Improved ORB-GRAND for PAC Codes

Polarization-adjusted convolutional (PAC) codes have been proposed to significantly improve error correction ability compared to polar codes by incorporating rate-1 convolutional precoding. However, the development of computationally efficient decoders for PAC codes is still an ongoing research area. Ordered Reliability Bit Guessing Random Additive Noise Decoding (ORB-GRAND), a universal near Maximum Likelihood (near-ML) decoder, has been introduced for decoding moderately redundant block codes by querying a list of putative test error patterns (TEP) in a fixed order, i.e. logistic weight order (LWO) and improved logistic weight order (iLWO). In this study, we undertake a comprehensive investigation into the performance of ORB-GRAND concerning high-rate PAC codes of short-to-medium length. Firstly, we conduct a comparative analysis between ORB-GRAND and successive cancellation list (SCL) decoding for PAC codes and integrate the Cyclic Redundancy Check (CRC) mechanism into ORB-GRAND. Distance properties of PAC and CRC-Aided PAC (CA-PAC) codes are explored to demonstrate the performance results. Secondly, we propose a novel TEP scheduling scheme in response to the distinctive reduction in BLER revealed by scheduling TEP in iLWO, particularly for short PAC codes under low Signal-to-Noise Ratio (SNR) conditions. This remarkable scheme demonstrates its efficacy by effectively mitigating the aforementioned BLER degradation while maintaining the exceptional performance of iLWO in high SNR conditions.