Average Finite-Blocklength Packet Error Rate over Nakagami-$m$ Fading via a Logistic--Lerch Approximation

2026-08-21

AI Summary

该研究通过使用Logistic-Lerch近似方法解决了在Nakagami-m衰落信道下计算有限码长传输平均包错误率的问题。

Abstract

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.

Problem

• Average Packet Error Rate
• Finite-Blocklength
• Nakagami-m Fading

Innovation

• Logistic Function
• Lerch Transcendent
• Finite-Blocklength
• Nakagami-m Fading
• QoS-aware Rate Selection