Channel polarization on q-ary discrete memoryless channels by arbitrary kernels

A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of q-ary channel polarization is considered by Şaşoğlu, Telatar, and Arikan. In this paper, we consider more general channel polarization on q-ary channels. We further show explicit constructions using Reed-Solomon codes, on which asymptotically fast channel polarization is induced.