Window Processing of Binary Polarization Kernels

A decoding algorithm for polar (sub)codes with binary $2^t\times 2^t$ polarization kernels is described. The proposed approach exploits the linear relationship of the considered kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbol log-likelihood ratio (LLR) by computing path scores of several paths in Arikan successive cancellation (SC) decoding. Further complexity reduction is achieved by identification and reusing of common subexpressions arising in this computation. The proposed algorithm is applied to kernels of size $16$ and $32$ with improved polarization properties. It enables polar (sub)codes with the considered kernels to provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.