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Efficient stochastic successive cancellation list decoder for polar codes

Abstract

Polar codes are one of the most favorable capacity-achieving codes owing to their simple structures and low decoding complexity. Successive cancellation list (SCL) decoders with large list sizes achieve performances very close to those of maximum-likelihood (ML) decoders. However, hardware cost is a severe problem because an SCL decoder with list size L consists of L copies of a successive cancellation (SC) decoder. To address this issue, a stochastic SCL (SSCL) polar decoder is proposed. Although stochastic computing can achieve a good hardware reduction compared with the deterministic one, its straightforward application to an SCL decoder is not well-suited owing to the precision loss and severe latency. Therefore, a doubling probability approach and adaptive distributed sorting (DS) are introduced. A corresponding hardware architecture is also developed. Field programmable gate array (FPGA) results demonstrate that the proposed stochastic SCL polar decoder can achieve a good performance and complexity tradeoff.

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References

  1. Arıkan E. Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans Inform Theor, 2009, 55: 3051–3073

    MathSciNet  Article  Google Scholar 

  2. Tal I, Vardy A. List decoding of polar codes. In: Proceedings of the IEEE International Symposium on Information Theory Proceedings, Petersburg, 2011. 1–5

  3. Chen K, Niu K, Lin J R. List successive cancellation decoding of polar codes. Electron Lett, 2012, 48: 500–501

    Article  Google Scholar 

  4. Zhou H Y, Zhang C, Song W Q, et al. Segmented CRC-aided SC list polar decoding. In: Proceedings of 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), 2016. 1–5

  5. Shen Y F, Zhang C, Yang J M, et al. Low-latency software successive cancellation list polar decoder using stage-located copy. In: Proceedings of IEEE International Conference on Digital Signal Processing (DSP), 2016. 84–88

  6. Gaines B R. Stochastic computing systems. In: Advances in Information Systems Science. Boston: Springer, 1969. 37–172

    Chapter  Google Scholar 

  7. Moons B, Verhelst M. Energy-efficiency and accuracy of stochastic computing circuits in emerging technologies. IEEE J Emerg Sel Top Circuits Syst, 2014, 4: 475–486

    Article  Google Scholar 

  8. Brown B D, Card H C. Stochastic neural computation. I. Computational elements. IEEE Trans Comput, 2001, 50: 891–905

    MathSciNet  Article  Google Scholar 

  9. Wang H Z, Zhang Z C, You X H, et al. Low-complexity Winograd convolution architecture based on stochastic computing. In: Proceedings of the IEEE International Conference on Digital Signal Processing, Shanghai, 2018. 1–5

  10. Ceroici C, Gaudet V C. FPGA implementation of a clockless stochastic LDPC decoder. In: Proceedings of the IEEE Workshop on Signal Processing Systems, Belfast, 2014. 1–5

  11. Chen J N, Hu J H, Sobelman G E. Stochastic MIMO detector based on the Markov chain Monte Carlo algorithm. IEEE Trans Signal Process, 2014, 62: 1454–1463

    MathSciNet  Article  Google Scholar 

  12. Chen J N, Hu J H, Sobelman G E. Stochastic iterative MIMO detection system: algorithm and hardware design. IEEE Trans Circ Syst I, 2015, 62: 1205–1214

    MathSciNet  MATH  Google Scholar 

  13. Liang X, Zhang C, Xu M H, et al. Efficient stochastic list successive cancellation decoder for polar codes. In: Proceedings of the IEEE International System-on-Chip Conference, Beijing, 2015. 421–426

  14. Tal I, Vardy A. List decoding of polar codes. In: Proceedings of the IEEE International Symposium on Information Theory Proceedings, Petersburg, 2011. 1–5

  15. Bakulin M, Kreyndelin V, Rog A, et al. MMSE based K-best algorithm for efficient MIMO detection. In: Proceedings of the International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, Munich, 2017. 258–263

  16. Yuan B, Parhi K K. Successive cancellation decoding of polar codes using stochastic computing. In: Proceedings of the IEEE International Symposium on Circuits and Systems, Lisbon, 2015. 3040–3043

  17. Tehrani S S, Mannor S, Gross W J. Fully parallel stochastic LDPC decoders. IEEE Trans Signal Process, 2008, 56: 5692–5703

    MathSciNet  Article  Google Scholar 

  18. Xu Z L, Niu K. Successive cancellation decoders of polar codes based on stochastic computation. In: Proceedings of the IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication, Washington, 2014. 908–912

  19. Zhang Z Y, Zhang L, Wang X B, et al. A split-reduced successive cancellation list decoder for polar codes. IEEE J Sel Areas Commun, 2016, 34: 292–302

    Article  Google Scholar 

  20. Liang X, Yang J M, Zhang C, et al. Hardware efficient and low-latency CA-SCL decoder based on distributed sorting. In: Proceedings of the IEEE Global Communications Conference, Washington, 2016. 1–6

  21. Zhang C, Parhi K K. Low-latency sequential and overlapped architectures for successive cancellation polar decoder. IEEE Trans Signal Process, 2013, 61: 2429–2441

    MathSciNet  Article  Google Scholar 

  22. Xiong C, Zhong Y, Zhang C, et al. An FPGA emulation platform for polar codes. In: Proceedings of the IEEE Workshop on Signal Processing Systems, 2016. 148–153

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Acknowledgements

This work was supported in part by National Key R&D Program of China (Grant No. 2020YFB220-5503), National Natural Science Foundation of China (Grant Nos. 61871115, 61501116), Jiangsu Provincial NSF for Excellent Young Scholars (Grant No. BK20180059), Six Talent Peak Program of Jiangsu Province (Grant No. 2018-DZXX-001), Distinguished Perfection Professorship of Southeast University, Fundamental Research Funds for the Central Universities, and Student Research Training Program of Southeast University.

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Correspondence to Chuan Zhang.

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Liang, X., Wang, H., Shen, Y. et al. Efficient stochastic successive cancellation list decoder for polar codes. Sci. China Inf. Sci. 63, 202303 (2020). https://doi.org/10.1007/s11432-019-2924-6

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  • DOI: https://doi.org/10.1007/s11432-019-2924-6

Keywords

  • SCL polar decoder
  • stochastic computing
  • 2-bit decoding
  • distributed sorting
  • hardware