Design of Polar Codes with Large Kernels

Design techniques for polar (sub)codes with large kernels are presented for the case of the binary input AWGN channel. Namely, methods are presented to estimate the capacities and Bhattacharyya parameters of the bit subchannels induced by a large kernel polarizing transformation. Upper and lower bounds relating the capacity and Bhattacharyya parameter of a channel are used to refine the obtained estimates. Furthermore, a method for finding an optimal kernel sequence in mixed-kernel polar codes is presented. The proposed approach can be immediately used to construct polar codes for the Rayleigh fading channel.