On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

TL;DR

This paper investigates probabilistic shaping for multi-span optical fiber systems, demonstrating that minimal PMFs can achieve near-optimal performance over large SNR ranges and distances, with manageable nonlinear effects.

Contribution

It provides a comprehensive analysis of probabilistic shaping in fiber channels, showing that a small set of PMFs suffices for near-optimal performance across various conditions.

Findings

Two shaped PMFs are sufficient for large SNR ranges with minimal penalty.

One PMF can achieve significant gains over uniform input for long distances.

Shaping provides a gain in effective SNR despite nonlinear interference effects.

Abstract

Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multi-span wavelength division multiplexing (WDM) optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1,400 km to 3,000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.