Littérature scientifique sur le sujet « Sequenze pseudorandom »

Classical cryptography theory holds that the true random sequence is better than any pseudorandom sequence on the security of stream cipher. So people prefer the pseudorandom sequence with long-period to the pseudorandom sequence with short-period. In this paper, it is proved through power spectrum analysis that the pseudorandom sequence with long-period cant effectively conceal message characteristics in frequency-domain. To combine the pseudorandom sequences with long cycle and short cycle may be the better encryption key.

In the applications it may occur that our initial pseudorandom binary sequence is not long enough, thus we have to take the concatenation of it with another pseudorandom binary sequences. Here we will consider concatenation of Legendre symbol sequences so that the resulting longer sequence has strong pseudorandom properties.

In a series of papers Mauduit and Sárközy studied finite pseudorandom sequences. In particular, in Part I they showed that the Legendre symbol forms an 'ideally good' pseudorandom sequence. In other parts of the series numerous other binary sequences have been tested for pseudorandomness but neither of them proved to be as 'good' as the Legendre symbol. Here another 'very good' sequence is constructed by using the notion of index.

<abstract><p>In 1997, Mauduit and Sárközy first introduced the measures of pseudorandomness for binary sequences. Since then, many pseudorandom binary sequences have been constructed and studied. In particular, Gyarmati presented a large family of pseudorandom binary sequences using the discrete logarithms. Ten years later, to satisfy the requirement from many applications in cryptography (e.g., in encrypting "bit-maps'' and watermarking), the definition of binary sequences is extended from one dimension to several dimensions by Hubert, Mauduit and Sárközy. They introduced the measure of pseudorandomness for this kind of several-dimension binary sequence which is called binary lattices. In this paper, large families of pseudorandom binary sequences and binary lattices are constructed by both discrete logarithms and multiplicative inverse modulo $ p $. The upper estimates of their pseudorandom measures are based on estimates of either character sums or mixed exponential sums.</p></abstract>

In Hadamard transform ion mobility spectrometry (HT IMS), the signal-to-noise ratio is always lower for non-modified pseudorandom sequences than for modified sequences. Since the use of non-modified modulating pseudorandom sequences is strategically preferable from a duty cycle standpoint, we investigated the change in the interference signal when transitioning from non-modified modulating sequences to sequences modified by the addition of 1,3,5 and 7 zeros. The interfering signal in HT IMS with modified pseudorandom sequences was shown to be mainly random noise for all the cases except for modifying by incorporation of 1 zero. For standard samples of tetraalkylammonium halides, modulation by non-modified pseudorandom sequences is beneficial in the case of small numbers of averaged spectra (below ∼40 averaged spectra compared to any modified pseudorandom sequences except for 1 zero modified and below ∼200 averaged spectra compared to signal averaging ion mobility spectrometry) and worsens the signal-to-noise ratio in the case of large numbers of averaged spectra. Contrarily, modulation by modified pseudorandom sequences is beneficial for any number of averaged spectra, except for very small ones (below 15 averaged spectra compared to modulation by non-modified sequences). Pseudorandom sequence modified with 1 zero incorporation is beneficial in the case of below ∼400 averaged spectra compared to any modified and non-modified pseudorandom sequences. The signal-to-noise ratio in conventional signal averaging mode ion mobility spectrometry is affected by random noise, whereas the HT IMS with non-modified pseudorandom sequences was demonstrated to be primarily affected by a systematic noise-like artefact signal. Because noise-like artefact signals were found to be reproducible, predicting models for interference signals could be generated to improve signal-to-noise ratio. This is significant because non-modified modulating sequences are limited by their poor signal-to-noise ratio. This improvement would increase the viability of non-modified modulating sequences which are preferred because of their higher sample utilization efficiency.

A pseudorandom sequence is a repeatable sequence with random statistical properties that is widely used in communication encryption, authentication and channel coding. The pseudorandom sequence generator based on the linear feedback shift register has the problem of a fixed sequence, which is easily tracked. Existing methods use the secret linear feedback shift register (LFSR) and built-in multiple LFSRs and is difficult to prevent cracking based on the hardware analysis. Since the plaintext depends on a specific language to be generated, using pseudo-random sequence encryption, it faces the problem that the encryptor cannot hide the characteristics of the plaintext data. Fractal functions have the following properties: chaotic, unpredictable and random. We propose a novel pseudorandom sequence generator based on the nonlinear chaotic systems, which is constructed by the fractal function. Furthermore, we design a data processing matrix to hide the data characteristics of the sequence and enhance the randomness. In the experiment, the pseudo-random sequences generator passed 16 rigorous test items from the National Institute of Standards and Technology (NIST), which means that the nonlinear pseudorandom sequence generator for the fractal function is effective and efficient.

