Optimized Non-Binary Polar Codes for Short Block-Length Communications

Internet of Things (IoT) and direct-access Satellite IoT (SIoT) systems demand short block-length communication to accommodate brief transmissions under strict power constraints. In this context, it is critical to ensure high error correction reliability with minimal energy. One prominent candidate for Forward Error Correction (FEC) is Polar codes. Introduced by Arikan in 2009, Polar codes achieve the capacity of binary-input discrete memoryless channels through the phenomenon of channel polarization. While generalizing Polar codes to non-binary fields $\mathbb{GF}(q)$ can yield improved performance compared to their binary counterpart at long block lengths, they fall short at short block length even when applying techniques such as frozen-bit-pattern and kernel optimization. In this paper, additional strategies are evaluated that go beyond these baseline techniques. In detail, kernel optimization is extended towards a multi-kernel approach and a joint optimization of modulation order and code rate on system level is proposed. Simulation results demonstrate that under these careful optimizations, non-binary Polar codes can indeed outperform binary Polar codes for short block length, as well, making them the optimal channel-coding choice for SIoT applications.