Skip to main content

Neural Successive Cancellation Flip Decoding of Polar Codes

Abstract

Dynamic successive cancellation flip (DSCF) decoding of polar codes is a powerful algorithm that can achieve the error correction performance of successive cancellation list (SCL) decoding, with an average complexity that is close to that of successive cancellation (SC) decoding at practical signal-to-noise ratio (SNR) regimes. However, DSCF decoding requires costly transcendental computations to calculate a bit-flipping metric, which adversely affect its implementation complexity. In this paper, we first show that a direct application of common approximation schemes on the conventional DSCF decoding results in a significant error-correction performance loss. We then introduce an additive perturbation parameter and propose an approximation scheme which completely removes the need to perform transcendental computations in DSCF decoding. Machine learning (ML) techniques are then utilized to optimize the perturbation parameter of the proposed scheme. Furthermore, a quantization scheme is developed to enable efficient hardware implementation. Simulation results show that when compared with DSCF decoding, the proposed decoder with quantization scheme only experiences a negligible error-correction performance degradation of less that 0.08 dB at a target frame-error-rate (FER) of 10− 4, for a polar code of length 512 with 256 information bits. In addition, the bit-flipping metric computation of the proposed decoder reduces up to around 31% of the number of additions used by the bit-flipping metric computation of DSCF decoding, without any need to perform costly transcendental computations and multiplications.

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Notes

  1. Since the channel output y is directly used in this paper as the decoding input, we set \(\alpha = \frac {0.6}{\sigma ^{2}}\) to obtain the same FER performance of the DSCF decoder in [5].

  2. We manually implement the computations in (20)-(33) instead of using the built-in automatic differentiation mechanism and SGD-based optimizers supported by Pytorch. The main purpose of using Pytorch is to make use of its GPU support to reduce the training time.

References

  1. 3GPP. (2018). Multiplexing and channel coding (Release 10) 3GPP TS 21.101 v10.4.0. http://www.3gpp.org/ftp/Specs/2018-09/Rel-10/21_series/21101-a40.zip.

  2. Afisiadis, O., Balatsoukas-Stimming, A., & Burg, A. (2014). A low-complexity improved successive cancellation decoder for polar codes. In 48Th asilomar conference on signals, systems, and computers (pp. 2116–2120), DOI https://doi.org/10.1109/ACSSC.2014.7094848.

  3. Arıkan, 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.

    MathSciNet  Article  MATH  Google Scholar 

  4. Balatsoukas-Stimming, A., Parizi, M.B., & Burg, A. (2015). LLR-Based successive cancellation list decoding of polar codes. IEEE Transactions on Signal Processing, 63 (19), 5165–5179. https://doi.org/10.1109/TSP.2015.2439211.

    MathSciNet  Article  MATH  Google Scholar 

  5. Chandesris, L., Savin, V., & Declercq, D. (2018). Dynamic-SCFlip decoding of polar codes. IEEE Transactions on Communications, 66(6), 2333–2345. https://doi.org/10.1109/TCOMM.2018.2793887.

    Article  Google Scholar 

  6. Condo, C., Ercan, F., & Gross, W.J. (2018). Improved successive cancellation flip decoding of polar codes based on error distribution. In IEEE wireless communications and networking conference workshops (pp. 19–24), DOI https://doi.org/10.1109/WCNCW.2018.8368991.

  7. Doan, N., Hashemi, S.A., Ercan, F., Tonnellier, T., & Gross, W.J. (2019). Neural dynamic successive cancellation flip decoding of polar codes. In IEEE international workshop on signal processing systems (pp. 272–277), DOI https://doi.org/10.1109/SiPS47522.2019.9020513.

  8. Doan, N., Hashemi, S.A., Mambou, E.N., Tonnellier, T., & Gross, W.J. (2019). Neural belief propagation decoding of CRC-polar concatenated codes. In IEEE international conference on communications (pp. 1–6), DOI https://doi.org/10.1109/ICC.2019.8761399.

  9. Ercan, F., Condo, C., & Gross, W.J. (2019). Improved bit-flipping algorithm for successive cancellation decoding of polar codes. IEEE Transactions on Communications, 67(1), 61–72. https://doi.org/10.1109/TCOMM.2018.2873322.

    Article  Google Scholar 

  10. Ercan, F., Condo, C., Hashemi, S.A., & Gross, W.J. (2017). On error-correction performance and implementation of polar code list decoders for 5g. In 2017 55th annual allerton conference on communication, control, and computing (allerton) (pp. 443–449), DOI https://doi.org/10.1109/ALLERTON.2017.8262771.

  11. Ercan, F., Condo, C., Hashemi, S.A., & Gross, W.J. (2018). Partitioned successive-cancellation flip decoding of polar codes. In IEEE international conference on communications (pp. 1–6), DOI https://doi.org/10.1109/ICC.2018.8422464.

  12. Han, S., Mao, H., & Dally, W.J. (2016). Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. International Conference on Learning Representative, arXiv:1510.00149.

  13. Hashemi, S.A., Condo, C., Ercan, F., & Gross, W.J. (2017). Memory-efficient polar decoders. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 7(4), 604–615. https://doi.org/10.1109/JETCAS.2017.2764421.

    Article  Google Scholar 

  14. Hashemi, S.A., Condo, C., & Gross, W.J. (2017). Fast and flexible successive-cancellation list decoders for polar codes. IEEE Transactions on Signal Processing, 65(21), 5756–5769. https://doi.org/10.1109/TSP.2017.2740204.

    MathSciNet  Article  MATH  Google Scholar 

  15. Hinton, G., Srivastava, N., & Swersky, K. (2012). Neural networks for machine learning lecture 6a overview of mini-batch gradient descent http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf.

  16. Krizhevsky, A., Sutskever, I., & Hinton, G.E. (2012). Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems (pp. 1097–1105).

  17. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436.

    Article  Google Scholar 

  18. 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(2), 289–299. https://doi.org/10.1109/TSP.2012.2223693.

    MathSciNet  Article  MATH  Google Scholar 

  19. Nachmani, E., Marciano, E., Lugosch, L., Gross, W.J., Burshtein, D., & Be’ery, Y. (2018). Deep learning methods for improved decoding of linear codes. IEEE Journal of Selected Topics in Signal Processing, 12(1), 119–131. https://doi.org/10.1109/JSTSP.2017.2788405.

    Article  Google Scholar 

  20. Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., & Lerer, A. (2017). Automatic differentiation in pytorch.

  21. Ryan, W., & Lin, S. (2009). Channel codes: classical and modern. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  22. 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.

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nghia Doan.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Doan, N., Hashemi, S.A., Ercan, F. et al. Neural Successive Cancellation Flip Decoding of Polar Codes. J Sign Process Syst 93, 631–642 (2021). https://doi.org/10.1007/s11265-020-01599-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11265-020-01599-y

Keywords

  • 5G
  • Polar codes
  • Deep learning
  • SC flip