Generators of pseudorandom sequences are widely used objects, not in the least place because of their application in stream ciphers. One of the ways to improve resistance to different types of attack is to use compression on the generated sequence in order to remove redundant information, that might lead to an attack against the generator. In this work we try to explore from a wider perspective the theoretical foundations for compressing pseudorandom sequences created thus far. Using this general view we will examine some known attacks against the PRN generators and look for a way to resist such attacks.

The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the "fairest possible" finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase (ΦNL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithm

La demande constante de capacité et la saturation prévue de la fibre monomode ont conduit récemment à des avances technologiques qui ont complètement changé le paysage des télécommunications à fibre optique. Le progrès le plus important était la mise en œuvre d'une détection cohérente à l'aide d'électronique rapide. Cela a permis pas seulement l'utilisation de formats de modulation qui promettent une utilisation plus efficace de la bande passante, mais aussi l’utilisation des algorithmes adaptés pour combattre la dégradation du signal optique due à la propagation. Cette thèse a commencé un peu après le début de cette « ère du cohérent » et son principal objectif était de revoir les effets physiques de la propagation dans des systèmes de transmission terrestres, utilisant le format de modulation QPSK (Quadrature Phase Shift Keying). Le manuscrit est divisé en deux parties. La première partie est consacrée à une étude sur les séquences des données qui doivent être utilisés dans les simulations numériques, lorsqu’un format de modulation avancée est impliqué. La propagation, et en particulier l'interaction entre la dispersion chromatique et les non-linéarités, introduisent une interférence inter-symbole (ISI). Vu que cet ISI dépend de l’enchainement des données transmises, il est évident que le choix de la séquence a une influence sur la qualité estimée du canal. Etant donné que des séquences aléatoires infinies ne sont pas pratiquement réalisables, nous utilisons souvent des séquences « pseudo-aléatoires » (PR), i.e. des séquences déterministes de longueur finie, avec des statistiques équilibrés, qui semblent être aléatoires. Dans la première partie, nous décrivons la méthode de génération de séquences PR avec M. niveaux (M> 2) et nous détaillons leurs propriétés. En outre, nous proposons des outils numériques pour caractériser les séquences non pseudo-aléatoires qu’on utilise souvent dans des simulations, ou parfois aussi dans des expériences au laboratoire. Enfin, nous présentons les résultats de simulations qui permettent de quantifier la nécessité d'utiliser des séquences PR en fonction des paramètres du système. Après avoir établi les séquences finies "les plus adaptées", dans la seconde partie du manuscrit, nous nous concentrons sur l'étude de la propagation, dans le contexte d'un système de transmission QPSK et en supposant une gestion de dispersion et un type de fibre variables. Plus précisément, nous étudions numériquement les statistiques de signaux dégradés dus à l'interaction de la dispersion chromatique avec les effets non linéaires, en négligeant tout effet de polarisation ou inter-canaux, aussi que le bruit des amplificateurs. Dans ce contexte, nous étions intéressés à déterminer si certaines lois empiriques développées pour les systèmes OOK, sont valable dans le cas d'une modulation QPSK, tels que le critère de la phase non-linéaire cumulée (ΦNL) ou des lois qui permettent une optimisation de la gestion de dispersion. Ensuite, nous révélons l'importance de la rotation de la constellation du signal initial, comme un paramètre qui peut fournir des informations pour la post-optimisation de notre système. Nous discutons également autour du fait que la forme de la constellation dépend de la gestion de dispersion et concernant les constellations nous concluons qu'il y en a généralement 3 types, avec: (1) une variance de phase supérieure à la variance d'amplitude (2) une variance d'amplitude supérieure à la variance de phase et (3) avec le signal ayant une constellation qui ressemble à la constellation d’un signal sous l'influence d'un bruit blanc gaussien additif. Enfin, nous fournissons une explication phénoménologique des formes des constellations révélant le fait que des sous-séquences différentes conduisent à un « type » différent de dégradation et nous utilisons ces informations pour définir un paramètre qui quantifie le bénéfice potentiel d'un algorithme de correction du type MAP(Maximum A Posteriori Probability) / The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the “fairest possible” finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase (ΦNL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithm

