A Simple Nonlinearity-Tailored Probabilistic Shaping Distribution for Square QAM

A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km nonlinear fiber transmission

Experimental Demonstration of Geometrically-Shaped Constellations Tailored to the Nonlinear Fibre Channel

A geometrically-shaped 256-QAM constellation, tailored to the nonlinear optical fibre channel, is experimentally demonstrated. The proposed constellation outperforms both uniform and AWGN-tailored 256-QAM, as it is designed to optimise the trade-off between shaping gain, nonlinearity and transceiver impairments

Exponentially-Weighted Energy Dispersion Index for the Nonlinear Interference Analysis of Finite-Blocklength Shaping

A metric called exponentially-weighted energy dispersion index (EEDI) is proposed to explain the blocklength-dependent effective signal-to-noise ratio (SNR) in probabilistically shaped fiber-optic systems. EEDI is better than energy dispersion index (EDI) at capturing the dependency of the effective SNR on the blocklength for long-distance transmission

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.Comment: 12 pages, 12 figure

On Probability Shaping for 5G MIMO Wireless Channel with Realistic LDPC Codes

Probability Shaping (PS) is a method to improve a Modulation and Coding Scheme (MCS) in order to increase reliability of data transmission. It is already implemented in some modern radio broadcasting and optic systems, but not yet in wireless communication systems. Here we adapt PS for the 5G wireless protocol, namely, for relatively small transport block size, strict complexity requirements and actual low-density parity-check codes (LDPC). We support our proposal by a numerical experiment results in Sionna simulator, showing 0.6 dB gain of PS based MCS versus commonly used MCS.Comment: Paper contains 14 pages, 10 figures, 2 tables, comments are welcome! Recommended for publication in Communications in Computer and Information Scienc

Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmission

\u3cp\u3eThis paper studies the impact of probabilistic shaping on effective signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a back-to-back configuration and in unrepeated nonlinear fiber transmissions. For the back-to-back setup, various shaped quadrature amplitude modulation (QAM) distributions are found to have the same implementation penalty as uniform input. By demonstrating in transmission experiments that shaped QAM input leads to lower effective SNR than uniform input at a fixed average launch power, we experimentally confirm that shaping enhances the fiber nonlinearities. However, shaping is ultimately found to increase the AIR, which is the most relevant figure of merit, as it is directly related to spectral efficiency. In a detailed study of these shaping gains for the nonlinear fiber channel, four strategies for optimizing QAM input distributions are evaluated and experimentally compared in wavelength division multiplexing (WDM) systems. The first shaping scheme generates a Maxwell-Boltzmann (MB) distribution based on a linear additive white Gaussian noise channel. The second strategy uses the Blahut-Arimoto algorithm to optimize an unconstrained QAM distribution for a split-step Fourier method based channel model. In the third and fourth approach, MB-shaped QAM and unconstrained QAM are optimized via the enhanced Gaussian noise (EGN) model. Although the absolute shaping gains are found to be relatively small, the relative improvements by EGN-optimized unconstrained distributions over linear AWGN optimized MB distributions are up to 59%. This general behavior is observed in 9-channel and fully loaded WDM experiments.\u3c/p\u3