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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,kurtosisis known to predict the modulation format-dependent NLI. These statistical properties can be used in the design of probabilistic amplitude shaping (PAS), which 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 arenon-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 calledenergy 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.
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Wu et al. (2021) studied this question.
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