Η παρούσα διπλωματική εργασία έγινε στα πλαίσια του Προγράμματος Μεταπτυχιακών Σπουδών Ηλεκτρονικής και Υπολογιστών, στο Τμήμα Φυσικής του Πανεπιστημίου Πατρών. Αντικείμενό της αποτελεί η μελέτη του φυσικού επιπέδου συστημάτων κινητής τηλεφωνίας τρίτης γενιάς και η εξομοίωση χαρακτηριστικού καναλιού του φυσικού επιπέδου σύμφωνα με την παγκόσμια προτυποποίηση 3GPP. Στο πρώτο κεφάλαιο γίνεται ιστορική ανασκόπηση των συστημάτων προηγούμενων γενεών. Αναφέρονται βασικά προβλήματα που πρέπει να αντιμετωπίσει ένα τηλεπικοινωνιακό σύστημα καθώς και η βασική δομή των κυψελοειδών συστημάτων. Γίνεται εισαγωγή στα συστήματα τρίτης γενιάς ως προς τις απαιτήσεις, τις υπηρεσίες που προσφέρουν, την προτυποποίηση και την αρχιτεκτονική τους. Στο δεύτερο κεφάλαιο μελετώνται οι τρόποι πολλαπλής πρόσβασης με ιδιαίτερη έμφαση στην προσπέλαση με διαίρεση κωδικών. Αναλύονται τα συστήματα διάχυσης φάσματος. Γίνεται εκτενής αναφορά και υλοποίηση προγραμμάτων για τις ψευδοτυχαίες ακολουθίες και τις ακολουθίες Gold. Στο τρίτο κεφάλαιο μελετάται η δομή δικτύων επικοινωνίας κατά το μοντέλο OSI. Αναφέρονται τα επίπεδα των τηλεπικοινωνιακών συστημάτων με διεξοδική μελέτη του φυσικού επιπέδου και στις διεπαφές που χρησιμοποιεί για επικοινωνία καθώς και στις υπηρεσίες που προσφέρει. Αναλύεται η δομή όλων των φυσικών καναλιών και εξομοιώνεται η διαδικασία ενθυλάκωσης του καναλιού PRACH. Στο τέταρτο κεφάλαιο αναλύονται οι κώδικες διάχυσης των φυσικών καναλιών ανερχόμενης ζεύξης καθώς και η διαδικασία διάχυσης τους. Δημιουργούνται προγράμματα που παράγουν αυτούς τους κώδικες και γίνεται εξομοίωση της διάχυσης και της αποδιάχυσης του PRACH καναλιού. Στο πέμπτο κεφάλαιο αναφέρεται η διαδικασία κωδικοποίησης πηγής και μελετάται η PSK διαμόρφωση και αποδιαμόρφωση που χρησιμοποιούν τα συστήματα τρίτης γενιάς. Υλοποιούνται προγράμματα που εξομοιώνουν τη συνολική διαδικασία σε ενθόρυβο κανάλι AWGN μελετώντας την επίδραση του θορύβου σε μεταδιδόμενο σήμα. Όλες οι εξομοιώσεις υλοποιήθηκαν με το πρόγραμμα Matlab 7.1. / This master thesis is a part of the post-graduate course of the Physics department of the University of Patras, on Electronics and Computers. Its main objective is the study of the physical layer of 3rd generation telecommunication systems and the simulation of a particular channel, in accordance to 3GPP specifications. In the first chapter we review telecommunication systems of previous generations. We also refer to major problems that need to be dealt with and also the basic structure of cellular networks. 3rd generation telecommunication systems, their requirements, offered services, standardisation and architecture are all introduced. In the second chapter we study multiple access methods, emphasising CDMA methods. Moreover, spread spectrum systems are analysed. Finally we refer to pseudorandom and Gold sequences. Programs are created which generate these sequences. In the third chapter we look into the structure of communication networks according to the OSI model. The layers of telecommunication systems are mentioned, laying emphasis on the physical layer, the interfaces used for communication as well as the offered services. We report all physical channels and we simulate the encapsulation of the PRACH channel. In the fourth chapter we analyse the spreading and scrambling codes referring to the uplink channels. Next we point out the code allocation process. Programs are created which generate these spreading and scrambling codes and we finally simulate the spreading and de-spreading process of the PRACH channel. In the fifth chapter we outline the source coding process using PCM, and we study PSK modulation and demodulation which are used by 3rd generation telecommunication systems. We create programs that simulate the whole procedure in a noisy channel, and we study the effect of AWGN. The programs were created and the simulations were run using Matlab version 7.1.