基于Logistic-Lerch近似的Nakagami-m衰落信道上的平均有限块长分组错误率
Average Finite-Blocklength Packet Error Rate over Nakagami-$m$ Fading via a Logistic--Lerch Approximation
AI总结：
本文针对Nakagami-m衰落信道的平均有限块长分组错误率问题，提出Logistic-Lerch近似方法，得到闭式解，误差优于基线方法，可用于QoS感知的速率选择规则。
AI中文摘要：
评估衰落信道上有限块长（FBL）编码传输的平均分组错误率（PER），需要将正态近似得到的块错误水降曲线与衰落分布积分，这对一般Nakagami-m信道而言难以处理。本文将条件水降曲线近似为斜率匹配的Logistic函数，证明其Nakagami-m平均可简化为单个Lerch超越函数项，该项可在FBL水降与经典中断极限之间插值，且归一化常数在速率和块长上显式表达。该闭式形式支持非整数衰落，结合有效容量目标可得到感知服务质量（QoS）的速率选择规则。在标称FBL工作区域内，其与正态近似积分的误差在m取任意值时均约为1%，而中断和线性化基线在高分集时误差超过数个百分点。
英文摘要：
Evaluating the average packet error rate (PER) of finite-blocklength (FBL) coded transmission over fading requires integrating the block-error waterfall, given by the normal approximation, against the fading distribution, which is intractable for general Nakagami-$m$ channels. This letter approximates the conditional waterfall by a slope-matched logistic function and shows that its Nakagami-$m$ average reduces to a single Lerch-transcendent term that interpolates between the FBL waterfall and the classical outage limit, with norming constants explicit in rate and blocklength. The closed form supports non-integer fading and, composed into an effective-capacity objective, yields a quality-of-service (QoS) aware rate-selection rule. It matches the normal-approximation integral to about 1\% uniformly in $m$ over the nominal FBL operating region, while outage and linearization baselines exceed several percent at high diversity.
