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

Abstract

Generalized mutual information (GMI) capacity has been comprehensively studied in multi-dimensional 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 capacity though the correlation is reduced at lower FEC coding rate. The correlation is completely lost in the PS quadrature amplitude modulation (QAM) scheme. Furthermore, GMI can be used to design optimized constellation together with generalized pairwise optimization algorithm to mitigate the GMI capacity loss in non-Gray-mapped constellation. The GMI-optimized 32QAM (opt32) shows $\sim$0.5dB signal-to-noise ratio (SNR) improvement between 3 and 4 b/s GMI capacity in both analytic and experimental results. Optimized 2-dimensional 8QAM is also designed to show the consistent GMI capacity improvement over multi-dimensional 8QAM-equivalent formats. In simulations, PS-64QAM outperforms opt32 when a long sequence block is used in the distribution matcher and Gaussian-like constellation.