Skip to main content
Springer Nature Link
Log in

Polar coded probabilistic amplitude shaping for non-terrestrial networks in 5G

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

The dominant Gaussian noise effect of the non-terrestrial network-to-user equipment (NTN-UE) channel presents an opportunity for polar coded probabilistic amplitude shaping (PAS) application. However, the 5G NTN serving a mobile device poses energy efficiency and short block-length support challenges. Given this, we propose a sphere-shaped polar coded PAS with path metric (PM) inheritance supported multi-level coding and multi-stage decoding (MLC-MSD) architecture. In the proposed design, a modified de-mapping and code construction approach addresses the inherent inaccuracy in Polar code construction for the most significant bit (MSB) level in the polar PAS scenario. It utilizes the widened inter-path PM gaps at MSB decoding to improve the average log-likelihood ratio (LLR) prediction as compared to the regular mutual information (MI) based calculation; this improves the Gaussian approximation (GA) design. In addition, we propose a sphere-class aided polar decoding that utilizes the sphere-shaped symbol sequence energy pattern during the CRC-aided successive cancellation list decoding (CASCL). The frame error rate (FER) results show up to 1.4 dB gain as compared to the regular polar PAS architecture. Furthermore, energy efficiency results show that the polar PAS architecture leads to a significant energy gap between the sphere shaping and the legacy distribution matching approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Algorithm 1
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. Latest updates are available at https://www.3gpp.org/specifications-technologies/releases/release-18.

References

  1. 3rd Generation Partnership Project. (2020). Study on new radio (NR) to support non-terrestrial networks. Technical specification group radio access network, 3GPP, TR 38.811, V15.4.0, 2020.

  2. Arikan, E. (2009). Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on Information Theory, 55(7), 3051–3073. https://doi.org/10.1109/TIT.2009.2021379

    Article  Google Scholar 

  3. Barrueco, J., Montalban, J., Iradier, E., et al. (2021). Constellation design for future communication systems: A comprehensive survey. IEEE Access, 9, 89778–89797. https://doi.org/10.1109/ACCESS.2021.3090774

    Article  Google Scholar 

  4. Böcherer, G. (2014). Achievable rates for shaped bit-metric decoding. Preprint at https://arxiv.org/abs/1410.8075.

  5. Böcherer, G. (2017). Achievable rates for probabilistic shaping. Preprint at https://arxiv.org/abs/1707.01134.

  6. Böcherer, G. (2018). Principles of coded modulation, habilitation thesis. Habilitation thesis, Technical University of Munich, Munich, Germany. http://www.georg-boecherer.de/bocherer2018principles.pdf.

  7. Böcherer, G., Prinz, T., Yuan, P., et al. (2017). Efficient polar code construction for higher-order modulation. In 2017 IEEE wireless communications and networking conference workshops (WCNCW) (pp. 1–6). https://doi.org/10.1109/WCNCW.2017.7919039.

  8. Böcherer, G., Steiner, F., & Schulte, P. (2015). Bandwidth efficient and rate-matched low-density parity-check coded modulation. IEEE Transactions on Communications, 63(12), 4651–4665. https://doi.org/10.1109/TCOMM.2015.2494016

    Article  Google Scholar 

  9. Calderbank, A., & Ozarow, L. (1990). Nonequiprobable signaling on the Gaussian channel. IEEE Transactions on Information Theory, 36(4), 726–740. https://doi.org/10.1109/18.53734

    Article  Google Scholar 

  10. Cho, J. (2020). Prefix-free code distribution matching for probabilistic constellation shaping. IEEE Transactions on Communications, 68(2), 670–682. https://doi.org/10.1109/TCOMM.2019.2924896

    Article  Google Scholar 

  11. Cho, J., & Winzer, P. (2019). Probabilistic constellation shaping for optical fiber communications. Journal of Lightwave Technology, 37(6), 1590–1607. https://doi.org/10.1109/JLT.2019.2898855

    Article  Google Scholar 

  12. Dong, S., Ji, H., Xu, Z. et al. (2021). Short blocklength distribution matching by linear programming. In 2021 European conference on optical communication (ECOC) (pp. 1–4). https://doi.org/10.1109/ECOC52684.2021.9605859.

  13. Fehenberger, T., Millar, D., Koike-Akino, T., et al. (2019). Multiset-partition distribution matching. IEEE Transactions on Communications, 67(3), 1885–1893. https://doi.org/10.1109/TCOMM.2018.2881091

    Article  Google Scholar 

  14. Fischer, R. F. H. (2005). Precoding and signal shaping for digital transmission. Hoboken: Wiley-IEEE Press. https://doi.org/10.1002/0471439002

    Book  Google Scholar 

  15. Forney, G., & Wei, L. F. (1989). Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations. IEEE Journal on Selected Areas in Communications, 7(6), 877–892. https://doi.org/10.1109/49.29611

    Article  Google Scholar 

  16. Forney, G., Gallager, R., Lang, G., et al. (1984). Efficient modulation for band-limited channels. IEEE Journal on Selected Areas in Communications, 2(5), 632–647. https://doi.org/10.1109/JSAC.1984.1146101

    Article  Google Scholar 

  17. Gallager, R. (1972). Information theory and reliable communication. Hoboken: Wiley. https://doi.org/10.1007/978-3-7091-2945-6

    Book  Google Scholar 

  18. Gültekin, Y., van Houtum, W., Şerbetli, S., et al. (2017). Constellation shaping for IEEE 802.11. In 2017 IEEE 28th annual international symposium on personal, indoor, and mobile radio communications (PIMRC) (pp. 1–7). https://doi.org/10.1109/PIMRC.2017.8292338.

