Reduced complexity window processing of binary polarization kernels

We propose a reduced complexity algorithm for computing log-likelihood ratios (LLRs) needed for successive cancellation (SC) decoding of polar codes with 2(t) x 2(t) polarization kernels. This algorithm is applied to some polarization kernels of length 16 and 32 with high polarization rate. The complexity reduction is achieved by exploiting linear relationship of the considered kernels and Arikan matrix. Further complexity reduction is achieved by identification of common subexpressions. The proposed approach enables SC list decoding of polar codes with some large kernels with lower complexity compared to the codes based on the Arikan kernel with the same performance.