Design Exploration of an FPGA-Based Multivariate Gaussian Random Number Generator

Monte Carlo simulation is one of the most widely used techniques for computationally intensive simulations in a variety of applications including mathematical analysis and modeling and statistical physics. A multivariate Gaussian random number generator (MVGRNG) is one of the main building blocks of such a system. Field Programmable Gate Arrays (FPGAs) are gaining increased popularity as an alternative means to the traditional general purpose processors targeting the acceleration of the computationally expensive random number generator block due to their fine grain parallelism and reconfigurability properties and lower power consumption. As well as the ability to achieve hardware designs with high throughput it is also desirable to produce designs with the flexibility to control the resource usage in order to meet given resource constraints. This work proposes a novel approach for mapping a MVGRNG onto an FPGA by optimizing the computational path in terms of hardware resource usage subject to an acceptable error in the approximation of the distribution of interest. An analysis on the impact of the error due to truncation/rounding operation along the computational path is performed and an analytical expression of the error inserted into the system is presented. Extra dimensionality is added to the feature of the proposed algorithm by introducing a novel methodology to map many multivariate Gaussian random number generators onto a single FPGA. The effective resource sharing techniques introduced in this thesis allows further reduction in hardware resource usage. The use of MVGNRG can be found in a wide range of application, especially in financial applications which involve many correlated assets. In this work it is demonstrated that the choice of the objective function employed for the hardware optimization of the MVRNG core has a considerable impact on the final performance of the application of interest. Two of the most important financial applications, Value-at-Risk estimation and option pricing are considered in this work

A Hardware Efficient Random Number Generator for Nonuniform Distributions with Arbitrary Precision

Nonuniform random numbers are key for many technical applications, and designing efficient hardware implementations of non-uniform random number generators is a very active research field. However, most state-of-the-art architectures are either tailored to specific distributions or use up a lot of hardware resources. At ReConFig 2010, we have presented a new design that saves up to 48% of area compared to state-of-the-art inversion-based implementation, usable for arbitrary distributions and precision. In this paper, we introduce a more flexible version together with a refined segmentation scheme that allows to further reduce the approximation error significantly. We provide a free software tool allowing users to implement their own distributions easily, and we have tested our random number generator thoroughly by statistic analysis and two application tests

Optimización de problemas de varios objetivos desde un enfoque de eficiencia energética aplicado a redes celulares heterogéneas 5G usando un marco de conmutación de celdas pequeñas

