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In this paper, we propose a new class of nonbinary polar codes with two-stagepolarization for ultra-reliable and low-latency communications (URLLC), wherethe outer (symbol-level) polarization is achieved by using a 2X2 q-ary matrix[1 0; \beta 1] as the kernel and the inner (bit-level) polarization is achievedby a binary polarization matrix for each input symbol. With the two-stagepolarization, bit-level code construction is introduced, resulting inpartially-frozen symbols, where the frozen bits in these symbols can be used asactive-check bits to facilitate the decoder. The encoder/decoder of theproposed codes has the same structure as the original binary polar codes,admitting an easily configurable and flexible implementation, which is anobvious advantage over the existing nonbinary polar codes based on Reed-Solomon(RS) codes. To support high spectral efficiency in URLLC, we also present, inaddition to the single level coded modulation scheme with field matchedmodulation order, a mixed multilevel coded modulation scheme with arbitrarymodulation order to trade off the latency against complexity. Simulationresults show that our proposed nonbinary polar codes exhibit comparableperformance with the RS4-based polar codes and outperform binary polar codeswith low decoding latency, suggesting a potential application for 5G URLLC.

Two-Stage Polarization-Based Nonbinary Polar Codes for 5G URLLC