Abstract
The choice of constellations largely affects the performance of both wireless and optical communications. To address increasing capacity requirements, constellation shaping, especially for high-order modulations, is imperative in high-speed coherent communication systems. This paper, thus, proposes novel mutual information neural estimation (MINE)-based geometric, probabilistic, and joint constellation shaping schemes, i.e., the MINE-GCS, MINE-PCS, and MINE-JCS, to maximize mutual information (MI) via emerging deep learning (DL) techniques. Innovatively, we first introduce the MINE module to effectively estimate and maximize MI through backpropagation, without clear knowledge of the channel state information. Then, we train encoder and probability generator networks with different signal-to-noise ratios to optimize the distribution locations and probabilities of the points, respectively. Note that MINE transforms the precise MI calculation problem into a parameter optimization problem. Our MINE-based schemes only optimize the transmitter end, and avoid the computational and structural complexity in traditional shaping. All the designs were verified through simulations as having superior performance for MI, among which the MINE-JCS undoubtedly performed the best for additive white Gaussian noise, compared to the unshaped QAMs and even the end-to-end training and other DL-based joint shaping schemes. For example, the low-order 8-ary MINE-GCS could achieve an MI gain of about 0.1 bits/symbol compared to the unshaped Star-8QAM. It is worth emphasizing that our proposed schemes achieve a balance between implementation complexity and MI performance, and they are expected to be applied in various practical scenarios with different noise and fading levels in the future.