In this paper, we consider the issue of upgrading the circuit of a digital generator of a pseudo-random pulse sequence, which can be used to create cryptographic encryption algorithms. The need to modernize the digital generator circuit is associated with an increase in the number of pseudorandom pulse train sequences generated at its output and with pseudorandom intervals between them. To achieve this, a small number of additional elements are included in the circuit of a digital pseudorandom sequence of pulses based on a five-digit shift register with linear feedback. Based on the modernized circuit of a digital generator of a pseudorandom sequence of pulses and an active secondorder Slenlen-Key RC low-pass filter, a digital acoustic noise generator is constructed, which, unlike the prototype, has a truly random output signal over a period of ~ 4 * (2N - 1), subject to circuit simplicity.

The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $\mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $\mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.

Probability on Finite and Discrete Set and Uniform DistributionA pseudorandom number generator plays an important role in practice in computer science. For example: computer simulations, cryptology, and so on. A pseudorandom number generator is an algorithm to generate a sequence of numbers that is indistinguishable from the true random number sequence. In this article, we shall formalize the "Uniform Distribution" that is the idealized set of true random number sequences. The basic idea of our formalization is due to [15].

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random" yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. One important type of pseudorandom sequences is the sequences generated by feedback with carry shift registers (FCSRs). In this dissertation, we study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2. These are called half-ℓ-sequences. More precisely, our work includes: The number of occurrences of one symbol within one period of a half-ℓ-sequence; The number of pairs of symbols with a fixed distance between them within one period of a half-ℓ-sequence; The number of triples of consecutive symbols within one period of a half-ℓ-sequence. In particular we give a bound on the number of occurrences of one symbol within one period of a binary half-ℓ-sequence and also the autocorrelation value in binary case. The results show that the distributions of half-ℓ-sequences are fairly flat. However, these sequences in the binary case also have some undesirable features as high autocorrelation values. We give bounds on the number of occurrences of two symbols with a fixed distance between them in an ℓ-sequence, whose period reaches the maximum and obtain conditions on the connection integer that guarantee the distribution is highly uniform. In another study of a cryptographically important statistical property, we study a generalization of correlation immunity (CI). CI is a measure of resistance to Siegenthaler's divide and conquer attack on nonlinear combiners. In this dissertation, we present results on correlation immune functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, to measure the proximity of two functions. We give two definitions of q-correlation immune functions and the relationship between them. Certain properties and constructions for q-correlation immune functions are discussed. We examine the connection between correlation immune functions and q-correlation immune functions.

A new application of chaos to electrical engineering is developed. By creating chaotic binary sequences, and using these as pulse compression codes for radar, many advantages are realized over codes that are presently used. These chaotic codes are generated by quantizing the iterates of one-dimensional chaotic difference equations to two levels. Being chaotic, these binary sequences are unpredictable in the long term, and are nonperiodic or can have periods of billions of bits. The autocorrelations of the sequences are derived, then the sequences are applied to radar, where the unpredictable and nonperiodic nature of these sequences is exploited. It is shown that chaotic codes offer advantages in maximum range performance, range resolution, low probability of intercept, and probability of false alarm compared to codes presently used.

