A Compact and Accurate Gaussian Variate Generator

Abstract

Abstract-A compact, fast, and accurate realization of a digital Gaussian variate generator (GVG) based on the Box-Muller algorithm is presented. The proposed GVG has a faster Gaussian sample generation rate and higher tail accuracy with a lower hardware cost than published designs. The GVG design can be readily configured to achieve arbitrary tail accuracy (i.e., with a proposed 16-bit datapath up to 15 times the standard deviation ) with only small variations in hardware utilization, and without degrading the output sample rate. Polynomial curve fitting is utilized along with a hybrid (i.e., combination of logarithmic and uniform) segmentation and a scaling scheme to maintain accuracy. A typical instantiation of the proposed GVG occupies only 534 configurable slices, two on-chip block memories, and three dedicated multipliers of the Xilinx Virtex-II XC2V4000-6 field-programmable gate array (FPGA) and operates at 248 MHz, generating 496 million Gaussian variates (GVs) per second within a range of 6 66 . To accurately achieve a range of 9 4 , the GVG uses 852 configurable slices, three block memories, and three on-chip dedicated multipliers of the same FPGA while still operating at 248 MHz, generating 496 million GVs per second. The core area and performance of a GVG implemented in a 90-nm CMOS technology are also given. The statistical characteristics of the GVG are evaluated and confirmed using multiple standard statistical goodness-of-fit tests.Index Terms-Box-Muller (BM) algorithm, field-programmable gate array (FPGA), Gaussian noise generator (GNG), low bit-error rate simulation, random number generation.

Generating high tail accuracy Gaussian Random Numbers in hardware using central limit theorem

“…The method is highly efficient both in terms of hardware and throughput compared to previously reported method. In [2], a fast and compact Gaussian noise generator based on Box-Muller method is described with lower hardware cost and maximum attainable sigma values larger than previously published designs. The method uses polynomial curve fitting with hybrid segmentation and scaling scheme to more accurately approximate the mathematical functions involved in Box-Muller method.…”

“…At least 10 11 samples are required to observe tail accuracy till 6σ [2]. At such high values of σ, it probability is so low (< 10 −9 ) that it is not observable at linear scale.…”

“…Any correlation between neighboring numbers can be seen as as regular lattice structure in the scatter plot [2]. This is an unwanted property in any random number sequence.…”

“…One such example is Bit Error Rate (BER) simulation of wireless radio standards, some of which have maximum allowable BER of less than 10 −10 . Simulating occurrence of such an event, requires a tail accuracy of at least 6σ [2].…”

Implementaciones de Funciones Elementales en Dispositivos FPGA

“…Este generador produce dos muestras por ciclo trabajando a frecuencia de 375 MHz y utilizando una FPGA Virtex-4 de Xilinx. Otra implementación basada en B-M ha sido propuesta por [87] y consiste en el uso técnicas de segmentación no-uniforme hibridas (logarítmica y uniforme) sobre las funciones elementales y obtienen una amplitud en las muestras de ruido generado de hasta ±9.4σ, con unos requerimientos de área relativamente bajos.…”