In state-of-the-art fiber-optics communication systems the fixed forward error correction (FEC) and constellation size are employed. While it is important to closely approach the Shannon limit by using turbo product codes (TPC) and low-density parity-check (LDPC) codes with soft-decision decoding (SDD) algorithm; rate-adaptive techniques, which enable increased information rates over short links and reliable transmission over long links, are likely to become more important with ever-increasing network traffic demands. In this invited paper, we describe a rate adaptive non-binary LDPC coding technique, and demonstrate its flexibility and good performance exhibiting no error floor at BER down to 10(-15) in entire code rate range, by FPGA-based emulation, making it a viable solution in the next-generation high-speed intelligent aggregation networks.

Forward error correction (FEC) is as one of the key technologies enabling the next-generation high-speed fiber optical communications. In this paper, we propose a rate-adaptive scheme using a class of generalized low-density parity-check (GLDPC) codes with a Hamming code as local code. We show that with the proposed unified GLDPC decoder architecture, a variable net coding gains (NCGs) can be achieved with no error floor at BER down to 10(-15), making it a viable solution in the next-generation high-speed fiber optical communications.

Cost automata are traditional finite state automata enriched with a finite set of counters that can be manipulated on each transition. Based on the evolution of counter values, a cost automaton defines a function from the set of structures under consideration to the natural numbers extended with infinity, modulo a boundedness relation that ignores exact values but preserves boundedness properties. Historically, variants of cost automata have been used to solve problems in language theory such as the star height problem. They also have a rich theory in their own right as part of the theory of regular cost functions, which was introduced by Colcombet as an extension to the theory of regular languages. It subsumes the classical theory since a language can be associated with the function that maps every structure in the language to 0 and everything else to infinity; it is a strict extension since cost functions can count some behaviour within the input. Regular cost functions have been previously studied over finite words and trees. This thesis extends the theory to infinite trees, where classical parity automata are enriched with a finite set of counters. Weak cost automata, which have priorities {0,1} or {1,2} and an additional restriction on the structure of the transition function, are shown to be equivalent to a weak cost monadic logic. A new notion of quasi-weak cost automata is also studied and shown to arise naturally in this cost setting. Moreover, a decision procedure is given to determine whether or not functions definable using weak or quasi-weak cost automata are equivalent up to the boundedness relation, which also proves the decidability of the weak cost monadic logic over infinite trees. The semantics of these cost automata over infinite trees are defined in terms of cost-parity games which are two-player infinite games where one player seeks to minimize the counter values and satisfy the parity condition, and the other player seeks to maximize the counter values or sabotage the parity condition. The main contributions and key technical results involve proving that certain cost-parity games admit positional or finite-memory strategies. These results also help settle the decidability of some special cases of long-standing open problems in the classical theory. In particular, it is shown that it is decidable whether a regular language of infinite trees is recognizable using a nondeterministic co-Büchi automaton. Likewise, given a Büchi or co-Büchi automaton as input, it is decidable whether or not there is a weak automaton recognizing the same language.

Background: Excess adiposity, diabetes mellitus, and ischaemic heart disease are common important causes of morbidity and premature mortality in postmenopausal women in the UK. A large amount of data exists on known risk factors for these conditions, and for risk factors men and women share there is little evidence to suggest sex-based differences. It has been suggested that factors unique to women (such as parity and breastfeeding) may also influence risk. The nature of the relationship between childbearing and these conditions remains to be clarified. In this thesis I explore the association between women’s childbearing histories and their adiposity, and risk of diabetes or ischaemic heart disease after the menopause, to provide evidence on the character, repeatability and public health relevance of the associations. Aim: To explore the hypothesis that childbearing (specifically parity and breastfeeding) is associated with women’s body weight and risk of excess adiposity, and also with women’s risk of diabetes mellitus, and ischaemic heart disease after the menopause. Methods: Data are analysed from a large population-based cohort of middle-aged UK women recruited in 1996 to 2001 (the Million Women Study) with complete childbearing information, and who had baseline anthropometry, and were followed for incident diabetes or ischaemic heart disease through repeat survey questionnaires, hospital admission records, and central registry databases. Results: In a large ethnically homogeneous population of postmenopausal UK women increasing parity was associated with an increase in BMI, however this increase was offset in women who breastfed. The associations between parity, breastfeeding and BMI were of a similar order of magnitude to established risk factors known to be associated with BMI, for example smoking, and physical activity. The associations between childbearing and women’s risk of diabetes mellitus after the menopause appear to be largely due to the effects of childbearing on maternal BMI. There is only limited evidence to suggest a direct effect of childbearing on women’s risk of diabetes after the menopause. There is statistically significant evidence of an association between childbearing and women’s risk of ischaemic heart disease after the menopause. Parity was associated with a modest increase in risk whereas breastfeeding was associated with a small decrease in risk, however the effects were small in comparison to known important risk factors. Conclusions In a large population of UK women childbearing was found to have a persistent influence on women’s mean BMI after the menopause, and through this postmenopausal risk of diabetes mellitus. Childbearing was also found to be mod-estly associated with women’s risk of ischaemic heart disease after the menopause.