Un dels majors problemes experimentats pels sistemes de detecció de gasos basats en sensors d'òxids metàl·lics és la seva manca de reproduibilitat, estabilitat i selectivitat. A fi i a efecte d'intentar resoldre aquest problemes, diferents estratègies han estat desenvolupades en paral·lel. Algunes es relacionen a la millora dels materials i d'altres impliquen el condicionament o el pre-tractament de les mostres. Les més emprades han consistit en aprofitar que els sensors presenten sensibilitats solapades per construir matrius de sensors i emprar tècniques de processament del senyal o bé utilitzar característiques de la resposta dinàmica dels sensors. En els darrers anys, modular la temperatura de treball del sensors d'òxids metàl·lics s'ha convertit en un dels mètodes més utilitzats per incrementar-ne la selectivitat. Això s'esdevé així donat que la resposta del sensor varia amb la seva temperatura de treball. Per això, en determinats casos, mesurant la resposta d'un sensor a n temperatures de treball diferents pot ser equivalent a tenir una matriu de n sensors diferents. Això permet obtenir informació multivariant de cada sensor individualment i ajuda a mantenir baixa la dimensionalitat del sistema de mesura per resoldre una determinada aplicació. Malgrat que molts i bons resultats han estat publicats dins aquest àmbit, la tria de les freqüències emprades en la modulació de la temperatura de treball dels sensor ha consistit fins ara en un procés empíric que no garanteix la obtenció dels millors resultats per una determinada aplicació. En aquest context, el principal objectiu d'aquesta tesi doctoral ha consistit en desenvolupar un mètode sistemàtic que permeti determinar quines són les freqüències de modulació òptimes que caldria emprar per resoldre un determinat problema d'anàlisi de gasos. Aquest mètode, extret del camp d'identificació de sistemes, ha esta desenvolupat i implementat per primer cop dins l'àmbit dels sensors de gasos. Aquest consisteix en estudiar la resposta dels sensors en presència de gasos mentre la temperatura de treball dels sensors és modulada per un senyal pseudo-aleatori de longitud màxima. Aquest senyals comparteixen algunes propietats amb el soroll blanc, i per tant poden ajudar a estimar la resposta lineal d'un sistema amb no-linealitats (per exemple, la resposta impulsional d'un sistema sensor-gas). El procés d'optimització es duu a terme mitjançant la selecció entre els components espectrals de les estimacions de la resposta impulsional, d'aquells que millor ajuden bé a discriminar o a quantificar els gasos objectiu dins una aplicació d'anàlisi de gasos donada. Tenint en compte que els components espectrals estan directament relacionats amb les xvii Improving the performance of micro-machined metal oxide gas sensors: Optimization of the temperature modulation mode via pseudo-random sequences. freqüències de modulació, la tria d'uns pocs components espectrals resulta en la determinació de les freqüències òptimes de modulació. En els primer experiments, senyals binaris pseudo-aleatoris van ser emprats per modular la temperatura de treball de sensors de gasos basats en òxids metàl·lics micro-mecanitzats dins d'un rang comprès entre 0 i 112,5 Hz. La freqüència superior és lleugerament superior a la frequència de tall de les membranes dels sensors. El resultat principal derivat d'aques estudi va ser que les freqüències de modulació interessants es trobaven en un rang comprès entre 0 i 1 Hz. Això és comprensible donat que la cinètica de les reaccions i dels processos d'adsorció que es produeixen en la superfície dels sensors són lentes i si aquestes s'han de veure modificades per la modulació térmica, llavors caldran senyals de modulació de baixa freqüència. Això explica perquè s'han vingut emprant senyals moduladores de temperatura en el rang dels mHz, malgrat que les membranes d'un dispositiu micromecanitzat presenten respostes tèrmiques molts més ràpides (típicament de l'ordre de 100 Hz). En els experiments que continuaren els primers, un mètode evolucionat per determinar les freqüències de modulació tèrmica òptimes va ser implementat. Aquest es basa en l'ús de seqüències pseudo-aleatòries multi-nivell de longitud màxima. Els senyals de tipus multi-nivell van ser considerats en substitució dels senyals binaris ja que els primers permeten obtenir una millor estimació que els segons de la dinàmica lineal d'un sistema amb no linealitats. I és ben conegut que els sensors de gasos basats en òxids metàl·lics presenten no linealitat en la seva resposta. Aquests estudis sistemàtics van ser completament validats mitjançant la síntesi de senyals multi-sinusoïdals amb les freqüències prèviament identificades emprant sequències pseudo-aleatòries. Quan la temperatura de treball dels sensors va ser modulada amb un senyal, el contingut freqüencial del qual era l'òptim, els gasos i les mescles de gasos considerades van poder ser discriminades perfectament i es va mostrar la possibilitat d'obtenir models de calibració acurats per predir la concentració dels gasos. En alguns casos, aquest procés de validació es va portar a terme emprant sensors que no havien estat utilitzats durant el procés d'optimització (per exemple, una agrupació de sensors diferent però del mateix lot de fabricació). En resum, el nou mètode desenvolupat en aquesta tesi per seleccionar les freqüències de modulació òptimes s'ha mostrat consistent i efectiu. El mètode és d'aplicació general i podria ser emprat en qualsevol problema d'anàlisi de gasos o bé estès a altres tipus de sensors (per exemple sensors polimèrics). Les contribucions científiques d'aquesta tesi s'han recollit en quatre articles en revistes internacionals i 13 llibres d'actes de conferències.
