On the Marginalization of Polarizing Kernels

In this paper, we analyze the decoding complexity of polarizing kernels of size larger than p = 2, proposing a general procedure which can be used to marginalize kernels of any size. We use this method to evaluate the decoding equations for optimal binary kernels up to size p = 8. Finally, we experimentally show that, even if T ₂ and T ₈ share the same polarization exponent, their performance may vary under list decoding, making large kernels of interest for long polar codes.