Recently, Erdal Arikan proposed a method “channel polarization” and then introduced polar codes based on this method. Polar codes are a breakthrough in coding theory because they are the first kind of codes to be proved to achieve capacity for a wide range of channels with linear encoding and decoding complexity O(N logN), where N is the blocklength of the code. In this work we investigate the construction of polar codes under additive white Gaussian noise (AWGN) channel and then improve their performance. The first problem we consider is the construction of polar codes under AWGN channel. In specific, polar codes are constructed based on Gaussian approximation. The formula of calculating Bhattacharyya parameter is also derived. The performance and implementation complexity of our scheme and the existing schemes are compared. Results show that the polar codes we construct are efficient, practical and achieve a good tradeoff between decoding performance and implementation complexity. To further improve the error performance, turbo polar codes are proposed. Turbo polar codes are constructed by concatenating two polar codes parallelly. An iterative decoding method is adopted to decode turbo polar codes. The encoder and decoder of turbo polar codes are designed. Besides, we analyze the performance of turbo polar codes by considering the effect of iteration number, interleaver size and different decoding algorithms. Moreover, the interleaver structure is devised to improve the performance. Finally, we compare turbo polar codes with polar codes and show that turbo polar codes achieve a better performance.