Polar Codes: Survey of Approaches and Research Directions
DOI: 10.21293/1818-0442-2025-28-3-14-26
Abstract: The authors examine modern methods for improving and adapting polar codes, a class of error-correcting codes with a theoretically proven ability to approach the Shannon limit. Polar codes were standardized in 5G NR for control channels and are considered a promising candidate for 6G communication systems owing to their high efficiency, flexibility, and scalability. The paper concisely outlines the fundamental principles of polar code construction, including the channel polarization process and basic decoding algorithms. Particular attention is paid to implementation in the 5G specifications, including segmentation, Cyclic Redundancy Check (CRC) attachment, interleaving, and rate matching. We then review current directions in the development of polar codes: advanced decoding schemes, including belief-propagation and fast simplified successive cancellation (Fast-SSC); multi-kernel–based codes; adaptation to multipath/fading channel conditions; and neural-network–based approaches aimed at optimizing decoders and code design for specific transmission scenarios. Finally, we discuss the surveyed methods, existing challenges and open problems, as well as the prospects for the further development of polar codes in the context of future wireless communication system requirements.
Keywords: 5G, 6G, SC, SCL, decoding, communication systems, multipath channels, multi-kernel architectures, polarization, polar codes
Funding: The study was supported by a grant from the Russian Science Foundation No. 24-29-00172, https://rscf.ru/project/24-29-00172/.
For citation:
Shalin G. N., Pokamestov D. A., Kryukov Ya. V., Shinkevich A. S., Eremeev S. A., Ilinskiy D. E. Polar Codes: Survey of Approaches and Research Directions. Doklady Tomskogo gosudarstvennogo universiteta sistem upravleniya i radioelektroniki, 2025, vol. 28, no. 3, pp. 14–26. DOI: 10.21293/1818-0442-2025-28-3-14-26
Authors and copyright holders:
- Shalin G. N. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- Pokamestov D. A. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- Kryukov Ya. V. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- Shinkevich A. S. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- Eremeev S. A. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- Ilinskiy D. E. , Tomsk State University of Control Systems and Radioelectronics (Tomsk, Russia)
- 1. Arikan E. A performance comparison of polar codes and Reed-Muller codes. IEEE Communications Letters, 2008, vol. 12, no. 6, pp. 447–449.
- 2. Arikan E. Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on information Theory, 2009, vol. 55, no. 7, pp, 3051–3073.
- 3. Dong Y., Dai J., Niu K., Wang S. Yuan Joint sourcechannel coding for 6G communica-tions. China Communications, 2022, vol. 19, no. 3, pp. 101–115.
- 4. Kasi S., Kaewell J., Jamieson K. A quantum annealerenabled decoder and hardware topology for nextg wireless polar codes. IEEE Transactions on Wireless Communications, 2023, vol. 23, no. 4, pp. 3780–3794.
- 5. Niu K., Zhang P., Dai J., Si Zh., Dong Ch. A golden decade of polar codes: From basic principle to 5G applications. China Communications, 2023, vol. 20 no. 2, pp. 94–121.
- 6. Kumar N., Kedia D., Purohit G. A review of channel coding schemes in the 5G standard. Tele-communication Systems, 2023 vol. 83, no. 4, pp. 423–448.
- 7. Pedarsani R. Polar Codes: Construction and Performance Analysis. Swiss Federal Institute of Technology (EPFL), 2011, pp. 48.
- 8. Chen K., Niu K., Lin J. R. List successive cancellation decoding of polar codes. Electron. Lett., 2012, vol. 48, no. 9, pp. 500–501.
- 9. Niu K., Chen K. Stack decoding of polar codes. Electronics letters, 2012, vol. 48, no. 12, pp. 695–697.
- 10. Tal I., Vardy A. List Decoding of Polar Codes. IEEE Transactions on Information Theory, 2015, vol. 61, no. 5, pp. 2213–2226.
- 11. Shen Y., Zhou W., Huang Y., Zhang Z., You X., Zhang Ch. Fast iterative soft-output list decoding of polar codes. IEEE Transactions on Signal Processing, 2022, vol. 70, pp. 1361–1376.
- 12. Sun H., Viterbo E., Dai B., Liu R. Fast decoding of polar codes for digital broadcasting services in 5G. IEEE Transactions on Broadcasting, 2024, vol. 70, no. 2, pp. 731–738.
- 13. Ren Y., Shen Y., Zhang L., Kristensen A.T. Highthroughput and flexible belief propagation list decoder for polar codes. IEEE Transactions on Signal Processing, 2024, vol. 72, pp. 1158–1174.
