On the generation of a smooth Gaussian random variable to 5 standard deviations

Abstract

The generation of a Gaussian random variable for use in a low-error-rate communication simulation is discussed. The authors describe the requirements for a uniform probability density function (PDF) pseudorandom number generator used as well as different methods of obtaining a Gaussian random number for various applications. A lookup table method is presented that was designed for digital signal processing cases where it is difficult to generate a logarithmic function for analytic synthesis of the Gaussian random number. The techniques and approach used are applicable to any probability distribution (other than a Gaussian PDF) for which the inverse cumulative density function either cannot be evaluated analytically or is too computationally intensive.<>