formation in presence of MWCNTs and interfaces between the CNTs/FE are addressed in this work. The ferroelectric response locally measured by Piezoresponse Force Microscopy (PFM) clearly evidenced that even at low processing temperatures FE on CNTs retain its ferroelectric nature. The work started by verifying the thermal decomposition behavior under different conditions of the multiwall CNTs (MWCNTs) used in this work. It was verified that purified MWCNTs are stable up to 420 ºC in air, as no weight loss occurs under non isothermal conditions, but morphology changes were observed for isothermal conditions at 400 ºC by Raman spectroscopy and Transmission Electron Microscopy (TEM). In oxygen-rich atmosphere MWCNTs started to oxidized at 200 ºC. However in argon-rich one and under a high heating rate MWCNTs remain stable up to 1300 ºC with a minimum sublimation. The activation energy for the decomposition of MWCNTs in air was calculated to lie between 80 and 108 kJ/mol. These results are relevant for the fabrication of MWCNTs – FE structures. Indeed we demonstrate that PZT can be deposited by sol gel at low temperatures on MWCNTs. And particularly interesting we prove that MWCNTs decrease the temperature and time for formation of PZT by ~100 ºC commensurate with a decrease in activation energy from 68±15 kJ/mol to 27±2 kJ/mol. As a consequence, monophasic PZT was obtained at 575 ºC for MWCNTs - PZT whereas for pure PZT traces of pyrochlore were still present at 650 ºC, where PZT phase formed due to homogeneous nucleation. The piezoelectric nature of MWCNTs - PZT synthesised at 500 ºC for 1 h was proved by PFM. In the continuation of this work we developed a low cost methodology of coating MWCNTs using a hybrid sol-gel / hydrothermal method. In this case the FE used as a proof of concept was BT. BT is a well-known lead free perovskite used in many microelectronic applications. However, synthesis by solid state reaction is typically performed around 1100 to 1300 ºC what jeopardizes the combination with MWCNTs. We also illustrate the ineffectiveness of conventional hydrothermal synthesis in this process due the formation of carbonates, namely BaCO3. The grown MWCNTs - BT structures are ferroelectric and exhibit an electromechanical response (15 pm/V). These results have broad implications since this strategy can also be extended to other compounds of materials with high crystallization temperatures. In addition the coverage of MWCNTs with FE can be optimized, in this case with non covalent functionalization of the tubes, namely with sodium dodecyl sulfate (SDS). MWCNTs were used as templates to grow, in this case single phase multiferroic BFO nanorods. This work shows that the use of nitric solvent results in severe damages of the MWCNTs layers that results in the early oxidation of the tubes during the annealing treatment. It was also observed that the use of nitric solvent results in the partial filling of MWCNTs with BFO due to the low surface tension (<119 mN/m) of the nitric solution. The opening of the caps and filling of the tubes occurs simultaneously during the refluxing step. Furthermore we verified that MWCNTs have a critical role in the fabrication of monophasic BFO; i.e. the oxidation of CNTs during the annealing process causes an oxygen deficient atmosphere that restrains the formation of Bi2O3 and monophasic BFO can be obtained. The morphology of the obtained BFO nano structures indicates that MWCNTs act as template to grow 1D structure of BFO. Magnetic measurements on these BFO nanostructures revealed a week ferromagnetic hysteresis loop with a coercive field of 956 Oe at 5 K. We also exploited the possible use of vertically-aligned multiwall carbon nanotubes (VA-MWCNTs) as bottom electrodes for microelectronics, for example for memory applications. As a proof of concept BiFeO3 (BFO) films were in-situ deposited on the surface of VA-MWCNTs by RF (Radio Frequency) magnetron sputtering. For in situ deposition temperature of 400 ºC and deposition time up to 2 h, BFO films cover the VA-MWCNTs and no damage occurs either in the film or MWCNTs. In spite of the macroscopic lossy polarization behaviour, the ferroelectric nature, domain structure and switching of these conformal BFO films was verified by PFM. A week ferromagnetic ordering loop was proved for BFO films on VA-MWCNTs having a coercive field of 700 Oe. Our systematic work is a significant step forward in the development of 3D memory cells; it clearly demonstrates that CNTs can be combined with FE oxides and can be used, for example, as the next 3D generation of FERAMs, not excluding however other different applications in microelectronics.