This dissertation examines Cassell's theory of purchasing power parity within the context of post-World War II foreign exchange markets and government policies.

L’objectif de la thèse est l’étude des codes correcteurs d’erreurs au niveau applicatif (Application Layer – Forward Error Correction, ou AL-FEC) pour les communications par satellite. Dans ce contexte, pendant les deux première années de thèse, nous avons proposé de nouvelles méthodes d’analyse, de construction et d’optimisation des codes à effacements définis par des matrices de parité à faible densité (code LDPC, pour « Low Density Parity Check » en anglais). La troisième année de la thèse a été consacrée à : (1) La suite des études portant sur de nouvelles méthodes de construction des codes LDPC non-binaires. D’une part, nous avons développé un nouvel algorithme (Scheduled-PEG) qui permet d’optimiser la construction des codes LDPC non-binaires pas rapport aux métriques de performance spécifiques à la couche application, notamment dans le cadre des systèmes de diffusion de contenu (broadcasting). D’autre part, nous avons proposé une nouvelle méthode de construction de codes à faible rendement, qui utilise l’image binaire étendue d’un code LDPC non-binaire. Ces études ont fait l’objet de deux publications dans deux conférences internationales : (a) “Scheduled-PEG construction of LDPC codes for Upper-Layer FEC”, International Workshop on Coding and Cryptography, April 2011, Paris, France. (b) “Extended Non-Binary Low-Density Parity-Check Codes over Erase Channels”, IEEE International Symposium on Wireless Communication Systems, November 2011, Aachen, Germany. (2) Une étude portant sur l’analyse asymptotique de codes cluster-LDPC non-binaires. Cette nouvelle classe de codes – introduite récemment (ISIT’2011) – se distingue par ses excellentes propriétés en termes de distance minimale. Notre étude a permis de déterminer de manière analytique la capacité de correction des codes cluster-LDPC non-binaires, aussi bien pour le décodage itératif par propagation de croyances (BP, pour « Belief Propagation ») que pour le décodage par maximum de vraisemblance (ML, pour « Maximum Likelihood »). Ces résultats seront intégrés à une publication scientifique sur les codes cluster-LDPC, en cours de rédaction, qui sera soumise à « IEEE Transactions on Information Theory », avant la fin de l’année 2011. (3) Une étude portant sur une méthode de construction des codes LDPC qui permet de réduire de manière significative le plancher d’erreur (« error floor ») du code, sans dégrader ses performances dans la région de « waterfall ». Ainsi, nous avons proposé la structuration de la matrice de parité du code, de manière à intégrer une partie irrégulière, optimisée pour la partie « waterfall », et une partie régulière, qui permet de réduire le plancher d’erreur du code. Cette étude fera l’objet d’une publication dans une conférence internationale (à déterminer), à soumettre début 2012. / The advent of content distribution, IPTV, video-on-demand and other similar services accelerate the demand for reliable data transmission over highly heterogeneous networks and toward terminals potentially heterogeneous too. In this context, Forward Error Correction (FEC) codes that operate at the transport or the Application Layer (AL-FEC) are used in conjunction with the FEC codes implemented at the physical layer, in order to improve the overall performance of the communication system. AL-FEC codes are aimed at recovering erased data packets and they are essential in many multicast/broadcast environments, no matter the way the information is transported, for instance using a wired or wireless link, and a terrestrial, satellite-based or hybrid infrastructure.This thesis addresses the design of Low Density Parity Check (LDPC) codes for AL-FEC applications. One the one hand, we provide an asymptotical analysis of non-binary LDPC codes over erasure channels, as well as waterfall and error-floor optimization techniques for finite-length codes. On the other hand, new concepts and coding techniques are developed in order to fully exploit the potential of non-binary LDPC codes.The first contribution of this thesis consists of the analysis and optimization of two new ensembles of LDPC codes. First, we have derived the density evolution equations for a very general ensemble of non-binary LDPC codes with rank-deficient coefficients. This allows improving the code performance, as well as designing ensembles of LDPC codes that can be punctured in an effective manner. The second approach allows the asymptotical optimization of a particular ensemble of LDPC codes, while ensuring low error-floors at finite lengths.The second contribution is the construction of finite length LDPC codes with good waterfall and error floor performance. Two approaches were investigated, according to the metric used to evaluate the code. The “Scheduled” Progressive Edge Growth (SPEG) algorithm is proposed, in order to optimize the waterfall performance of the code. Another method is proposed which consists in optimizing a specific structure of the parity check matrix. This approach gives low error-floors.The third contribution investigates a new technique of rate adaptability for non-binary LDPC codes. We propose a new method to generate “on-the-fly” incremental redundancy, which allows designing codes with flexible coding rates, in order to cope with severe channel conditions or to enable Fountain-like distribution applications.The fourth contribution focuses on a new class of LDPC codes, called non-binary cluster-LDPC codes. We derive exact equations of the density evolution for the iterative decoding and an upper bound for the maximum-likelihood decoding.Finally, we propose a practical solution to the problem of reliable communication via satellite to high-speed trains. Here, the challenge is that obstacles present along the track regularly interrupt the communication. Our solution offers optimal performance with a minimum amount of redundancy.

