Maximum-likelihood (ML) decoding can be used to obtain the optimal performance of error correction codes. However, the size of the search space and consequently the decoding complexity grows exponentially, making it impractical to be employed for long codes. In this paper, we propose an approach to constrain the search space for error patterns under a recently introduced near ML decoding scheme called guessing random additive noise decoding (GRAND). In this approach, the syndrome-based constraints which divide the search space into disjoint sets are progressively evaluated. By employing $p$ constraints extracted from the parity check matrix, the average number of queries reduces by a factor of $2^p$ while the error correction performance remains intact.

翻译：最大可能性解码可用于获取错误校正代码的最佳性能,然而,搜索空间的大小及其解码复杂性成倍增长,使得使用长代码不切实际。在本文件中,我们建议采用一种办法,限制最近在ML解码方案附近引入的误差模式搜索空间,称为随机添加噪音解码(GRAND),在这种方法中,逐步评估了将搜索空间分为脱节组合的基于综合的制约因素。通过使用从平价检查矩阵中提取的$p$的限制,平均查询次数减少2美元,差错校正性能保持不变。