Efficient decoding of polar codes with some 16$\times$16 kernels

Abstract: A decoding algorithm for polar codes with binary 16$\times$16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the Arikan matrix to significantly reduce the decoding complexity without any performance loss. Simulation results show that polar (sub)codes with 16$\times$16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.