References & Further Reading

References

  1. G. Böcherer, F. Steiner, and P. Schulte, Bandwidth efficient and rate-matched low-density parity-check coded modulation, 2015

    The PAS paper — the architectural blueprint of modern probabilistic shaping in coded modulation.

  2. P. Schulte and G. Böcherer, Constant Composition Distribution Matching, 2016

    Formal CCDM analysis with the $O(\\log n / n)$ rate-loss theorem.

  3. G. D. Forney Jr., Coset codes — Part I: Introduction and geometrical classification, 1988

    Classical Forney coset code treatment. Used here as the predecessor to modern shaping approaches.

  4. G. D. Forney Jr., M. D. Trott, and S.-Y. Chung, Sphere-Bound-Achieving Coset Codes and Multilevel Coset Codes, 2000

    Establishes the sphere bound — the theoretical foundation for the 1.53 dB shaping ceiling.

  5. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer (3rd ed.), 1999

    The reference on lattice theory. Discusses sphere packings and coset codes underlying shaping gains.

  6. G. D. Forney Jr. and G. Ungerboeck, Modulation and Coding for Linear Gaussian Channels, 1998

    Tutorial on coded modulation over Gaussian channels with explicit discussion of shaping.

  7. F. Steiner and G. Böcherer, Comparison of geometric and probabilistic shaping for terrestrial broadcasting with ATSC 3.0, 2018

    Head-to-head PS vs GS comparison on the ATSC 3.0 channel model.

  8. R. A. Amjad and G. Böcherer, Fixed-to-Variable Length Resolution Coding for Probabilistic Shaping, 2013

    Hierarchical DM for short blocks — smaller rate loss than CCDM.

  9. T. O'Shea and J. Hoydis, An introduction to deep learning for the physical layer, 2017

    Autoencoder-based end-to-end learning — forward-ref to Ch 22.

  10. Optical Internetworking Forum, Implementation Agreement 400ZR, OIF-400ZR-01.0, 2020

    First mass-market deployment of PAS in optical coherent systems.

  11. ETSI, EN 302 307-2: DVB-S2 Extensions (DVB-S2X), ETSI, 2021

    DVB-S2X extends DVB-S2 with PAS-based shaping and higher-order APSK constellations.

  12. J. G. Proakis and M. Salehi, Digital Communications, McGraw-Hill (5th ed.), 2008

    Standard reference on digital modulation theory.

  13. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley (2nd ed.), 2006

    Foundational reference for maximum-entropy distribution theory underlying MB shaping.

Further Reading

For readers who want to go deeper into specific aspects of shaping and coded modulation.

  • PAS tutorial

    G. Böcherer, "Principles and Practice of Probabilistic Shaping for Bandwidth Efficient Communications", IEEE Commun. Mag., 2016.

    Accessible introduction to PAS for non-specialists.

  • Short-block distribution matching

    R. A. Amjad, G. Böcherer, "Fixed-to-Variable Length Resolution Coding for Probabilistic Shaping," IEEE Trans. Commun., 2013.

    Reduces short-block rate loss, important for URLLC.

  • PAS for optical coherent

    F. Buchali et al., "Rate adaptation and reach increase by probabilistically shaped 64-QAM: An experimental demonstration," J. Lightwave Tech., 2016.

    Experimental validation of PAS on optical fibre at 400 Gb/s.

  • Deep shaping and autoencoders

    S. Cammerer et al., "Trainable Communication Systems: Concepts and Prototypes," IEEE Commun. Mag., 2020.

    Modern deep-learning approach to joint shaping and coding.

  • 5G NR shaping studies

    3GPP Technical Report TR 38.887 (preliminary), Shaping for NR Rel-18, 2023.

    Standards-body perspective on bringing PAS to cellular.

ExercisesCh 20 →