Uno de los mayores problemas experimentados en los sistemas de detección de gases basados en dispositivos de óxidos metálicos es su falta de reproducibilidad, estabilidad y selectividad. Con el fin de intentar resolver estos problemas, diferentes estrategias han sido desarrolladas en paralelo. Algunas de ellas se relacionan con la mejora de los materiales y otras implican acondicionamiento o pre-tratamiento de las muestras. Otras estrategias ampliamente empleadas consisten en aprovechar que los sensores presentan sensibilidades solapadas para construir matrices de sensores y emplear técnicas de procesamiento de señal o bien utilizar características de la respuesta dinámica de los sensores.En los últimos años, modular la temperatura de trabajo de los sensores de óxidos metálicos se ha convertido en uno de los métodos más utilizados para incrementar su selectividad. Esto se debe a, dado que la respuesta del sensor varía con su propia temperatura de trabajo, entonces, en determinados casos, midiendo la respuesta de un sensor a n temperaturas de trabajo diferentes, es equivalente a tener una matriz de n sensores diferentes. Esto permite obtener información multivariante de cada sensor individualmente y ayuda a mantener baja la dimensionalidad del sistema de medida para resolver una determinada aplicación. A pesar de los buenos resultados que han sido publicados dentro de este ámbito, la selección de las frecuencias empleadas en la modulación de la temperatura de trabajo de los sensores ha consistido, hasta el momento, en un proceso empírico lo que no garantiza la obtención de los mejores resultados para una determinada aplicación.En este contexto, el principal objetivo de esta tesis doctoral ha consistido en desarrollar un método sistemático que permita determinar cuales son las frecuencias de modulación óptimas que podrían emplearse para resolver un determinado problema de análisis de gases. Este método, extraído del campo de identificación de sistemas, ha sido desarrollado e implementado por primera vez dentro del ámbito de los sensores de gases. Éste consiste en estudiar la respuesta de los sensores en presencia de gases mientras la temperatura de trabajo de los sensores es modulada mediante una señal pseudo-aleatoria de longitud máxima. Estas señales comparten algunas propiedades con el ruido blanco, y por tanto pueden ayudar a estimar la respuesta lineal de un sistema con no-linealidades (por ejemplo, la respuesta impulsional de un sistema sensor-gas).El proceso de optimización es llevado a cabo mediante la selección entre las componentes espectrales de las estimaciones de la respuesta impulsional, de aquellas que más ayudan ya sea a discriminar o a cuantificar los gases objetivo dentro de una aplicación de análisis de gases dada. Teniendo en cuenta que las componentes espectrales están directamente relacionadas con las frecuencias de modulación, la selección de unas pocas componentes espectrales resulta en la determinación de las frecuencias optimas de modulación.En los primeres experimentos, señales binarias pseudo-aleatorias fueron utilizadas para modular la temperatura de trabajo de los sensores de gases basados en óxidos metálicos micro-mecanizados en un rango comprendido entre 0 a 112.5 Hz. La frecuencia superior es ligeramente mayor a la frecuencia de corte de las membranas de los sensores. El resultado principal derivado de estos estudios fue que las frecuencias de modulación interesantes se encuentran en un rango comprendido entre 0 y 1 Hz. Esto es comprensible dado que la cinética de las reacciones y de los procesos de adsorción que se producen en la superficie del sensor son lentos y si estos se han de alterar mediante la modulación térmica, se habrá de elaborar señales de modulación a bajas frecuencias. Esto explica por que se han venido empleado señales moduladoras de temperatura en el rango de los mHz, a pesar que las membranas de un dispositivo micro-mecanizado presentan respuestas mucho más rápidas (típicamente en el orden de los 100 Hz).En los experimentos posteriores a los primeros, un método evolucionado para determinar las frecuencias de modulación óptimas de los sensores micro-mecanizados fue implementado, el cual se basa en el uso de secuencias pseudo-aleatorias multi-nivel de longitud máxima (MLPRS). Las señales de tipo multi-nivel fueron consideradas en lugar de las binarias ya que las primeras permiten obtener una mejor estimación que las segundas de la dinámica lineal de un sistema con no linealidades. Y es bien conocido que los sensores de gases basados en óxidos metálicos presentan no-linealidades en su respuesta.Estos estudios sistemáticos fueron completamente validados mediante la síntesis de señales multi-senoidales con las frecuencias previamente identificadas utilizando secuencias pseudo-aleatorias. Cuando la temperatura de trabajo de los sensores fue modulada por una señal, el contenido frecuencial de la cual es el óptimo, los gases y mezclas de gases considerados pudieron ser discriminados perfectamente y se verificó la posibilidad de obtener modelos de calibración precisos para predecir la concentración de los gases. En algunos casos, estos procesos de validación se llevaron a cabo con sensores que no habían sido utilizados durante el proceso de optimización (por ejemplo, una agrupación de sensores diferentes pero del mismo lote de fabricación).En resumen, El nuevo método desarrollado in esta tesis para seleccionar las frecuencias de modulación optimas se a mostrado consistente y efectivo. El método es de aplicación general y podría ser utilizado en cualquier problema de análisis de gases o bien extendido a otro tipo de sensores (por ejemplo sensores poliméricos).Las contribuciones científicas de esta tesis se han recogido en 4 artículos en revistas internacionales y trece actas de conferencias.
