  Polar codes based on $2\times2$ non-binary kernels are discussed in this
work. The kernel over $\text{GF}(q)$ is selected by maximizing the polarization
effect and using Monte-Carlo simulation. Belief propagation (BP) and successive
cancellation (SC) based decoding algorithms are extended to non-binary codes.
Additionally, a successive cancellation list (SCL) decoding with a pruned tree
is proposed. Simulation results show that the proposed decoder performs very
close to a conventional SCL decoder with significantly lower complexity.
