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High-throughput and low-cost LDPC reconciliation for quantum key distribution

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Abstract

Reconciliation is a crucial procedure in post-processing of quantum key distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the efficiency, throughput optimizations have become the highlight in high-speed QKD systems. Many researchers adopt high-cost GPU implementations to improve the throughput. In this paper, an alternative high-throughput and high-efficiency solution implemented in low-cost CPU is proposed. The main contribution of the research is the design of a quantized LDPC decoder including improved RCBP-based check node processing and saturation-oriented variable node processing. Experiment results show that the throughput up to 60 Mbps is achieved using the bidirectional approach with reconciliation efficiency approaching to 1.1, which is the optimal combination of throughput and efficiency in discrete-variable QKD. Meanwhile, the performance remains stable when quantum bit error rate varies from 1 to 8%.

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References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7–11 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2001)

    Article  ADS  MATH  Google Scholar 

  3. Renner, R.: Security of quantum key distribution. Int. J. Quantum Inf. 6(1), 1–127 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Walenta, N., Burg, A., Caselunghe, D., Constantin, J., Gisin, N., Guinnard, O., Houlmann, R., Junod, P., Korzh, B., Kulesza, N.: A fast and versatile quantum key distribution system with hardware key distillation and wavelength multiplexing. New J. Phys. 16(1), 83–97 (2014)

    Article  Google Scholar 

  5. Dixon, A.R., Sato, H.: High speed and adaptable error correction for megabit/s rate quantum key distribution. Sci. Rep. 4, 7275 (2014)

    Article  ADS  Google Scholar 

  6. Li, Q., Le, D., Mao, H., Niu, X., Liu, T., Guo, H.: Study on error reconciliation in quantum key distribution. Quantum Inf. Comput. 14(13–14), 1117–1135 (2014)

    MathSciNet  Google Scholar 

  7. Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. In: Workshop on the Theory and Application of Cryptographic Techniques, pp. 410–423. Springer (1993)

  8. Sugimoto, T., Yamazaki, K.: A study on secret key reconciliation protocol. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 83(10), 1987–1991 (2000)

    Google Scholar 

  9. Nakassis, A., Bienfang, J.C., Williams, C.J.: Expeditious reconciliation for practical quantum key distribution. In: Proceedings of SPIE—The International Society for Optical Engineering, vol. 5436, pp. 28–35. International Society for Optics and Photonics (2004)

  10. Yan, H., Ren, T., Peng, X., Lin, X., Jiang, W., Liu, T., Guo, H.: Information reconciliation protocol in quantum key distribution system. In: Fourth International Conference on Natural Computation. ICNC’08, vol. 3, pp. 637–641. IEEE (2008)

  11. Pedersen, T.B., Toyran, M.: High performance information reconciliation for QKD with CASCADE. Quantum Inf. Comput. 15(5–6), 419–434 (2013)

    MathSciNet  Google Scholar 

  12. Pacher, C., Grabenweger, P., Martinez-Mateo, J., Martin, V.: An information reconciliation protocol for secret-key agreement with small leakage. In: IEEE International Symposium on Information Theory, pp. 730–734. IEEE (2015)

  13. Arikan, 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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jouguet, P., Kunz-Jacques, S.: High performance error correction for quantum key distribution using polar codes. Quantum Inf. Comput. 14(3–4), 329–338 (2014)

    MathSciNet  Google Scholar 

  15. Yan, S., Wang, J., Fang, J., Lin, J., Wang, X.: An improved polar codes-based key reconciliation for practical quantum key distribution. Chin. J. Electron. 27(2), 250–255 (2018)

    Article  Google Scholar 

  16. Yuan, Z., Plews, A., Takahashi, R., Doi, K., Tam, W., Sharpe, A.W., Dixon, A.R., Lavelle, E., Dynes, J.F., Murakami, A.: 10-mb/s quantum key distribution. J. Lightw. Technol. 36(16), 3427–3433 (2018)

    Article  ADS  Google Scholar 

  17. Elkouss, D., MartinezMateo, J., Martin, V.: Information reconciliation for quantum key distribution. Quantum Inf. Comput. 11(3), 226–238 (2011)

    MathSciNet  MATH  Google Scholar 

  18. Martinez-Mateo, J., Elkouss, D., Martin, V.: Blind reconciliation. Quantum Information & Computation 12(9–10), 791–812 (2012)

    MATH  Google Scholar 

  19. Kiktenko, E., Truschechkin, A., Lim, C., Kurochkin, Y., Federov, A.: Symmetric blind information reconciliation for quantum key distribution. Phys. Rev. Appl. 8(4), 044017 (2017)