This Ph.D. dissertation addresses the Many-Objective Optimization Problem (MaOP) study to reduce the inter-cell interference and the power consumption for realistic Centralized, Collaborative, Cloud, and Clean Radio Access Networks (C-RANs). It uses the Cell Switch-Off (CSO) scheme to switch-off/on Remote Radio Units (RRUs) and the Coordinated Scheduling (CS) technique to allocate resource blocks smartly. The EF1-NSGA-III (It is a variation of the NSGA-III algorithm that uses the front 1 to find extreme points at the normalization procedure extended in this thesis) algorithm is employed to solve a proposed Many-Objective Optimization Problem (MaOP). It is composed of four objective functions, four constraints, and two decision variables. However, the above problem is redefined to have three objective functions to see the performance comparison between the NSGA-II and EF1-NSGA-III algorithms. The OpenAirInterface (OAI) platform is used to evaluate and validate the performance of an indoor coverage system because most of the user-end equipment of next-generation cellular networks will be in an indoor environment. It constitutes the fastest growing 5G open-source platform that implements 3GPP technology on general-purpose computers, fast Ethernet transport ports, and Commercial-Off-The-Shelf (COTS) software-defined radio hardware. This document is composed of five contributions. The first one is a survey about testbed, emulators, and simulators for 4G/5G cellular networks. The second one is the extension of the KanGAL's NSGA-II code to implement the EF1-NSGA-III, adaptive EF1-NSGA-III (A-EF1-NSGA-III), and efficient adaptive EF1-NSGA-III (A$^2$-EF1-NSGA-III). They support up to 10 objective functions, manage real, integer, and binary decision variables, and many constraints. The above algorithms outperform other works in terms of the Inverted Generational Distance (IGD) metric. The third contribution is the implementation of real-time emulation methodologies for C-RANs using a frequency domain representation in OAI. It improves the average computation time 10-fold compared to the time domain without using Radio Frequency hardware and avoids their uncertainties. The fourth one is the implementation of the Coordination Scheduling (CS) technique as a proof-of-concept to validate the advantages of frequency domain methodologies and to allocate resource blocks dynamically among RRUs. Finally, a many-objective optimization problem is defined and solved with evolutionary algorithms where diversity is managed based on crowded-distance and reference points to reduce the power consumption for C-RANs. The solutions obtained are considered to control the scheduling task at the Radio Cloud Center (RCC) and to switch RRUs.Este disertación aborda el estudio del problema de optimización de varios objetivos (MaOP) para reducir la interferencia entre células y el consumo de energía para redes de acceso de radio en tiempo real, colaborativas, en la nube y limpias (C-RAN). Utiliza el esquema de conmutacion de celdas (CSO) para apagar / encender unidades de radio remotas (RRU) y la técnica de programación coordinada (CS) para asignar bloques de recursos de manera inteligente. El algoritmo EF1-NSGA-III (es una variación del algoritmo NSGA-III que usa el primer frente de pareto para encontrar puntos extremos en el procedimiento de normalización extendido en esta tesis) se utiliza para resolver un problema de optimización de varios objetivos (MaOP) propuesto. Se compone de cuatro funciones objetivos, cuatro restricciones y dos variables de decisión. Sin embargo, el problema anterior se redefine para tener tres funciones objetivas para ver la comparación de rendimiento entre los algoritmos NSGA-II y EF1-NSGA-III. La plataforma OpenAirInterface (OAI) se utiliza para evaluar y validar el rendimiento de un sistema de cobertura en interiores porque la mayoría del equipos móviles de las redes celulares de próxima generación estarán en un entorno interior. Ella constituye la plataforma de código abierto 5G de más rápido crecimiento que implementa la tecnología 3GPP en computadoras de uso general, puertos de transporte Ethernet rápidos y hardware de radio definido por software comercial (COTS). Este documento se compone de cinco contribuciones. La primera es una estudio sobre banco de pruebas, emuladores y simuladores para redes celulares 4G / 5G. El segundo es la extensión del código NSGA-II de KanGAL para implementar EF1-NSGA-III, EF1-NSGA-III adaptativo (A-EF1-NSGA-III) y EF1-NSGA-III adaptativo eficiente (A $^ 2$ -EF1-NSGA-III). Admiten hasta 10 funciones objetivas, gestionan variables de decisión reales, enteras y binarias, y muchas restricciones. Los algoritmos anteriores superan a otros trabajos en términos de la métrica de distancia generacional invertida (IGD). La tercera contribución es la implementación de metodologías de emulación en tiempo real para C-RAN utilizando una representación de dominio de frecuencia en OAI. Mejora el tiempo de cálculo promedio 10 veces en comparación con el dominio del tiempo sin usar hardware de radiofrecuencia y evita sus incertidumbres. El cuarto es la implementación de la técnica de Programación de Coordinación (CS) como prueba de concepto para validar las ventajas de las metodologías de dominio de frecuencia y asignar bloques de recursos dinámicamente entre las RRU. Finalmente, un problema de optimización de muchos objetivos se define y resuelve con algoritmos evolutivos en los que la diversidad se gestiona en función de la distancia de crouding y los puntos de referencia para reducir el consumo de energía de las C-RAN. Las soluciones obtenidas controlan la tarea de programación en Radio Cloud Center (RCC) y conmutan las RRU.Proyecto personal: Redes celulares de próxima generaciónDoctorad

