Nonbinary polar coding with low decoding latency and complexity

Abstract

In this paper, we propose a new class of nonbinary polar codes, where the symbol-level polarization is achieved by using a 2 × 2 q-ary matrix $\left(\begin{array}{cc}1& 0\\ \beta & 1\end{array}\right)$ as the kernel. Under bit-level code construction, some partially-frozen symbols exist, where the frozen bits in these symbols can be used as active-check bits to facilitate the decoder. The encoder/decoder of the proposed codes has a similar structure to the original binary polar codes, admitting an easily configurable and flexible implementation, which is an obvious advantage over the existing nonbinary polar codes based on Reed-Solomon (RS) codes. A low-complexity decoding method is also introduced, in which only more competitive symbols are considered rather than the whole q symbols in the finite field. To support high spectral efficiency, we also present, in addition to the single level coded modulation scheme with field-matched modulation order, a mixed multilevel coded modulation scheme with arbitrary modulation in order to trade off the latency against complexity. Simulation results show that our proposed nonbinary polar codes exhibit comparable performance with the RS4-based polar codes and outperform binary polar codes with low decoding latency, suggesting a potential application for future ultra-reliable and low-latency communications (URLLC).