Probabilistic Shaping for Multidimensional Signals with Autoencoder-based End-to-end Learning

This work proposes a system that optimises multidimensional signal transmission, utilising signals with probabilistic shaping designed with the aid of end-to-end learning of an autoencoder-based architecture. For the first time, this work reports bit mapping optimisation for multidimensional signals and applied the newly derived optimised signals to the probabilistic shaping system. The autoencoder employs two neural networks for the transceiver, separated by the embedded channel. The optimisation of the autoencoder configuration is implemented for probabilistic shaping for n-dimensional signals. Specifically, We investigate a 4-dimensional (4D) signal employing 2 successive time slots that has better noise immunity relative to regular 2-dimensional quadrature amplitude modulation (QAM) signals. We propose a new application of autoencoders in communication systems based on 4D signals and apply machine learning to optimise the 4D probabilistic shaping on the basis of receiver signal-to-noise-ratio (SNR). The performance of the optimised probabilistically shaped 4D signals is evaluated in terms of the bit error rate (BER) and mutual information. Simulation results show that the proposed probabilistically shaped 4D signal achieves better BER performance relative to the unshaped 4D and regular 2D QAM. We demonstrate the mutual information of the proposed signal with varying SNR, showing its improved capacity in comparison with other constellations.