A Construction of Non-binary Polar codes with 4 by 4 kernels

In this paper, we propose a specific type of non-binary 4 by 4 kernel for non-binary polar codes. The non-binary polar codes generated by such type of kernel have same encoding and successive cancellation decoding complexities as the non-binary polar codes generated by the $\left[\begin{array}{ccc} 1 & 0 \\ \eta & 1 \end{array} \right]$ type of non-binary 2 by 2 kernel with same code length. At certain code parameters, we investigate the FER for the polar codes with all the $\left[\begin{array}{ccc} 1 & 0 \\ \eta & 1 \end{array} \right]$ type of non-binary 2 by 2 kernels. And then, we experimentally confirm the existence of several non-binary 4 by 4 kernels of the proposed type which generate non-binary polar codes with better FER performance than non-binary polar codes generated by any $\left[\begin{array}{ccc} 1 & 0 \\ \eta & 1 \end{array} \right]$ type of non-binary 2 by 2 kernel.