Abstract
Probabilistic constellation shaping is investigated in the context of nonlinear fiber optic communication channels. Based on a general framework, different link types are considered—1. dispersion-managed channels, 2. unrepeatered transmission channels and 3. ideal distributed Raman amplified channels. These channels exhibit nonlinear effects to a degree that conventional probabilistic constellation shaping strategies for the additive white Gaussian (AWGN) noise channel are suboptimal. A channel-agnostic optimization strategy is used to optimize the constellation probability mass functions (PMFs) for the channels in use. Optimized PMFs are obtained, which balance the effects of additive amplified spontaneous emission noise and nonlinear interference. The obtained PMFs cannot be modeled by the conventional Maxwell-Boltzmann PMFs and outperform optimal choices of these in all the investigated channels. Suboptimal choices of constellation shapes are associated with increased nonlinear effects in the form of non-Gaussian noise. For dispersion-managed channels, a reach gain in 2 spans is seen and across the three channel types, gains of >0.1 bits/symbol over unshaped quadrature-amplitude modulation (QAM) are seen using channel-optimized probablistic shaping.
Highlights
Future demands for data transmission applications push optical fiber communication to operate with increasingly higher spectral efficiency
We investigate by simulations circumstances where the additive white Gaussian noise (AWGN) channel assumptions lead to a suboptimal constellation design compared to what can be achieved through optimization of the constellation probability mass functions (PMFs) without assuming the distribution should be a Maxwell-Boltzmann distribution
The constellations are defined by their underlying PMF and are—a uniform constellation; an signal-to-noise ratio (SNR)-designed Maxwell-Boltzmann constellation, which is based upon the AWGN channel assumptions and an effective SNR measurement on a uniform constellation; an optimal
Summary
Future demands for data transmission applications push optical fiber communication to operate with increasingly higher spectral efficiency. Higher-order modulation is well-suited for this since it is independent of the operating bandwidth [1], but conventional quadrature-amplitude modulation (QAM) formats leave a gap to the channel capacity. Constellation shaping has the potential to close this gap through the selection of modulation symbols tailored to the characteristics of the channel in use. Both geoemtric and probabilistic schemes are possible [1]. For the classical additive white Gaussian noise (AWGN) channel, the capacity and the potential in constellation shaping are well-understood, with known optimal results [2]. The Maxwell-Boltzmann distribution is known to be a near-optimal choice of a discrete probability mass function (PMF) for constellation shaping [3] and this
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