Multi-Kernel Polar Codes: Concept and Design Principles

In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. These multi-kernel polar codes allow for more flexibility in terms of the code length and for various new design principles. Next to the common reliability design, we provide a design to maximize the minimal distance and a hybrid design combining reliability and distance properties. Numerical results demonstrate the advantage of multi-kernel polar codes under the new design principles compared to punctured and shortened Arikan polar codes.