  19. Gültekin, Y., van Houtum, W., & Willems, F. (2018). On constellation shaping for short block lengths. In L. Spreeuwers & J. Goseling (Eds.), Proceedings of the 2018 symposium on information theory and signal processing in the Benelux (pp. 86–96). Enschede: Twente University.

    Google Scholar 

  20. Gültekin, Y., Willems, F., van Houtum, W., et al. (2018). Approximate enumerative sphere shaping. In 2018 IEEE international symposium on information theory (ISIT) (pp. 676–680). https://doi.org/10.1109/ISIT.2018.8437623.

  21. Gültekin, Y., Fehenberger, T., Alvarado, A., et al. (2020). Probabilistic shaping for finite blocklengths: distribution matching and sphere shaping. Entropy. https://doi.org/10.3390/e22050581

    Article  Google Scholar 

  22. Gültekin, Y., van Houtum, J., Koppelaar, W. A., et al. (2020). Enumerative sphere shaping for wireless communications with short packets. IEEE Transactions on Wireless Communications, 19(2), 1098–1112. https://doi.org/10.1109/TWC.2019.2951139

    Article  Google Scholar 

  23. Iqbal, S., Yankov, M., & Forchhammer, S. (2018). Rate-adaptive polar-coded constellation shaping for flexible optical networks. In 2018 European conference on optical communication (ECOC) (pp. 1–3). https://doi.org/10.1109/ECOC.2018.8535280.

  24. Iqbal, S., Yankov, M., & Forchhammer, S. (2019). Rate-adaptive probabilistic shaping enabled by punctured polar codes with pre-set frozen bits. In 2019 Optical fiber communications conference and exhibition (OFC) (pp. 1–3). https://doi.org/10.1364/OFC.2019.M4B.1.

  25. İşcan, O., Böhnke, R., & Xu, W. (2018). Probabilistically shaped multi-level coding with polar codes for fading channels. In 2018 IEEE Globecom workshops (GC Wkshps) (pp. 1–5). https://doi.org/10.1109/GLOCOMW.2018.8644197.

  26. İşcan, O., Böhnke, R., & Xu, W. (2020). Sign-bit shaping using polar codes. Transactions on Emerging Telecommunications Technologies, 31(10), e4058. https://doi.org/10.1002/ett.4058

    Article  Google Scholar 

  27. ITU-R. (2019). Propagation data required for the design systems in the land mobile-satellite service. Recommendation ITU-R, P.681-11, 2019.

  28. Kschischang, F., & Pasupathy, S. (1993). Optimal nonuniform signaling for Gaussian channels. IEEE Transactions on Information Theory, 39(3), 913–929. https://doi.org/10.1109/18.256499

    Article  Google Scholar 

  29. Laroia, R., Farvardin, N., & Tretter, S. (1994). On optimal shaping of multidimensional constellations. IEEE Transactions on Information Theory, 40(4), 1044–1056. https://doi.org/10.1109/18.335969

    Article  Google Scholar 

  30. Liu, L., Yan, Y., Ling, C., et al. (2019). Construction of capacity-achieving lattice codes: Polar lattices. IEEE Transactions on Communications, 67(2), 915–928. https://doi.org/10.1109/TCOMM.2018.2876113

    Article  Google Scholar 

  31. Mahdavifar, H., El-Khamy, M., Lee, J., et al. (2016). Polar coding for bit-interleaved coded modulation. IEEE Transactions on Vehicular Technology, 65(5), 3115–3127. https://doi.org/10.1109/TVT.2015.2443772

    Article  Google Scholar 

  32. Matsumine, T., Koike-Akino, T., Millar, D., et al. (2019). Polar-coded modulation for joint channel coding and probabilistic shaping. In 2019 optical fiber communications conference and exhibition (OFC) (pp. 1–3). https://doi.org/10.1364/OFC.2019.M4B.2.

  33. Prinz, T., Yuan, P., Böcherer, G., et al. (2017). Polar coded probabilistic amplitude shaping for short packets. In 2017 IEEE 18th international workshop on signal processing advances in wireless communications (SPAWC) (pp. 1–5). https://doi.org/10.1109/SPAWC.2017.8227653.

