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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. 1.

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

  2. 2.

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

  3. 3.

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

  4. 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)

  5. 5.

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

  6. 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)

  7. 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. 8.

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

  9. 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. 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. 11.

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

  12. 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. 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)

  14. 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)

  15. 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)

  16. 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)

  17. 17.

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

  18. 18.

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

  19. 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)

  20. 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)

  21. 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)

  22. 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)

  23. 23.

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

  24. 24.

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

  25. 25.

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

  26. 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. 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. 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. 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)

  30. 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)

  31. 31.

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

  32. 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. 33.

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

  34. 34.

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

  35. 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)

  36. 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. 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)

  38. 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) doi:10.1007/s11128-019-2342-2

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Keywords

  • Quantum key distribution
  • Information reconciliation
  • Low-density parity-check code
  • SIMD
  • Rate-compatible