  In this paper, we investigate the construction of polar codes by Gaussian
approximation (GA) and develop an approach based on piecewise Gaussian
approximation (PGA). In particular, with the piecewise approach we obtain a
function that replaces the original GA function with a more accurate
approximation, which results in significant gain in performance. The proposed
PGA construction of polar codes is presented in its integral form as well as an
alternative approximation that does not rely on the integral form. Simulations
results show that the proposed PGA construction outperforms the standard GA for
several examples of polar codes and rates.
