Joint Learning of Probabilistic and Geometric Shaping for Coded Modulation Systems
This work addresses the need for more flexible and efficient modulation schemes in communication systems, offering an incremental improvement over PAS by removing restrictions on probability distributions and enabling optimization for any channel model.
The paper tackles the problem of optimizing coded modulation systems by jointly learning probabilistic and geometric shaping for various channel models and SNRs, achieving improved performance over existing methods like probabilistic amplitude shaping (PAS) in simulations on AWGN and Rayleigh fading channels.
We introduce a trainable coded modulation scheme that enables joint optimization of the bit-wise mutual information (BMI) through probabilistic shaping, geometric shaping, bit labeling, and demapping for a specific channel model and for a wide range of signal-to-noise ratios (SNRs). Compared to probabilistic amplitude shaping (PAS), the proposed approach is not restricted to 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 channel use and $k$ an integer within the range from $1$ to $m-1$. The proposed scheme enables learning of a continuum of constellation geometries and probability distributions determined by the SNR. Additionally, the PAS architecture with Maxwell-Boltzmann (MB) as shaping distribution was extended with a neural network (NN) that controls the MB shaping of a quadrature amplitude modulation (QAM) constellation according to the SNR, enabling learning of a continuum of MB distributions for QAM. Simulations were performed to benchmark the performance of the proposed joint probabilistic and geometric shaping scheme on additive white Gaussian noise (AWGN) and mismatched Rayleigh block fading (RBF) channels.