Hybrid Constrcution Method for Multi-kernel Polar Codes

Polar codes are the first class of error correction codes that achieve the Shannon channel capacity when their code length approaches infinity, but the code lengths of polar codes are limited to powers of 2. Therefore, multi-kernel polar codes are proposed, and their generator matrices are constructed from a variety of polarized kernels with different sizes. In this paper, we study the effect of different kernel orders on the channel polarization in the Gaussian approximation construction for multi-kernel polar codes. Besides, we study the minimum-distance spectrum of polarized kernels and the generator matrices of multi-kernel polar codes, and we calculate the minimum-distance spectrum for some larger kernels. We experimentally compare the advantages and disadvantages of the Gaussian approximation and minimum-distance construction. Finally, we propose a hybrid construction method which considers both the reliability and distance, and experimental results show that the proposed construction method outperforms the construction method that only considers distance and reliability.