A New Construction of Nonbinary Polar Codes with Two-stage Polarization

In this paper, we propose a new class of nonbinary polar codes with two-stage polarization, where the outer polarization (symbol-level polarization) kernel is a nonbinary matrix resembling Ar{\i}kan's kernel, and the inner polarization (bit-level polarization) kernel is a properly designed binary matrix. The encoder/decoder of the proposed nonbinary polar codes have the same structure as the original binary polar codes, admitting an easily configurable and flexible implementation. This is an obvious advantage over the nonbinary polar codes based on Reed-Solomon (RS) codes. Simulation results show that, compared with modified RS-based polar codes, our proposed nonbinary polar codes can achieve similar performance but with a smaller list size. When compared with binary polar codes, the proposed nonbinary polar codes exhibit better performance and lower decoding latency (benefitted from the fact that multiple bits can be decoded as a symbol simultaneously).