Seeking Log-Likelihood Ratio Expressions for Polar Code Kernels with Arbitrary Dimension

This paper focus on seeking log-likelihood ratio (LLR) expressions for polar code kernels with an arbitrary dimension. On the basis of constructing linear transformed input matrixes for a given polar code kernel, it is proved that the LLR expressions can be computed by iterative pattern matchings based on the common factor extraction of the input matrixes. As a result, an algorithm for computing LLR expressions is proposed. Simulations show that the LLR expressions attained by the proposed scheme works well in decoding for multi-kernel polar codes.