Hardware Architecture of a Gaussian Noise Generator Based on the Inversion Method

Abstract

In this brief, we present a hardware-based Gaussian noise generator (GNG) with low hardware cost, high generation rate, and high Gaussian tail accuracy. The proposed generator is based on a piecewise polynomial approximation of the inverse cumulative distribution function (ICDF). We propose to avoid the area-demanding barrel-shifter of the ICDF approximation by means of creating a new uniform random sequence from the uniform random number generator output. The GNG architecture has been implemented in field-programmable gate array devices, and the implementation results are compared with other published designs, achieving a higher deviation with fewer hardware resources. Our GNG generates 242 Msps of random noise and achieves a tail of 13.1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $\sigma$</tex></formula> with 442 slices, two multipliers, and two Block-RAM of a Virtex-II device. The generator output successfully passed commonly used statistical tests.