- 14. 3GPP TS 38.212 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; NR; Multiplexing and channel coding (Release 16) V16.0.0 (2019-12). Available at: https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3214 (Аccessed: 13 May 2025).
- 15. Bioglio V., Condo C., Land I. Design of polar codes in 5G new radio. IEEE Communications Sur-veys & Tutorials, 2020, vol. 23, no. 1, pp. 29–40.
- 16. Niu K., Chen K. CRC-aided decoding of polar codes. IEEE Communications Letters, 2012, vol. 16, no. 10, pp. 1668–1671.
- 17. Ali M. H., Al-Rubaye G. A. Performance Evaluation of 5G New Radio Polar Code over Different Multipath Fading Channel Models. International Journal of Intelligent Engineering & Systems, 2024, vol. 17, no. 2.
- 18. Shar-ma A., Salim M. Polar code: The channel code contender for 5G scenarios. 2017 International conference on computer, communications and electronics (Comptelix). IEEE. Jaipur, India, 2017, pp. 676–682.
- 19. Bioglio V., Gabry F., Land I., Belfiore J. Minimumdistance based construction of multi-kernel polar codes. GLOBECOM 2017-2017 IEEE Global Communications Conference IEEE. Singapore, 2017, pp. 1–6.
- 20. Bioglio V., Gabry F., Land I., Belfiore J. Multi-kernel polar codes: Concept and design principles. IEEE Transactions on Communications, 2020, vol. 68, no. 9, pp. 5350–5362.
- 21. Hassani S.H., Alishahi K., Urbanke R.L. Finitelength scaling for polar codes. IEEE Transactions on Information Theory, 2014, vol. 60, no. 10, pp. 5875–5898.
- 22. Guruswami V., Xia P. Polar codes: Speed of polarization and polynomial gap to capacity. IEEE Transactions on Information Theory, 2014, vol. 61, no. 1, pp. 3–16.
- 23. Mori R., Tanaka T. Non-binary polar codes using reed-solomon codes and algebraic geometry codes. in Proc. IEEE ITW. Cairo, Egypt, 2010. pp. 1–5.
- 24. Mori R., Tanaka T. Channel polarization on q-ary discrete memoryless channels by arbitrary kernels. in Proc. IEEE ISIT. Austin, TX, USA, 2010, pp. 894–898.
- 25. Cheng N., Zhang R., Ge Y., Shi W., Zhang Q., Shen X. Encoder and list decoder of Reed-Solomon kernel based polar codes. in Proc. IEEE WCSP. Yangzhou, China, 2016, pp. 1–6.
- 26. Trifonov P. Binary successive cancellation decoding of polar codes with Reed-Solomon kernel. in Proc. IEEE ISIT. Honolulu, HI, USA, 2014.
- 27. Zhao J., Zhang W., Liu Y. An Efficient Construction Method Based on Partial Distance of Polar Codes with ReedSolomon Kernel. IEEE Transactions on Communications, 2024.
- 28. Coppolino G., Condo C., Masera G., Gross W.J. A multi-kernel multi-code polar decoder architecture. IEEE Transactions on Circuits and Systems I: Regular Papers, 2018, vol. 65, no. 12, pp. 4413–4422.
- 29. Giard P., Balatsoukas-Stimming A., Sarkis G., Thibeault C., Gross W.J. Fast Low-Complexity Decoders for Low-Rate Polar Codes. Journal of Signal Processing Systems, 2018, vol. 90, no. 5, pp. 675–685.
- 30. Rezaei H., Rajatheva N., Latva-Aho M. Low-latency multi-kernel polar decoders. IEEE Access, 2022, vol. 10, pp. 119460–119 474.
- 31. Chen P., Bai B., Ma X. Nonbinary polar coding with low decoding latency and complexity. Journal of Information and Intelligence, 2023, vol. 1, no. 1, pp. 36–53.
- 32. Rezaei H., Rajatheva N., Latva-Aho M. Highthroughput rate-flexible combina-tional decoders for multi-kernel polar codes. IEEE Transactions on Circuits and Systems I: Regular Papers, 2023.
- 33. Trifonov P. Design of polar codes for rayleigh fading channel. International Symposium on Wireless Communication Systems (ISWCS). IEEE. Brussels, Belgium, 2015, pp. 331–335.
- 34. Zhou D., Niu K., Dong C. Construction of polar codes in rayleigh fading channel. IEEE Com-munications Letters, 2019, vol. 23, no. 3, pp. 402–405.
- 35. Niu K, Li Y. Polar codes for fast fading channel: Design based on polar spectrum. IEEE Transactions on Vehicular Technology, 2020, vol. 69, no. 9, pp. 10103–10114.
