Fig. 1. Schematic diagram of probabilistic shaping algorithm of information bit inversion

Fig. 2. 16 QAM constellation diagrams. (a) Traditional Gray-coded mapping; (b) approximate Gray-coded mapping

Fig. 3. 32 QAM constellation diagrams with approximate Gray-coded mapping. (a) Conventional mapping; (b) improved mapping

Fig. 4. Schematic diagram of sender of probabilistic shaping algorithm of grouping inversion combined with hierarchical modulation technology

Fig. 5. 16 QAM constellation diagrams. (a) Information bit inversion; (b) outer constellation point inversion

Fig. 6. Bit-error rate curves of 16 QAM with different n in information bit inversion

Fig. 7. Bit-error rate curves of 16 QAM with different m in information bit inversion

Fig. 8. Bit-error rate curves of 16 QAM with different m in outer constellation point inversion

Fig. 9. Bit-error rate curves of 32 QAM with different m in information bit inversion

Fig. 10. Bit-error rate curves of 16 QAM with Gray-coded and approximate Gray-coded mappings with m=4and n=2

Fig. 11. Bit-error rate curves of 32 QAM with conventional and improved approximate Gray-coded mappings with m=4 and n=2

Fig. 12. Bit-error rate curves of probabilistic shaping algorithm of information bit inversion combined with hierarchical modulation technology

Fig. 13. Bit-error rate curves of probabilistic shaping algorithm of outer constellation point inversion combined with hierarchical modulation technology