Novel exponential type approximations of the q-function

In this paper, we propose several solutions for approximating the Q-function using one exponential function or the sum of two exponential functions. As the novel Q-function approximations have simple analytical forms and are therefore very suitable for further derivation of expressions in closed forms, a large number of applications are feasible. The application of the novel exponential type approximations of the Q-function is especially important for overcoming issues arising in designing scalar companding quantizers for the Gaussian source, which are caused by the non-existence of a closed form expression for the Q-function. Since our approximations of the Q-function have simple analytical forms and are more accurate than the approximations of the Q-function previously used for the observed problem in the scalar companding quantization of the Gaussian source, their application, especially for this problem is of great importance.