New construction and performance analysis of Polar codes over AWGN channels

We propose a new construction algorithm for Polar codes operating over Additive White Gaussian Noise channels under Successive Cancellation decoding. Our approach is based on tracking the bit error probabilities of the bit channels as they evolve through the decoder, allowing us on the one hand to characterize the performance of these channels, and on the other hand, providing a solid construction algorithm. We then use our approach to derive a modification for the density evolution (with Gaussian approximation) based construction, providing better accuracy and implementation.