We study the typical-code (quenched) behavior of the false-alarm (FA) and missed-detection (MD) error exponents of the Neyman-Pearson test associated with soft covering, complementing the average-code (annealed) analysis that has been carried out in a companion paper [1]. We prove that, as the block-length tends to infinity, for almost every randomly selected fixed-composition codebook, the negative normalized logarithms of both error probabilities converge to their respective average-code exponents. In other words, the error exponents are self-averaging. We then extend the scope and study a mismatched likelihood ratio test that assumes the wrong channel model. Here, we derive the mismatched error exponents, show that self-averaging persists under mismatch, and characterize the degradation. In particular, we characterize the coding rate beyond which the two kinds of error exponents cannot be positive at the same time, which in the matched case, is given by the channel input-output mutual information rate.

翻译：我们研究了软覆盖相关的奈曼-皮尔逊检验中虚警(FA)和漏检(MD)错误指数的典型码（淬火）行为，补充了伴随论文[1]中已进行的平均码（退火）分析。我们证明，随着分组长度的增长，对于几乎任意随机选择的固定组成码本，两种错误概率的负归一化对数均收敛于其各自的平均码指数。换言之，错误指数具有自平均特性。随后我们扩展研究范围，考虑了假设错误信道模型的失配似然比检验。在此，我们推导出失配错误指数，证明自平均特性在失配情况下依然存在，并刻画了性能退化程度。特别地，我们确定了两种错误指数无法同时为正的编码速率阈值，在匹配情况下该阈值由信道输入输出互信息率给出。