Optimized Coefficients for the Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function

This is a supplementary dataset for the publication:

I. M. Tanash and T. Riihonen, "Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function with Optimized Coefficients," in IEEE Communications Letters, in press.

The dataset contains the sets of the optimized coefficients for the novel GKL minimax approximations and bounds of the Gaussian Q-function, and the optimized coefficients for the GKL approximations in terms of the total error. The corresponding optimized coefficients are found up to 10 terms (N=10) for the two variations of the absolute error and for the relative error in terms of the minimax and the total errors.

The Matlab function (func_extract_coef.m) extracts the required set of optimal coefficients from the provided dataset according to the selected optimization_criterion, error_type, number of terms, the bound or approximation type, and the variation. See help func_extract_coef for more information.

A Matlab script (Example.m) is also provided as an example to illustrate the use of the provided Matlab function in extracting the required coefficients from the dataset, to calculate and plot the corresponding minimax absolute error function which is shown by figure Example.jpg. Another example is given in the same script to extract the coefficients of the total relative error.