One of the major problems in gas sensing systems that use metal oxide devices is the lack of reproducibility, stability and selectivity. In order to tackle these troubles experienced with metal oxide gas sensors, different strategies have been developed in parallel. Some of these are related to the improvement of materials, or the use of sample conditioning and pre-treating methods. Other widely used techniques include taking benefit of the unavoidable partially overlapping sensitivities by using sensor arrays and pattern recognition techniques or the use of dynamic features from the gas sensor response.In the last years, modulating the working temperature of metal oxide gas sensors has been one of the most used methods to enhance sensor selectivity. This occurs because, since, the sensor response is different at different working temperatures, and therefore, measuring the sensor response at n different temperatures is, in some cases, similar to the use of an array comprising n different sensors. This allows for measuring multivariate information from every single sensor and helps in keeping low the dimensionality of the measurement system needed to solve a specific application. Although the good results reported, until now, the selection of the frequencies used to modulate the working temperature remained an empirical process and that is not an accurate method to ensure that the best results are reached for a given application.In view of this context, the principal objective of this doctoral thesis was to develop a systematic method to determine which are the optimal temperature modulation frequencies to solve a given gas analysis problem. This method, which is borrowed from the field of system identification, has been developed and introduced for the first time in the area of gas sensors. It consists of studying the sensor response to gases when the operating temperature is modulated via maximum-length pseudo-random sequences. Such signals share some properties with white noise and, therefore, can be of help to estimate the linear response of a system with non-linearity (e.g., the impulse response of a sensor-gas system).The optimization process is conducted by selecting among the spectral components of the impulse response estimates, the few that better help either discriminating or quantifying the target gases of a given gas analysis application. Since spectral components are directly related to modulating frequencies, the selection of spectral components results in the determination of the optimal temperature modulating frequencies.In the first experiments, pseudo-random binary signals (PRBS) were employed to modulate the working temperature of micro-machined metal oxide gas sensors in a frequency range from 0 up to 112.5 Hz. The upper frequency is slightly higher than the cutoff frequency of the sensor membranes. The outcome of this initial study was that the important modulating frequencies were in the range between 0 and 1 Hz. This is understandable, since the kinetics of reaction and adsorption processes taking place at the sensor surface (i.e., physisorption/chemisorption/ionosorption) are slow and if these are to be altered by the thermal modulation, low frequency modulating signals need to be devised. This explains why low-frequency temperature-modulating signals (i.e. in the mHz range) have been used with micro-hotplate gas sensors, even though the thermal response of their membranes is much faster (typically, near 100 Hz).In the experiments that followed the first ones, an evolved method to determine the optimal temperature modulating frequencies for micro-hotplate gas sensors was introduced, which was based on the use of maximum length multilevel pseudo-random sequences (MLPRS). Multilevel signals were considered instead of the binary ones because the former can provide a better estimate than the latter of the linear dynamics of a process with non-linearity. And it is well known that temperature-modulated metal oxide gas sensors present non-linearity in their response.These systematic studies were fully validated by synthesizing multi-sinusoidal signals at the optimal frequencies previously identified using pseudo-random sequences. When the sensors had their operating temperatures modulated by a signal with a frequency content that corresponded to the optimal, the gases and gas mixtures considered could be perfectly discriminated and the building of accurate calibration models to predict gas concentration was found to be possible. In some cases, the validation process was conducted on sensors that had not been used for optimization purposes (e.g. a different sensor array from the same fabrication batch).Summarizing, the new method developed in this thesis for selecting the optimal modulating frequencies is shown to be consistent and effective. The method applies generally and could be used in any gas analysis problem or extended to other type of sensors (e.g. conducting polymer sensors).The scientific contributions of this thesis are collected in four journal papers and thirteen conference proceedings.

