Generalized Mutual Information (GMI) extends the concept of mutual information to more than two variables. In scenarios involving multiple random variables, GMI provides a measure of the overall dependence among all variables. The formula for GMI depends on the specific context and the number of variables involved.

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Spectrally-Efficient 200G Probabilistically-Shaped 16QAM over 9000km Straight Line Transmission with Flexible Multiplexing Scheme

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Flexible wavelength-multiplexing technique in backbone submarine networks has been deployed to accommodate the trend of variable-rate modulation formats. In this paper, we propose a new design of flexible-rate transponders in the scenario of flexible multiplexing scheme to achieve near-Shannon performance. Probabilistic-shaped (PS) M-QAM is capable of adjusting the bit rate at very finer granularity by adapting the entropy of the distribution matcher. Instead of delivering variable bit rates at the fixed baud rate, various baud rates of 200Gb/s PS-16QAM is demonstrated to fit into the flexible grid multiple 3.125GHz bandwidth. This flexible baud rate saves the limited optical bandwidth assigned by the flexible multiplexing scheme to improve bandwidth utilization. The 200G PS-16QAM signals are experimentally demonstrated over 9000km straight-line testbed to achieve 3.05b/s/Hz~5.33 b/s/Hz spectral efficiency (SE) with up to 4dB Q margin. In addition, the high baud rate signals are used for lower SE while low baud rate signals are targeting at high SE transmission to reduce the implementation penalty.

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Spectrally Efficient Submarine Transmission with Flexible WME

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By adjusting single shaping factor in the distribution matcher, probabilistic-shaped M-QAM is reviewed to provide both flex-rate and near-Shannon performance at the given flex-grid bandwidth and filling ratio.

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Constellation Design with Geometric and Probabilistic Shaping

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A systematic study, including theory, simulation and experiments, is carried out to review the generalized pairwise optimization algorithm for designing optimized constellation. In order to verify its effectiveness, the algorithm is applied in three testing cases: 2-dimensional 8 quadrature amplitude modulation (QAM), 4-dimensional set-partitioning QAM, and probabilistic-shaped (PS) 32QAM. The results suggest that geometric shaping can work together with PS to further bridge the gap toward the Shannon limit.

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Design and Comparison of Advanced Modulation Formats Based on Generalized Mutual Information

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Generalized mutual information (GMI) has been comprehensively studied in multidimensional constellation and probabilistic-shaped (PS) constellation together with different forward error correction (FEC) coding schemes. The simulation results confirm that GMI is an efficient and accurate tool to compare their post-FEC performance. In particular for uniformly geometric-shaped constellation, the pre-FEC Q-factor is highly correlated with GMI though the correlation is reduced at lower FEC coding rate. Furthermore, GMI can be used to design optimized constellation together with generalized pairwise optimization algorithm to mitigate the GMI loss in non-Gray-mapped constellation. The GMI-optimized 32QAM (opt32) shows ~0.5 dB signal-to-noise ratio improvement between 3 and 4 b/s GMI in both simulated and experimental results. Optimized two-dimensional 8 QAM is also designed to show the consistent GMI improvement over multi-dimensional 8 QAM-equivalent formats. In simulations, PS-64 QAM outperforms opt32 when a long sequence block is used in the distribution matcher.

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