A Psychological Exploration of Long-Term LSD Users

All research involving the psychoactive compound lysergic acid diethylamide (LSD) was terminated globally following its prohibition more than 50 years ago, though illicit use remained fairly stable. A considerable resurgence of research interest in LSD has received considerable attention in various publications and professional fora. One of the main applications considered is LSD-assisted psychotherapy to address a number of difficulties like end-of-life anxiety, addiction/alcoholism, post-traumatic stress, and depression. However, due to the highly contradictory nature of early research findings and division in the literature, one is left uncertain as to whether psychology as a profession is currently equipped to critically evaluate these advances, let alone embrace them. The purpose of the present study was to contribute to current psychological knowledge on long-term LSD use. A group of long-term LSD users who claimed beneficial use were the focus here. A mixed methods design was employed. 110 users completed an online survey assessing for demographics, patterns of use, and specific personality traits through three psychometric measures, Big Five Inventory (BFI), General Self Efficacy scale (GSE) and Satisfaction With Life Scale (SWLS). Eight individual interviews were also conducted and analysed by Thematic Analysis (TA). Gaining different perspectives on reality and increasing self- awareness appeared to be essential elements of the belief system that these non-problematic long-term LSD users adopted in order to make sense of their LSD use. Qualitative findings also suggested the existence of a common set of life values, rules and the adoption of a hierarchical system between LSD users. Novices appeared to be tutored and guided by elders whose presence and input was valued and who were listened to and respected. A role for ‘wiser/elder’ users as those imparting valuable knowledge to novices was therefore also suggested. The underlying aim may possibly be an attempt to minimise risks and maximise potential benefits of LSD use. A prospective role for LSD as a deterrent of substance misuse, a ‘gateway drug to no drugs’ was also hinted and remains in need of iv further investigation. Claims regarding beneficial LSD use and ‘change’ through LSD use were confirmed by the participant sample. No noteworthy differences between psychometric scores of the LSD-using group and those of the general population (as suggested by normative data comparisons) were found, possibly due to methodological limitations, especially considering the highly subjective nature of the LSD experience and its effects. The determining role of extra-pharmacological variables or ‘set and setting’ in the outcome of LSD use suggested in earlier literature was re-validated. Knowledge on their specific components was enriched, and a potentially significant value for adopting a flexible, adaptable and solution-focused mind-set in order to better manage the effects of LSD was highlighted. Due to the highly selected nature of the participant sample, present findings should serve as suggestions for further research in order to clarify the aforementioned issues and to make explicit the mechanisms by which they operate. The complex nature of LSD, its use and its effects have been re-confirmed here. It is imperative that the current knowledge base on the substance is enriched before LSD is introduced in a clinical psychology professional context.

Disparity energy model with keypoint disparity validation

A biological disparity energy model can estimate local depth information by using a population of V1 complex cells. Instead of applying an analytical model which explicitly involves cell parameters like spatial frequency, orientation, binocular phase and position difference, we developed a model which only involves the cells’ responses, such that disparity can be extracted from a population code, using only a set of previously trained cells with random-dot stereograms of uniform disparity. Despite good results in smooth regions, the model needs complementary processing, notably at depth transitions. We therefore introduce a new model to extract disparity at keypoints such as edge junctions, line endings and points with large curvature. Responses of end-stopped cells serve to detect keypoints, and those of simple cells are used to detect orientations of their underlying line and edge structures. Annotated keypoints are then used in the leftright matching process, with a hierarchical, multi-scale tree structure and a saliency map to segregate disparity. By combining both models we can (re)define depth transitions and regions where the disparity energy model is less accurate.

História da filosofia da educação em Portugal : dos programas de ensino ao campo disciplinar : (1976-2006)

Tese de doutoramento, Educação (História da Educação), Universidade de Lisboa, Instituto de Educação, 2014

Métodos probabilísticos e estatísticos na gestão de fogos florestais

Tese de doutoramento, Estatística e Investigação Operacional (Probabilidades e Estatística), Universidade de Lisboa, Faculdade de Ciências, 2014

A Meteorological and Snow observational data set from Snoqualmie Pass (921 m), Washington Cascades, U.S.

We introduce a quality controlled observational atmospheric, snow, and soil data set from Snoqualmie Pass, Washington, U.S.A., to enable testing of hydrometeorological and snow process representations within a rain-snow transitional climate where existing observations are sparse and limited. Continuous meteorological forcing (including air temperature, total precipitation, wind speed, specific humidity, air pressure, short- and longwave irradiance) are provided at hourly intervals for a 24-year historical period (water years 1989-2012) and at half-hourly intervals for a more-recent period (water years 2013-2015), separated based on the availability of observations. Additional observations include 40-years of snow board new snow accumulation, multiple measurements of total snow depth, and manual snow pits, while more recent years include sub-daily surface temperature, snowpack drainage, soil moisture and temperature profiles, and eddy co-variance derived turbulent heat flux. This data set is ideal for testing hypotheses about energy balance, soil and snow processes in the rain-snow transition zone. Plots of live data can be found here: http://depts.washington.edu/mtnhydr/cgi/plot.cgi

A comparative study on the modified Max-Log-MAP turbodecoding by extrinsic information scaling

A simple but effective technique to improve the performance of the Max-Log-MAP algorithm is to scale the extrinsic information exchanged between two MAP decoders. A comprehensive analysis of the selection of the scaling factors according to channel conditions and decoding iterations is presented in this paper. Choosing a constant scaling factor for all SNRs and iterations is compared with the best scaling factor selection for changing channel conditions and decoding iterations. It is observed that a constant scaling factor for all channel conditions and decoding iterations is the best solution and provides a 0.2-0.4 dB gain over the standard Max- Log-MAP algorithm. Therefore, a constant scaling factor should be chosen for the best compromise.

The modified Max-Log-MAP turbo decoding algorithm by extrinsic information scaling for wireless applications

The iterative nature of turbo-decoding algorithms increases their complexity compare to conventional FEC decoding algorithms. Two iterative decoding algorithms, Soft-Output-Viterbi Algorithm (SOVA) and Maximum A posteriori Probability (MAP) Algorithm require complex decoding operations over several iteration cycles. So, for real-time implementation of turbo codes, reducing the decoder complexity while preserving bit-error-rate (BER) performance is an important design consideration. In this chapter, a modification to the Max-Log-MAP algorithm is presented. This modification is to scale the extrinsic information exchange between the constituent decoders. The remainder of this chapter is organized as follows: An overview of the turbo encoding and decoding processes, the MAP algorithm and its simplified versions the Log-MAP and Max-Log-MAP algorithms are presented in section 1. The extrinsic information scaling is introduced, simulation results are presented, and the performance of different methods to choose the best scaling factor is discussed in Section 2. Section 3 discusses trends and applications of turbo coding from the perspective of wireless applications.