Evolving approximations for the Gaussian Q-function by Genetic Programming with semantic based crossover

The Gaussian Q-function is of great importance in the field of communications, where the noise is often characterized by the Gaussian distribution. However, no simple exact closed form of the Q-function is known. Consequently, a number of approximations have been proposed over the past several decades. In this paper, we use Genetic Programming with semantic based crossover to approximate the Q-function in two forms: the free and the exponential forms. Using this form, we found approximations in both forms that are more accurate than all previous approximations designed by human experts.