Performance Analysis of Bit-Interleaved Polar Coded Modulation

  • Kun Zhao
  • Yong Liu
  • Haiqing DuEmail author
  • Baoku Yuan


Polar codes have been applied to the construction of bit-interleaved polar coded modulation schemes in recent years. Bit-interleaved polar coded modulation schemes consist of the concatenation of multi-order modulation and polar codes. The structure of polar codes has some similar features to bit-interleaved coded modulation schemes. This similar features motivate us to transform the concatenated transmission schemes into a universal equivalent channel model, which consists of independent parallel channels, through considering polar coding and modulation synthetically in practical applications. We also propose a general polar codes constructing algorithm to design the constituent polar codes for the equivalent channel model. Then we employ a bijective mapper to accomplish the modulation i.e., binary address mapping, from coded bits to signals in constellation with Gray labeling or set partition labeling rule in different order modulations. We analyze and compare the performance of the equivalent channel model with different order modulations under different decoding algorithms. Simulation results show that the performance of our proposed schemes outperforms that of low-density parity-check codes in WiMAX standard and Turbo codes.


Bit-interleaved coded modulation Polar codes Equivalent channel model Polar codes constructing algorithm 



Manuscript submitted December 14, 2017. This work was supported by the National Natural Science Foundation of China under Grant 61671073.


  1. 1.
    Ungerboeck, G. (1982). Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory, 28(1), 55–67.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Zehavi, E. (1989). 8-PSK trellis codes on Rayleigh channel. In Proceedings of IEEE military communications conference (pp. 536–540).Google Scholar
  3. 3.
    Caire, G., Taricco, G., & Biglieri, E. (1998). Bit-interleaved coded modulation. IEEE Transactions on Information Theory, 44(3), 927–946.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Arkan, 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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Tal, I., & Vardy, A. (2011). List decoding of polar codes. In Proceedings of IEEE international symposium on information theory (pp. 1–5).Google Scholar
  6. 6.
    MacKay, D. J. C. (1999). Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory, 45, 399–431.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Berrou, C., Glavieux, A., & Thitimajshima, P. (1993). Near Shannon limit error correcting coding and decoding: Turbo-codes. In Proceedings of IEEE international conference on communications (ICC), (Geneva, Switzerland) (Vol. 2, pp. 1064–1070).Google Scholar
  8. 8.
    Leroux, C, Tal, I., Vardy, A., & Gross, W. J. (2011). Hardware architectures for successive cancellation decoding of polar codes. In Proceedings of IEEE international conference on acoustics, speech and signal processing (ICASSP), (pp. 1665–1668).Google Scholar
  9. 9.
    Arikan, E. (2008). A performance comparison of polar codes and Reed–Muller codes. IEEE Communications Letters, 12(6), 447–449.CrossRefGoogle Scholar
  10. 10.
    Arikan, E. (2010). Polar codes: A pipelined implementation. In Proceedings of 4th international symposium broadcasting communications (ISBC), (pp. 11–14).Google Scholar
  11. 11.
    Afser, H., & Tirpan, N. (2014). Bit interleaved polar coded modulation. IEEE wireless communications and networking conference (WCNC), (pp. 480–484).Google Scholar
  12. 12.
    Seidl, M., Schenk, A., Stierstorfer, C., & Huber, J. B. (2013). Polar-coded modulation. IEEE Transactions on Communications, 61(10), 4108–4119.CrossRefGoogle Scholar
  13. 13.
    Shin, D. M., Lim, S. C., & Yang, K. (2012). Mapping selection and code construction for 2m-ary polar coded modulation. IEEE Communications Letters, 16(6), 905–908.CrossRefGoogle Scholar
  14. 14.
    GPP. (2016). Study on new radio access technology physical layer aspects. TR 38.802.Google Scholar
  15. 15.
    Chandesris, L., Savin, V., Declercq, D. (2018). Lasting successive-cancellation based decoders for multilevel polar coded modulation. In IEEE conferences, 2018 25th international conference on telecommunications (ICT), (pp. 264–268).Google Scholar
  16. 16.
    Pottie, G. J., & Taylor, D. P. (1989). Multi-level codes based on partitioning. IEEE Transactions on Information Theory, 35(1), 87–98.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Alvarado, A., Graell i Amat, A., Brannstrom, F., & Agrell, E. (2012). On the equivalence of TCM encoders. In Proceedings of IEEE international symposium on information theory (ISIT), (pp. 2401–2405).Google Scholar
  18. 18.
    Wachsmann, U., Fischer, R. F. H., & Huber, J. B. (1999). Multilevel codes: Theoretical concepts and practical design rules. IEEE Transactions on Information Theory, 45, 1361–1391.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Martinez, A., Guillen, A., Fabregas, I., Caire, G., & Willems, F. (2009). Bit-interleaved coded modulation revisited: A mismatched decoding perspective. IEEE Transactions on Information Theory, 55, 2756–2765.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Martinez, A., & Willems, F. (2006). A coding theorem for bit-interleaved coded modulation. In 27th symposium on information theory in the Benelux (WIC 2006), Noordwijk, the Netherlands.Google Scholar
  21. 21.
    Cover, T. M., & Thomas, J. A. (1991). Elements of information theory (pp. 22–23). New York: Wiley.CrossRefzbMATHGoogle Scholar
  22. 22.
    Trifonov, P., Miloslavskaya, V., & Morozov, R. (2018). Fast sequential decoding of polar codes. Available:
  23. 23.
    Leroux, C., Raymond, A. J., Sarkis, G., & Gross, W. J. (2013). A semi-parallel successive-cancellation decoder for polar codes. IEEE Transactions on Signal Processing, 61(9), 289–299.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Stimming, A. B., Parizi, M. B., & Bury, A. (2015). LLR based successive cancellation list decoding of polar codes. IEEE Transactions on Signal Processing, 63(19), 5165–5179.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Stierstorfer, C., & Fischer, R. F. H. (2007). (Gray) mappings for bit-interleaved coded modulation. In Proceedings of IEEE vehicle technology conference (pp. 1703–1707).Google Scholar
  26. 26.
    Mori, R., & Tanaka, T. (2009). Performance of polar codes with the construction using density evolution. IEEE Communications Letters, 13(7), 519–521.CrossRefGoogle Scholar
  27. 27.
    Wu, D., Li, Y., & Sun, Y. (2014). Construction and block error rate analysis of polar codes over AWGN channel based on Gaussian approximation. IEEE Communication Letters, 18(7), 1099–1102.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Beijing Key Laboratory of Network System Architecture and ConvergenceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Beijing Laboratory of Advanced Information NetworksBeijing University of Posts and TelecommunicationsBeijingChina
  3. 3.School of Information and Communication EngineeringBeijing University of Posts and TelecommunicationsBeijingChina

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