39 research outputs found
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-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 -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 or 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