- 36. Pokamestov D., Kryukov Y., Rogozhnikov E., Shalin G., Shimkevich A., Novichkov S. Adaptation of signal with NOMA and polar codes to the Rayleigh channel. Symmetry, 2022, vol. 14, no. 10, pp. 2103.
- 37. Shalin G., Pokamestov D., Kryukov Y., Shinkevich A., Eremeev S., Ilinskiy D. Adaptation of Polar Codes to Enhance BER Performance in Next-Generation Communication Systems. 2025 IEEE 26th International Conference of Young Professionals in Electron Devices and Materials (EDM). IEEE. Altai, Russian Federation, 2025, pp. 330–333.
- 38. Wang C.X., You X., Gao X., Zhu X., Li Z., Zhang Ch., Wang H., Huang Y., Chen Y., Haas H., Thompson J.S., Larsson E.G., Renzo M.D., Tong W., Zhu P., Shen X., Poor H.V., Hanzo L. On the road to 6G: Visions, requirements, key technologies, and testbeds. // IEEE Communications Surveys & Tutorials, 2023, vol. 25, no. 2, pp. 905–974.
- 39. Banafaa M., Shayea I., Din J., Azmi M.H., Alash-bi A., Daradkeh Y. I., Alhammadi A. 6G mobile communication technology: Requirements, targets, applications, challenges, advantages, and opportunities. Alexandria Engineering Journal, 2023, vol. 64, pp. 245–274.
- 40. Pokamestov D., Kryukov Y., Abenov R., Rogozh-nikov E., Brovkin A., Shinkevich A., Shalin G. 6G communication systems: concept, trends, physical level technologies. Radiotehnika i èlektronika, 2024, vol. 69, no. 1, pp. 3–33.
- 41. Arıkan E. From sequential decoding to channel polarization and back again. IEEE Information Theory Society Newsletter, 2019, pp. 10.
- 42. Rowshan M., Qiu M., Xie Y., Gu X., Yuan J. Channel coding toward 6G: Technical overview and outlook. IEEE Open Journal of the Communications Society, 2024, vol. 5, pp. 2585–2685.
- 43. Gu X., Rowshan M., Yuan J. Selective reverse PAC coding for sphere decoding. Information Theory, 2022, pp. 5.
- 44. Gu X., Rowshan M., Yuan J. Improved convolutional precoder for PAC codes. GLOBECOM 2023-2023 IEEE Global Communications Conference. IEEE. Kuala Lumpur, Malaysia, 2023, pp. 1836–1841.
- 45. Rowshan M., Burg A., Viterbo E. Polarization-adjust-ed convolutional (PAC) codes: Sequential decoding vs list decoding. IEEE Transactions on Vehicular Technology, 2021, vol. 70, no. 2, pp. 1434–1447.
- 46. Yao H., Fazeli A., Vardy A. List decoding of Arıkan’s PAC codes. Entropy, 2021, vol. 23, no. 7, pp. 841.
- 47. Zhang X., Jiang M., Zhu M., Liu K., Zhao Ch. CRCaided adaptive BP decoding of PAC codes. Entropy, 2022, vol. 24, no. 8, pp. 1170.
- 48. Shen L., Wu Y., Xu Y., You X., Gao X., Zhang W. GLDPC-PC Codes: Channel Coding Toward 6G Communications. IEEE Communications Magazine, 2025.
- 49. Adel M., El Ramly S. Abdelhamid B. Adaptive Transmission Based On Polar Code And Hierarchical Modulation For Future Wireless Communications. IEEE Access, 2024.
- 50. Huang L., Zhang H., Li R., Ge Y., Wang J. AI coding: Learning to construct error correction codes. IEEE Transactions on Communications, 2019, vol. 68, no. 1, pp. 26–39.
- 51. Huang L., Zhang H., Li R., Ge Y., Wang J. Reinforcement learning for nested polar code construction. 2019 IEEE Global Communications Conference (GLOBECOM). Waikoloa, HI, USA, 2019, pp. 1–6.
- 52. Liao Y., Hashemi S.A., Cioffi J. M., Goldsmith A. Construction of polar codes with reinforcement learning. IEEE Transactions on Communications, 2021, vol. 70, no. 1, pp. 185–198.
- 53. Leonardon M., Gripon V. Using deep neural networks to predict and improve the performance of polar codes. 2021 11th International Symposium on Topics in Coding (ISTC). IEEE. Montreal, QC, Canada, 2021. pp. 1–5.
- 54. Liao Y., Hashemi S. A., Yang H., Cioffi J. M. Scalable polar code construction for successive cancellation list decoding: A graph neural network-based approach. IEEE Transactions on Communications, 2023, vol. 71, no. 11, pp. 6231–6245.
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