Customisable arithmetic hardware designs

Imperial Users onl

Gaussian Sampling Precision in Lattice Cryptography

Security parameters and attack countermeasures for Lattice-based cryptosystems have not yet matured to the level that we now expect from RSA and Elliptic Curve implementations. Many modern Ring-LWE and other lattice-based public key algorithms require high precision random sampling from the Discrete Gaussian distribution. The sampling procedure often represents the biggest implementation bottleneck due to its memory and computational requirements. We examine the stated requirements of precision for Gaussian samplers, where statistical distance to the theoretical distribution is typically expected to be below $2^{-90}$ or $2^{-128}$ for 90 or 128 ``bit\u27\u27 security level. We argue that such precision is excessive and give precise theoretical arguments why half of the precision of the security parameter is almost always sufficient. This leads to faster and more compact implementations; almost halving implementation size in both hardware and software. We further propose new experimental parameters for practical Gaussian samplers for use in Lattice Cryptography

From phenomenological modelling of anomalous diffusion through continuous-time random walks and fractional calculus to correlation analysis of complex systems

This document contains more than one topic, but they are all connected in ei- ther physical analogy, analytic/numerical resemblance or because one is a building block of another. The topics are anomalous diffusion, modelling of stylised facts based on an empirical random walker diffusion model and null-hypothesis tests in time series data-analysis reusing the same diffusion model. Inbetween these topics are interrupted by an introduction of new methods for fast production of random numbers and matrices of certain types. This interruption constitutes the entire chapter on random numbers that is purely algorithmic and was inspired by the need of fast random numbers of special types. The sequence of chapters is chrono- logically meaningful in the sense that fast random numbers are needed in the first topic dealing with continuous-time random walks (CTRWs) and their connection to fractional diffusion. The contents of the last four chapters were indeed produced in this sequence, but with some temporal overlap. While the fast Monte Carlo solution of the time and space fractional diffusion equation is a nice application that sped-up hugely with our new method we were also interested in CTRWs as a model for certain stylised facts. Without knowing economists [80] reinvented what physicists had subconsciously used for decades already. It is the so called stylised fact for which another word can be empirical truth. A simple example: The diffusion equation gives a probability at a certain time to find a certain diffusive particle in some position or indicates concentration of a dye. It is debatable if probability is physical reality. Most importantly, it does not describe the physical system completely. Instead, the equation describes only a certain expectation value of interest, where it does not matter if it is of grains, prices or people which diffuse away. Reality is coded and “averaged” in the diffusion constant. Interpreting a CTRW as an abstract microscopic particle motion model it can solve the time and space fractional diffusion equation. This type of diffusion equation mimics some types of anomalous diffusion, a name usually given to effects that cannot be explained by classic stochastic models. In particular not by the classic diffusion equation. It was recognised only recently, ca. in the mid 1990s, that the random walk model used here is the abstract particle based counterpart for the macroscopic time- and space-fractional diffusion equation, just like the “classic” random walk with regular jumps ±∆x solves the classic diffusion equation. Both equations can be solved in a Monte Carlo fashion with many realisations of walks. Interpreting the CTRW as a time series model it can serve as a possible null- hypothesis scenario in applications with measurements that behave similarly. It may be necessary to simulate many null-hypothesis realisations of the system to give a (probabilistic) answer to what the “outcome” is under the assumption that the particles, stocks, etc. are not correlated. Another topic is (random) correlation matrices. These are partly built on the previously introduced continuous-time random walks and are important in null- hypothesis testing, data analysis and filtering. The main ob jects encountered in dealing with these matrices are eigenvalues and eigenvectors. The latter are car- ried over to the following topic of mode analysis and application in clustering. The presented properties of correlation matrices of correlated measurements seem to be wasted in contemporary methods of clustering with (dis-)similarity measures from time series. Most applications of spectral clustering ignores information and is not able to distinguish between certain cases. The suggested procedure is sup- posed to identify and separate out clusters by using additional information coded in the eigenvectors. In addition, random matrix theory can also serve to analyse microarray data for the extraction of functional genetic groups and it also suggests an error model. Finally, the last topic on synchronisation analysis of electroen- cephalogram (EEG) data resurrects the eigenvalues and eigenvectors as well as the mode analysis, but this time of matrices made of synchronisation coefficients of neurological activity