Abstract
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.
Highlights
C ONSTELLATION shaping (CS) and forward error correction (FEC) are two crucial elements to realize near capacity-achieving transmission for the additive white Gaussian noise (AWGN) channel
We study the effective signalto-noise ratio (SNR) in (4), where nonlinear interference (NLI) is a substantial part of the total noise at relatively high power, and where NLI changes produce a change in effective SNR
Nonlinear noise caused by the Kerr effect, as well as amplified spontaneous emission (ASE) and chromatic dispersion (CD) are taken into consideration
Summary
C ONSTELLATION shaping (CS) and forward error correction (FEC) are two crucial elements to realize near capacity-achieving transmission for the additive white Gaussian noise (AWGN) channel. Mitigation of NLI can be achieved by optimizing statistical properties of the transmitted symbol sequences. Given a number of constellation points, it is possible to change the constellation geometry [17], [18] or the probability mass function (PMF) of the constellation symbols [9], [19], [20] These techniques are often referred to as geometric and probabilistic shaping, respectively. In both cases, by assuming symbols to be independent identically distributed (i.i.d.), the stationary statistical properties of symbols are optimized. Perhaps the most important question is that a metric that accounts for time-varying statistical properties of symbol sequences and enables a precise NLI prediction is still unknown.
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