The stationary statistical properties of independent, identically distributed (i.i.d.) input symbols provide insights on the induced nonlinear interference (NLI) during fiber transmission. For example, kurtosis is known to predict the modulation format-dependent NLI. These statistical properties can be used in the design of probabilistic amplitude shaping (PAS), which is a popular scheme that relies on an amplitude shaper for increasing spectral efficiencies of fiber-optic systems. One property of certain shapers used in PAS -- including constant-composition distribution matchers -- that is often overlooked is that a time-dependency between amplitudes is introduced. This dependency results in symbols that are non-i.i.d., which have time-varying statistical properties. Somewhat surprisingly, the effective signal-to-noise ratio (SNR) in PAS has been shown to increase when the shaping blocklength decreases. This blocklength dependency of SNR has been attributed to time-varying statistical properties of the symbol sequences, in particular, to variation of the symbol energies. In this paper, we investigate the temporal energy behavior of symbol sequences, and introduce a new metric called energy dispersion index (EDI). EDI captures the time-varying statistical properties of symbol energies. Numerical results show strong correlations between EDI and effective SNR, with absolute correlation coefficients above 99% for different transmission distances.

中文翻译：

---

基于能量色散指数的光纤非线性干涉建模符号序列的时态能量分析

独立的，均匀分布的（iid）输入符号的静态统计特性提供了有关光纤传输过程中引起的非线性干扰（NLI）的见解。例如，已知峰度可预测依赖于调制格式的NLI。这些统计属性可用于概率振幅整形（PAS）的设计中，这是一种流行的方案，它依赖于振幅整形器来提高光纤系统的光谱效率。PAS中使用的某些整形器的一个特性-包括恒定成分分布匹配器-经常被忽略的是，引入了幅度之间的时间依赖性。这种依赖性导致非iid符号具有随时间变化的统计属性。有点令人惊讶 研究表明，当整形块长度减小时，PAS中的有效信噪比（SNR）会增加。SNR的这种块长相关性已归因于符号序列的时变统计特性，尤其是符号能量的变化。在本文中，我们研究了符号序列的时间能量行为，并引入了一种新的度量标准，称为能量分散指数（EDI）。EDI捕获符号能量的时变统计属性。数值结果表明，EDI与有效SNR之间具有很强的相关性，对于不同的传输距离，绝对相关系数都超过99％。改变符号能量。在本文中，我们研究了符号序列的时间能量行为，并引入了一种新的度量标准，称为能量分散指数（EDI）。EDI捕获符号能量的时变统计属性。数值结果表明，EDI与有效SNR之间具有很强的相关性，对于不同的传输距离，绝对相关系数都超过99％。改变符号能量。在本文中，我们研究了符号序列的时间能量行为，并引入了一种新的度量标准，称为能量分散指数（EDI）。EDI捕获符号能量的时变统计属性。数值结果表明，EDI与有效SNR之间具有很强的相关性，对于不同的传输距离，绝对相关系数都超过99％。