Polar coding without alphabet extension for asymmetric channels

We consider channel coding of binary asymmetric memoryless channels with polar codes. The difficulty for asymmetric channels comes from the fact that the optimal input probability distributions are not always uniform. Şaşoğlu et al. realized a nonuniform input distribution by mapping multiple auxiliary symbols distributed uniformly to an actual input symbol. However, the complexity of the scheme increases considerably for the case that the input distribution cannot be approximated by simple rational numbers. To overcome this problem, we propose another polar coding scheme for asymmetric channels, which realizes the optimal nonuniform input distribution by randomizing symbols in the frozen bits with an appropriate probability distribution.