Segmented GRAND: Complexity Reduction through Sub-Pattern Combination

Abstract: The ordered-reliability bits (ORB) variant of guessing random additive noise decoding (GRAND), known as ORBGRAND, achieves remarkably low time complexity at high code rates compared to other GRAND variants. However, its computational complexity remains higher than other near-ML universal decoders like ordered-statistics decoding (OSD). To address this, we propose segmented ORBGRAND, which partitions the error pattern search space based on code properties, generates syndrome-consistent sub-patterns (reducing invalid error patterns), and combines them in a near-ML order using sub-weights derived from two-level integer partitions of logistic weight. Numerical results show that segmented ORBGRAND reduces the average number of queries by at least 66\% across all SNRs and cuts basic operations by over an order of magnitude, depending on segmentation and code rate. Further efficiency gains come from leveraging pre-generated shared sub-patterns, reducing average decoding time. Furthermore, with abandonment ($b=10^{5}$ or smaller), segmented ORBGRAND provides a 0.2 dB power gain over ORBGRAND. Additionally, we provide an analytical justification for why the logistic weight-based ordering of error patterns in ORBGRAND closely approximates the ML order and discuss the underlying assumptions of ORBGRAND.