Generalized Schematic Successive Cancellation Decoding for Polar Codes

Recently, generalized polar codes were introduced to provide more code lengths and rates without the need for shortening or puncturing. However, as the size of the kernel matrix increases, computing the Log-Likelihood Ratio (LLR) functions in successive cancellation decoder for these codes becomes mathematically more complicated. In this paper, a new simplified general method is proposed to calculate these LLR functions based on the schematic diagram of the selected kernel matrix for sizes higher than 2. Our proposed method fragments the main block into some basic components whose formulas have been previously proven by Arikan for 2 x 2 kernel matrix. The validity of the resulting LLR functions is tested on different kernel matrices and proven to be similar to those in literature.