  34. Runge, C., Wiegart, T., Lentner, D., et al. (2022). Multilevel binary polar-coded modulation achieving the capacity of asymmetric channels. In 2022 IEEE international symposium on information theory (ISIT) (pp. 2595–2600). https://doi.org/10.1109/ISIT50566.2022.9834740.

  35. Schulte, P., & Böcherer, G. (2016). Constant composition distribution matching. IEEE Transactions on Information Theory, 62(1), 430–434. https://doi.org/10.1109/TIT.2015.2499181

    Article  Google Scholar 

  36. Schulte, P., & Steiner, F. (2019). Divergence-optimal fixed-to-fixed length distribution matching with shell mapping. IEEE Wireless Communications Letters, 8(2), 620–623. https://doi.org/10.1109/LWC.2018.2890595

    Article  Google Scholar 

  37. Seidl, M., Schenk, A., Stierstorfer, C., et al. (2013). Polar-coded modulation. IEEE Transactions on Communications, 61, 4108–4119. https://doi.org/10.1109/TCOMM.2013.090513.130433

    Article  Google Scholar 

  38. Tal, I., & Vardy, A. (2015). List decoding of polar codes. IEEE Transactions on Information Theory, 61(5), 2213–2226. https://doi.org/10.1109/TIT.2015.2410251

    Article  Google Scholar 

  39. Tavildar, S. (2017). Bit-permuted coded modulation for polar codes. In 2017 IEEE wireless communications and networking conference workshops (WCNCW) (pp. 1–6). https://doi.org/10.1109/WCNCW.2017.7919038.

  40. Trifonov, P. (2012). Efficient design and decoding of polar codes. IEEE Transactions on Communications, 60(11), 3221–3227. https://doi.org/10.1109/TCOMM.2012.081512.110872

    Article  Google Scholar 

  41. Vangala, H., Viterbo, E., & Hong, Y. (2015). A comparative study of polar code constructions for the awgn channel. https://arxiv.org/abs/1501.02473. arXiv:1501.02473.

  42. Wachsmann, U., Fischer, R., & Huber, J. (1999). Multilevel codes: Theoretical concepts and practical design rules. IEEE Transactions on Information Theory, 45(5), 1361–1391. https://doi.org/10.1109/18.771140

    Article  Google Scholar 

  43. Wang, L., Song, D., Areces, F., et al. (2023). Probabilistic shaping for trellis-coded modulation with CRC-aided list decoding. IEEE Transactions on Communications, 71(3), 1271–1283. https://doi.org/10.1109/TCOMM.2023.3237263

    Article  Google Scholar 

  44. Willems, F., & Wuijts, J. (1993). A pragmatic approach to shaped coded modulation. In Proceedings of the IEEE 1st symposium on communications and vehicular technology.

  45. Wu, B., Niu, K., & Dai, J. (2023). Conditional entropy-based construction of multilevel polar-coded modulation with probabilistic shaping. IEEE Communications Letters, 27(5), 1262–1266. https://doi.org/10.1109/LCOMM.2023.3254214

  46. Yuan, P., Böcherer, G., Schulte, P., et al. (2020). Error detection using symbol distribution in a system with distribution matching and probabilistic amplitude shaping. Patent, US 10,880,037 B2.

  47. Zhang, D., Wu, B., & Niu, K. (2021). Path metric inherited SCL decoding of multilevel polar-coded systems. In 2021 IEEE wireless communications and networking conference workshops (WCNCW) (pp. 1–6). https://doi.org/10.1109/WCNCW49093.2021.9420011.

  48. Zhou, D., Niu, K., Dong, C. (2016). Constellation shaping for bit-interleaved polar coded-modulation. In 2016 IEEE 27th annual international symposium on personal, indoor, and mobile radio communications (PIMRC) (pp. 1–5). https://doi.org/10.1109/PIMRC.2016.7794697.

Download references

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Author information

Author notes

  1. Danish Ilyas and Rongke Liu have contributed equally to this work.

Authors and Affiliations

  1. School of Electronic and Information Engineering, Beihang University, Xue Yuan, Beijing, 100091, Beijing, China

    Danish Ilyas & Rongke Liu

  2. Department of Electrical Engineering, National University of Sciences and Technology, H-12, Islamabad, Islamabad, 44000, Pakistan

    Danish Ilyas, Abdul Wakeel & Mir Yasir Umair

Authors
  1. Danish Ilyas
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Rongke Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Abdul Wakeel
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Mir Yasir Umair
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

All authors contributed to the study conception and design. DI performed the conceptualization. Formal analysis and investigation were performed by DI and AW together. The first draft of the manuscript was written by DI, review and editing was done by MYU and all authors commented on previous versions of the manuscript. The supervision and funding acquisition was done by RL All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Danish Ilyas or Rongke Liu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ilyas, D., Liu, R., Wakeel, A. et al. Polar coded probabilistic amplitude shaping for non-terrestrial networks in 5G. Telecommun Syst 88, 39 (2025). https://doi.org/10.1007/s11235-024-01232-4

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11235-024-01232-4

Keywords