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High-Speed Decoders for Polar Codes pp 1–13Cite as

Polar Codes

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Abstract

This chapter reviews polar codes, their construction, representations, and encoding and decoding algorithms. It also briefly goes over results for the state-of-the-art decoder implementations from the literature.

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References

  1. Alamdar-Yazdi, A., Kschischang, F.R.: A simplified successive-cancellation decoder for polar codes. IEEE Commun. Lett. 15(12), 1378–1380 (2011). DOI 10.1109/LCOMM.2011.101811.111480

    Article  Google Scholar 

  2. Arıkan, E.: Channel polarization: A method for constructing capacity-achieving codes. In: IEEE Int. Symp. on Inf. Theory (ISIT), pp. 1173–1177 (2008). DOI 10.1109/ISIT.2008.4595172

    Google Scholar 

  3. Arıkan, E.: Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009). DOI 10. 1109/TIT.2009.2021379

    Google Scholar 

  4. Arıkan, E.: Systematic polar coding. IEEE Commun. Lett. 15(8), 860–862 (2011). DOI 10.1109/LCOMM.2011.061611.110862

    Article  Google Scholar 

  5. Goela, N., Korada, S.B., Gastpar, M.: On lp decoding of polar codes. In: IEEE Inf. Theory Workshop (ITW), pp. 1–5 (2010). DOI 10.1109/ CIG.2010.5592698

    Google Scholar 

  6. Hussami, N., Urbanke, R., Korada, S.B.: Performance of polar codes for channel and source coding. In: IEEE Int. Symp. on Inf. Theory (ISIT), pp. 1488–1492 (2009). DOI 10.1109/ISIT.2009.5205860

    Google Scholar 

  7. Kahraman, S., Çelebi, M.E.: Code based efficient maximum-likelihood decoding of short polar codes. In: IEEE Int. Symp. on Inf. Theory (ISIT), pp. 1967–1971 (2012). DOI 10.1109/ISIT.2012.6283643

    Google Scholar 

  8. Leroux, C., Raymond, A., Sarkis, G., Gross, W.: A semi-parallel successive-cancellation decoder for polar codes. IEEE Trans. Signal Process. 61(2), 289–299 (2013). DOI 10.1109/TSP.2012.2223693

    Article  MathSciNet  Google Scholar 

  9. Leroux, C., Raymond, A.J., Sarkis, G., Tal, I., Vardy, A., Gross, W.J.: Hardware implementation of successive-cancellation decoders for polar codes. J. Signal Process. Syst. 69(3), 305–315 (2012). DOI 10.1007/ s11265-012-0685-3

    Article  Google Scholar 

  10. Leroux, C., Tal, I., Vardy, A., Gross, W.J.: Hardware architectures for successive cancellation decoding of polar codes. In: IEEE Int. Conf. on Acoust., Speech and Signal Process. (ICASSP), pp. 1665–1668 (2011). DOI 10.1109/ICASSP.2011.5946819

    Google Scholar 

  11. Li, B., Shen, H., Tse, D., Tong, W.: Low-latency polar codes via hybrid decoding. In: Int. Symp. on Turbo Codes and Iterative Inf. Process. (ISTC), pp. 223–227 (2014). DOI 10.1109/ISTC.2014.6955118

    Google Scholar 

  12. Li, Y., Alhussien, H., Haratsch, E., Jiang, A.: A study of polar codes for MLC NAND flash memories. In: Int. Conf. on Comput., Netw. and Commun. (ICNC), pp. 608–612 (2015). DOI 10.1109/ICCNC.2015. 7069414

    Google Scholar 

  13. Mishra, A., Raymond, A., Amaru, L., Sarkis, G., Leroux, C., Meinerzhagen, P., Burg, A., Gross, W.: A successive cancellation decoder ASIC for a 1024-bit polar code in 180nm CMOS. In: IEEE Asian Solid State Circuits Conf. (A-SSCC), pp. 205–208 (2012). DOI 10.1109/IPEC. 2012.6522661

    Google Scholar 

  14. Pamuk, A., Arıkan, E.: A two phase successive cancellation decoder architecture for polar codes. In: IEEE Int. Symp. on Inf. Theory (ISIT), pp. 1–5 (2013). DOI 10.1109/ISIT.2013.6620368

    Google Scholar 

  15. Raymond, A.J.: Design and hardware implementation of decoder architectures for polar codes. Master’s thesis, McGill University (2014)

    Google Scholar 

  16. Raymond, A.J., Gross, W.J.: Scalable successive-cancellation hardware decoder for polar codes. In: IEEE Glob. Conf. on Signal and Inf. Process. (GlobalSIP), pp. 1282–1285 (2013). DOI 10.1109/GlobalSIP. 2013.6737143

    Google Scholar 

  17. Sarkis, G.: Efficient encoders and decoders for polar codes: Algorithms and implementations. Ph.D. thesis, McGill University (2016)

    Google Scholar 

  18. Sarkis, G., Giard, P., Vardy, A., Thibeault, C., Gross, W.J.: Fast polar decoders: Algorithm and implementation. IEEE J. Sel. Areas Commun. 32(5), 946–957 (2014). DOI 10.1109/JSAC.2014.140514

    Article  Google Scholar 

  19. Sarkis, G., Gross, W.J.: Increasing the throughput of polar decoders. IEEE Commun. Lett. 17(4), 725–728 (2013). DOI 10.1109/LCOMM. 2013.021213.121633

    Article  Google Scholar 

  20. Sarkis, G., Tal, I., Giard, P., Vardy, A., Thibeault, C., Gross, W.J.: Flexible and low-complexity encoding and decoding of systematic polar codes. IEEE Trans. Commun. 64(7), 2732–2745 (2016). DOI 10.1109/ TCOMM.2016.2574996

    Article  Google Scholar 

  21. Tal, I., Vardy, A.: How to construct polar codes. IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013). DOI 10.1109/TIT.2013.2272694

    Article  MathSciNet  MATH  Google Scholar 

  22. Tal, I., Vardy, A.: List decoding of polar codes. IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015). DOI 10.1109/TIT.2015.2410251

    Article  MathSciNet  MATH  Google Scholar 

  23. Yuan, B., Parhi, K.: Low-latency successive-cancellation polar decoder architectures using 2-bit decoding. IEEE Trans. Circuits Syst. I 61(4), 1241–1254 (2014). DOI 10.1109/TCSI.2013.2283779

    Article  Google Scholar 

  24. Yuan, B., Parhi, K.K.: Early stopping criteria for energy-efficient low-latency belief-propagation polar code decoders. IEEE Trans. Signal Process. 62(24), 6496–6506 (2014). DOI 10.1109/TSP.2014.2366712

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Electrical Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, VD, Switzerland

    Pascal Giard

  2. Department of Electrical Engineering, École de Technologie Supérieure, Montréal, QC, Canada

    Claude Thibeault

  3. Department of Electrical and Computer Engineering, McGill University, Montréal, QC, Canada

    Warren J. Gross

Authors
  1. Pascal Giard
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  2. Claude Thibeault
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  3. Warren J. Gross
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Giard, P., Thibeault, C., Gross, W.J. (2017). Polar Codes. In: High-Speed Decoders for Polar Codes. Springer, Cham. https://doi.org/10.1007/978-3-319-59782-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-59782-9_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59781-2

  • Online ISBN: 978-3-319-59782-9

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