短分组长度码的猜测译码 (Guessing Decoding of Short Blocklength Codes)

Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order of decreasing (exact or approximate) likelihood, offers a universal framework applicable to short codes. In this paper, we present a unified treatment of two prominent recent families of guessing decoding: guessing random additive noise decoding (GRAND) and guessing codeword decoding (GCD). For each, we (i) present algorithmic implementations and ordering strategies; (ii) prove maximum-likelihood (ML) optimality under appropriate stopping criteria; (iii) derive saddle-point approximations for the average number of queries; and (iv) validate theoretical predictions with simulations. We further analyze the performance degradation due to limited search budgets relative to ML performance, compare key metrics (worst-case and average complexity, hardware considerations), and highlight how advances in one approach transfer naturally to the other. Our results clarify the operating regimes where GRAND and GCD demonstrate superior performance. This work provides both theoretical insights and practical guidelines for deploying universal guessing decoders in next-generation short-blocklength communications.

翻译：未来的超5G和6G系统要求具有短分组长度的超可靠、低时延通信，这推动了通用译码算法的发展。猜测译码通过按（精确或近似）似然度递减的顺序推断噪声或候选码字，为短码提供了一种通用框架。本文对近期两类重要的猜测译码方法——猜测随机加性噪声译码（GRAND）和猜测码字译码（GCD）——进行了统一论述。针对每种方法，我们（i）介绍了算法实现与排序策略；（ii）证明了在适当停止准则下的最大似然（ML）最优性；（iii）推导了平均查询次数的鞍点近似；（iv）通过仿真验证了理论预测。我们进一步分析了相对于ML性能，有限搜索预算导致的性能下降，比较了关键指标（最坏情况与平均复杂度、硬件考量），并阐明了一种方法的进展如何自然地迁移至另一种方法。我们的结果明确了GRAND和GCD表现出优越性能的工作区间。本研究为在下一代短分组长度通信中部署通用猜测译码器提供了理论洞见与实践指导。