Within the Guessing Random Additive Noise Decoding (GRAND) family, ordered reliability bits GRAND (ORBGRAND) has received considerable attention for its hardware-friendly exploitation of soft information. Existing information-theoretic results for ORBGRAND are asymptotic in blocklength and do not quantify its performance at short-to-moderate blocklengths. This paper develops a finite-blocklength analysis for ORBGRAND over general bit channel, addressing the key challenge that the rank-induced decoding metric is non-additive and coupled across symbols. We first derive an ORBGRAND-specific random-coding union (RCU)-type achievability (ORB-RCU) bound on the ensemble-average error probability. We then characterize two governing decoding metrics: the transmitted-codeword metric is treated as a U-statistic and analyzed via Hoeffding decomposition, while the competing-codeword metric is reduced to a weighted sum of independent and identically distributed Bernoulli random variables and analyzed through strong large-deviation analysis. Combining these ingredients with a Berry-Esseen argument yields a second-order achievable-rate expansion and the associated normal approximation, whose first-order term is shown to equal the ORBGRAND generalized mutual information and whose second-order term defines an ORBGRAND dispersion with a single-letter variance representation. Numerical results for BPSK-modulated additive white Gaussian noise channel validate the tightness of ORB-RCU relative to the maximum-likelihood based RCU benchmark and the accuracy of the normal approximation in the operating regime of practical interest.

翻译：在猜测随机加性噪声解码（GRAND）系列中，有序可靠性比特GRAND（ORBGRAND）因其对软信息的硬件友好型利用而受到广泛关注。现有的ORBGRAND信息论结果在码长上是渐近的，未能量化其在短到中等码长下的性能。本文针对一般比特信道发展了ORBGRAND的有限码长分析，解决了由排序诱导的解码度量具有非加性且跨符号耦合这一关键挑战。我们首先推导了ORBGRAND特有的随机编码并集（RCU）型可达性（ORB-RCU）界，该界针对集合平均错误概率。随后，我们刻画了两个主导解码度量：将发送码字的度量视为U统计量并通过霍夫丁分解进行分析，而将竞争码字的度量简化为独立同分布伯努利随机变量的加权和，并通过强大偏差分析进行研究。将这些要素与贝里-埃森论证相结合，得到了二阶可达率展开及其对应的正态近似，其中一阶项被证明等于ORBGRAND广义互信息，二阶项则定义了具有单字母方差表示的ORBGRAND色散。针对BPSK调制加性高斯白噪声信道的数值结果验证了ORB-RCU相对于基于最大似然的RCU基准的紧致性，以及在实际感兴趣的工作区间内正态近似的准确性。