Probabilistic shaping for arbitrary modulation formats

A system for optical data transport, comprising:

• a memory operatively coupled to a processor device, the processor being configured to control data transport across an optical transmission medium by:
• generating two-dimensional (2D) distribution matchers (DMs) based on probabilistic fold shaping (PFS) and arbitrary probabilistic shaping (APS);
• wherein the 2D PFS-based DM is configured to encode any N-fold rotationally symmetrical Quadrature Amplitude Modulation (QAM) format by applying the 2D PFS-based DM only to symbols in one quadrant based on a target entropy, determining a fold index yield uniform distribution, and utilizing the fold index to carry generated uniform distributed parity check bits across the optical transmission medium;
• and
• wherein the 2D APS-based DM is configured to encode any arbitrary modulation formats by encoding uniform binary data to generate non-uniform target symbols, and generating a probability distribution for the target symbols by indirectly applying the 2D APS-based DM based on a target probability distribution and a detected code rate of generated FEC code.