On Efficient Decoding of Polar Codes with Large Kernels

Defined through a certain 2×2 matrix called Arikan's kernel, polar codes are known to achieve the symmetric capacity of binary-input discrete memoryless channels under the successive cancellation (SC) decoder. Yet, for short blocklengths, polar codes fail to deliver a compelling performance under the low complexity SC decoding scheme. Recent studies provide evidence for improved performance when Arikan's kernel is replaced with larger kernels that have smaller scaling exponents. However, for l×l kernels the time complexity of the SC decoding increases by a factor of 2^l. In this paper we study a special type of kernels called permuted kernels. The advantage of these kernels is that the SC decoder for the corresponding polar codes can be viewed as a permuted version of the SC decoder for the conventional polar codes that are defined through Arikan's kernel. This permuted successive cancellation (PSC) decoder outputs its decisions on the input bits according to a permuted order of their indices. We introduce an efficient PSC decoding algorithm and show simulations for two 16×16 permuted kernels that have better scaling exponents than Arikan's kernel.