Tutorial: Design and Decoding of Polar Codes with Large Kernels

Polar codes with large kernels were recently shown to asymptotically achieve optimal scaling exponent.  However, these codes were believed to be impractical due to lack of efficient decoding algorithms. In this tutorial we present a toolset for design and decoding of polar codes with large kernels. In particular, detailed treatment of recursive trellis and window kernel processing algorithms will be provided. These algorithms together with the successive cancellation list decoder allow one to obtain the same performance with lower complexity compared to polar codes with Arikan kernel. We present also techniques for construction of polar codes with large kernels, as well as kernels with good polarization properties and low decoding complexity.