    Article  ADS  Google Scholar 

  20. Wang, X., Zhang, Y., Yu, S., Guo, H.: High speed error correction for continuous-variable quantum key distribution with multi-edge type LDPC code. Sci. Rep. 8(1), 10543 (2018)

    Article  ADS  Google Scholar 

  21. Milicevic, M., Chen, F., Zhang, L.M., Gulak, P.G.: Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography. NPJ Quantum Inf. 4(1), 1–9 (2018)

    Article  ADS  Google Scholar 

  22. Gal, B.L., Jego, C.: High-throughput multi-core LDPC decoders based on x86 processor. IEEE Trans. Parallel Distrib. Syst. 27(5), 1373–1386 (2016)

    Article  Google Scholar 

  23. Gallager, R.: Low-density parity-check codes. IRE Trans. Inf. Theory 8(1), 21–28 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ryan, W., Lin, S.: Channel Codes: Classical and Modern. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  25. MacKay, D.J.: Good error-correcting codes based on very sparse matrices. IEEE Trans. Inf. Theory 45(2), 399–431 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hocevar, D.E.: A reduced complexity decoder architecture via layered decoding of LDPC codes. In: IEEE Workshop on Signal Processing Systems, pp. 107–112. IEEE (2004)

  27. Jones, C., Vallés, E., Smith, M., Villasenor, J.: Approximate-min constraint node updating for LDPC code decoding. In: 2003 IEEE Military Communications Conference. MILCOM’03, vol. 1, pp. 157–162. IEEE (2003)

  28. Jones, C., Dolinar, S., Andrews, K., Divsalar, D., Zhang, Y., Ryan, W.: Functions and architectures for LDPC decoding. In: IEEE Information Theory Workshop, pp. 577–583. IEEE (2007)

  29. Fossorier, M.P., Mihaljevic, M., Imai, H.: Reduced complexity iterative decoding of low-density parity check codes based on belief propagation. IEEE Trans. Commun. 47(5), 673–680 (1999)

    Article  Google Scholar 

  30. Chen, J., Fossorier, M.P.: Near optimum universal belief propagation based decoding of low-density parity check codes. IEEE Trans. Commun. 50(3), 406–414 (2002)

    Article  Google Scholar 

  31. Richardson, T., Novichkov, V.: Node processors for use in parity check decoders. US Patent 6,938,196 (2005)

  32. Viens, M., Ryan, W.E.: A reduced-complexity box-plus decoder for LDPC codes. In: International Symposium on Turbo Codes and Related Topics, pp. 151–156. IEEE (2008)

  33. Deilmann, M., et al.: A guide to vectorization with intel c++ compilers. Intel Corporation (2012)

  34. Levinthal, D.: Performance analysis guide for intel core i7 processor and intel Xeon 5500 processors. Intel Perform. Anal. Guide 30, 18 (2009)

    Google Scholar 

  35. Lan, L., Zeng, L., Tai, Y.Y., Chen, L., Lin, S., Abdel-Ghaffar, K.: Construction of quasi-cyclic LDPC codes for AWGN and binary erasure channels: A finite field approach. IEEE Trans. Inf. Theory 53(7), 2429–2458 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Elkouss, D., Leverrier, A., Alléaume, R., Boutros, J.: Efficient reconciliation protocol for discrete-variable quantum key distribution. In: IEEE International Conference on Symposium on Information Theory, pp. 1879–1883. IEEE (2009)

  37. Hu, X.Y., Eleftheriou, E., Arnold, D.M.: Regular and irregular progressive edge-growth tanner graphs. IEEE Trans. Inf. Theory 51(1), 386–398 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  38. Wang, G., Wu, M., Yang, S., Cavallaro, J.R.: A massively parallel implementation of QC-LDPC decoder on GPU. In: Application Specific Processors (2011)

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Acknowledgements

This work is supported by the Space Science and Technology Advance Research Joint Funds (6141B06110105) and the National Natural Science Foundation of China (Grant Numbers: 61531003, 61771168, 61702224). Many thanks are extended to Prof. Z.F. Han and Prof. T. Liu for the helpful discussion.

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Correspondence to Qiong Li.

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Mao, H., Li, Q., Han, Q. et al. High-throughput and low-cost LDPC reconciliation for quantum key distribution. Quantum Inf Process 18, 232 (2019). https://doi.org/10.1007/s11128-019-2342-2

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