The recently introduced maximum-likelihood (ML) decoding scheme called guessing random additive noise decoding (GRAND) has demonstrated a remarkably low time complexity in high signal-to-noise ratio (SNR) regimes. However, the complexity is not as low at low SNR regimes and low code rates. To mitigate this concern, we propose a scheme for a near-ML variant of GRAND called ordered reliability bits GRAND (or ORBGRAND), which divides codewords into segments based on the properties of the underlying code, generates sub-patterns for each segment consistent with the syndrome (thus reducing the number of inconsistent error patterns generated), and combines them in a near-ML order using two-level integer partitions of logistic weight. The numerical evaluation demonstrates that the proposed scheme, called segmented ORBGRAND, significantly reduces the average number of queries at any SNR regime. Moreover, the segmented ORBGRAND with abandonment also improves the error correction performance.

翻译：近期提出的名为“猜随机加性噪声解码”（GRAND）的最大似然（ML）解码方案在高信噪比（SNR）区域展现出极低的时间复杂度。然而，在低信噪比区域和低码率场景下，其复杂度并未显著降低。为解决此问题，我们提出了一种针对GRAND近ML变体（即有序可靠度比特GRAND，简称ORBGRAND）的改进方案。该方案根据底层编码特性将码字划分为若干分段，为每个分段生成与校正子一致（从而减少生成的不一致错误模式数量）的子模式，并通过对数权重的二级整数划分以近ML顺序组合这些子模式。数值评估结果表明，该方案（称为分段ORBGRAND）在任何信噪比区域均能显著减少平均查询次数。此外，带终止判定的分段ORBGRAND还能提升纠错性能。