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

This thesis deals with a method of spectrum-spreading of the data signals transmitted in the radio channel. There exist three different ways of spreading application, they uses pseudorandom sequences and also orthogonal sequences. In these systems we can find various kinds of modulations, one of them (Quadrature Phase Shift Keying) is shown at the end of the thesis. Spectrum spreading orthogonal multiplex OFDM is based on this method. The thesis wants to present the principle of the spectrum spreading method and the description of systems, transmitters and receivers that are using this method.

A Linear Feedback Shift Register (LFSR) is a standard parallel shift register with output taps on some of its stages. If the output taps are combined and fed back to the initial stage, on each clock cycle the shift register will change to a new state. By appropriate selection of the tap connections an n-stage LFSR can be made to cycle through all possible 2n-1 states before repeating the sequence. The output from any stage is called a maximal length pseudorandom sequence. Such a sequence has many of the statistical properties of a sequence of ideal random numbers, but obviously results from a very well defined process. Once a LFSR is known, its associated pseudorandom sequence can be described in full. The inverse problem of identifying the LFSR which generated a given pseudorandom sequence is far more difficult.

We have recently shown that pseudorandom sequences of solitons can be generated and transmitted at 5 GHz by direct modulation of laser diodes (LD) when biasing slightly below threshold (C.R. Mirasso and L. Pesquera, IEEE PTL 7. p. 437, 1995). Using this bias current pattern effects are avoided and the fluctuations originated in the LD are reduced. Here we perform numerical simulations to study the transmission of pseudorandom sequences of solitons at 15 GHz and 20 GHz obtained by time division multiplexing (TDM) of 1.55 µm LD modulated at 5GHz and biased slightly below threshold. A narrowband optical filter is used to limit the large bandwidth of the signal produced by the chirping. To reduce soliton interaction the pulses are compressed by using 0.6 km of a normal dispersion fiber (D = −20 ps/nm km). In this way the pulses launched in the fiber have a 10 ps witdh. A large timing jitter is obtained after transmission over transoceanic distances due to the pulse-to-pulse frequency jitter originated in the LD. This jitter is reduced by using guiding filters every 25 km with a bandwidth of 250 GHz. The results in the figure for 15 GHz (left) show that filters are effective to reduce timing jitter. However, in the 20 GHz (right) transmission sequence the interaction leads to errors (see the set ”11” near the end of the sequence). Then more effective soliton control systems (i.e. sliding-frequency filtering) should be used to reduce interaction effects.

The ability to perform all-optical digital information processing is one of the key requirements for future photonic networks. Recently, the use of semiconductor optical amplifier based all-optical interferometric switches [1] has allowed practical demonstrations of advanced functionality to be demonstrated. These have included a bit-serial regenerative optical memory which is capable of long term storage [2] and has the ability to restore the optical logic level [3]. Here we describe a further advance in all-optical digital functionality with a demonstration of an all-optical pseudorandom bit sequence (PRBS) generator. The all-optical PRBS comprises two coupled regenerative memories [2] which act as a time-of-flight shift register for optical pulses. A digital PRBS can be generated by applying the logical XOR function between the output of the register and a tap point and feeding the logical result back into the start of the register [4]. We use two TOAD all-optical switching gates [5] to create the all-optical PRBS architecture. One TOAD is used for the XOR function and the other acts as a wavelength converter and all-optical regenerator. The PRBS output depends on the number of pulses m in the shift register and the tap position n (n<m). At present, the experimental latency is several hundred bits at a IGHz clock rate and so we use multiples of lower length sequences in order to measure the performance of the design. We have experimentally demonstrated a maximal length 231-1 PRBS ({m,n}={713,552} ≡ 23 x {m,n}={31,24}) and also sub-maximal sequences. The figure below shows a digitally sampled part of the maximal 231-1 PRBS. The apparent amplitude modulation of the pulses is an artefact of the relatively low sampling rate (400Msamples/s). We were only able to record short temporal sequences since the repeat period of the PRBS is ~50s.