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We introduce a trainable coded modulation scheme that enables jointoptimization of the bit-wise mutual information (BMI) through probabilisticshaping, geometric shaping, bit labeling, and demapping for a specific channelmodel and for a wide range of signal-to-noise ratios (SNRs). Compared toprobabilistic amplitude shaping (PAS), the proposed approach is not restrictedto symmetric probability distributions, can be optimized for any channel model,and works with any code rate $k/m$, $m$ being the number of bits per channeluse and $k$ an integer within the range from $1$ to $m-1$. The proposed schemeenables learning of a continuum of constellation geometries and probabilitydistributions determined by the SNR. Additionally, the PAS architecture withMaxwell-Boltzmann (MB) as shaping distribution was extended with a neuralnetwork (NN) that controls the MB shaping of a quadrature amplitude modulation(QAM) constellation according to the SNR, enabling learning of a continuum ofMB distributions for QAM. Simulations were performed to benchmark theperformance of the proposed joint probabilistic and geometric shaping scheme onadditive white Gaussian noise (AWGN) and mismatched Rayleigh block fading (RBF)channels.

Joint Learning of Probabilistic and Geometric Shaping for Coded Modulation Systems