La démocratie paritaire est un objectif partagé par la Communauté internationale. La construction du droit des femmes à la participation à la vie politique et publique s'inscrit dans la logique du principe d'égalité entre les hommes et les femmes et répond à une double approche, neutre et sexuée, des sujets de droits. Ce droit à la participation des femmes aux différents processus de décision est également perçu comme l'une des conditions d'une démocratie véritable, impliquant une participation équilibrée des hommes et des femmes et la prise en compte de leurs intérêts et besoins. Dans la pratique, les femmes sont encore très largement sous-représentées à tous les niveaux du pouvoir. Afin de tendre vers une démocratie paritaire, l'adoption de mesures est indispensable. Certaines répondent à une approche de l'égalité des chances, tandis que d'autres vont plus loin en réalisant une égalité de résultat. Le contrôle des progrès effectués opéré par une panoplie de mécanismes de contrôle et de suivi, respecte également la distinction entre système neutre ou sexué. Contrairement au second type, qui place les femmes au coeur de son processus, le premier se révèle moins précis et moins détaillé dans l'analyse et la formulation de recommandations / Parity democracy is a goal shared by the International Community. The construction of the women's right to participation in political and public life is part of the logic of the principle of equality between men and women and respond both to a neutral and a gender approach of subjects of rights. This right of women to participate in the decision-making process is also one of the conditions of a genuine democracy, which implies a balanced participation of men and women and a taking into account their interests and needs. In practice, women are still under-represented at all levels of the decision-making. In order to move towards parity democracy, measures are therefore essential. Some belong to an equality of opportunity approach, while others go further in realizing equality of result. The follow-up of progress which occurs through a variety of mechanisms, also respects the distinction between neutral or gendered system. Unlike the second type, which places women at the heart of the process, the first appears to be less accurate and detailed in the analysis and recommendations making.

The Standard Model predicts existence of one Higgs boson with combined parity CP = +1. In MSSM there exist Higgs boson with CP = −1 in addition. The work develops one method of Higgs boson CP determination on the basis of angular correlations of pions and ρ-mesons born in cascade decay H/A → τ− τ+ → ρ− /π− ντ ρ+ /π+ ¯ντ . The calculations are done in the leading order of perturbation theory. Further, the possibility of signal (Higgs boson decay) and background (Z boson decay) differentiation is studied. The processes in question are simulated using Monte Carlo generators Pythia and Tauola. Simulation outputs are compared with calculated theoretical results. 1

Low-density parity-check (LDPC) codes are linear error correcting codes which are capable of performing near channel capacity. Furthermore, they admit efficient decoding algorithms that provide near optimum performance. Their main disadvantage is that most LDPC codes have relatively complex encoders. In this thesis, we begin by giving a detailed discussion of the sum-product decoding algorithm, we then study the performance of LDPC codes on the binary erasure channel under sum-product decoding to obtain criteria for the design of codes that allow reliable transmission at rates arbitrarily close to channel capacity. Using these criteria we show how such codes are designed. We then present experimental results and compare them with theoretical predictions. Finally, we provide an overview of several approaches to solving the complex encoder problem.

Research Report: BUSA7167 (MM Finance and Investment Management). Submitted in Partial Fulfillment of the Requirements for the (Master of Management in Finance and Investments). Submitted on 06th June 2016 / The findings of the research have implications on the efficiency of the South African exchange rate market, and by extension, the efficiency of similar emerging foreign exchange markets. The study used Ordinary Least Square Approach and Johansen cointegration. Despite their theoretical appeal, and in line with a dozen of related past literature, the findings of the research generally favour the rejection UIP, PPP and IFE. The findings have implications on some regulatory measures that can be undertaken by the financial authority to improve the efficiency of the foreign exchange market. While there have been extensive studies on uncovered interest parity (UIP), purchasing power parity(PPP), and the international Fisher effect(IFE), research has scarcely tested these hypotheses in the context of emerging markets. This study attempts to bridge the existing gap by testing the three related parity condition for South Africa. / MT2016