Non-Binary LDPC Forward Error Correction for Coding Gain in LoRa

Abstract

LoRa is widely used for low-power long-range communication, yet its legacy forward error correction (FEC) based on Hamming codes provides limited error correction capability. This study investigates the use of non-binary low-density paritycheck (NB-LDPC) codes as an alternative FEC scheme for LoRa, operating over Galois fields which align naturally with the highorder modulation used by LoRa chirp spread spectrum (CSS). Symbol-level log-likelihood ratios (LLRs) are derived for the NB-LDPC-based decoder and pseudo-soft LLRs are introduced for devices with unmodified commercial chipsets in which reliability metrics are unavailable. Under additive white Gaussian noise (AWGN), soft and hard decision-based NB-LDPC codes achieve approximately 2.5 dB and 0.7 dB coding gain, respectively, at a target 10% frame error rate (FER). Under correlated frequencyflat Rayleigh fading, gains of approximately 6.5 dB (soft) and 3.5 dB (hard) are observed, highlighting the increased robustness of NB-LDPC to fading. Comparison with a binary LDPC reference further highlights the advantage of symbol-level coding in LoRa as binary LDPC with soft-decision decoding underperforms the hard-decision NB-LDPC configuration with the gap becoming more pronounced in the presence of fading.