Abstract

Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
    [Crossref]
  2. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
    [Crossref]
  3. H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
    [Crossref] [PubMed]
  4. H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
    [Crossref]
  5. S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
    [Crossref] [PubMed]
  6. X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005).
    [Crossref] [PubMed]
  7. C. H. Bennet and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers Systems and Signal Processing (IEEE, 1984), pp. 175–179.
  8. I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
    [Crossref]
  9. H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
    [Crossref]
  10. N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
    [Crossref] [PubMed]
  11. P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.
  12. E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
    [Crossref]
  13. S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
    [Crossref]
  14. Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
    [Crossref]
  15. C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
    [Crossref]
  16. C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
    [Crossref]
  17. J. Zhang and M. Fossorier, “Shuffled belief propagation decoding,” in Proceedings of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers (IEEE, 2002), pp. 8–15.
    [Crossref]
  18. D. E. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes,” in Proceedings of IEEE Workshop on Signal Processing Systems (IEEE, 2004), pp. 107–112.
  19. E. Sharon, S. Litsyn, and J. Goldberger, “An efficient message-passing schedule for LDPC decoding,” in Proceedings of IEEE Convention of Electrical and Electronics Engineers (IEEE, 2004), pp. 223–226.
  20. J. Zhang and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes,” IEEE Commun. Lett. 8(3), 165–167 (2004).
    [Crossref]
  21. Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.
  22. S. Park, S. Lee, and K. Whang, “Shuffled BP decoding for punctured LDPC codes,” in Proceedings of 14th Asia-Pacific Conference on Communications (IEEE, 2008), pp. 1–5.
  23. S. Wu, X. Jiang, and Z. Nie, “Alternate iteration of shuffled belief propagation decoding,” in Proceedings of International Conference on Communications and Mobile Computing (IEEE, 2010), pp. 278–281.
  24. C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
    [Crossref]
  25. E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
    [Crossref]
  26. R. G. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).
    [Crossref]
  27. R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27(5), 533–547 (1981).
    [Crossref]
  28. A. I. V. Casado, M. Griot, and R. D. Wesel, “Informed dynamic scheduling for belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2007), pp. 932–937.
  29. T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47(2), 599–618 (2001).
    [Crossref]
  30. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
    [Crossref]
  31. E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
    [Crossref]
  32. A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
    [Crossref]
  33. M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
    [Crossref]
  34. D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.
  35. T. B. Pedersen and M. Toyran, “High performance information reconciliation for QKD with CASCADE,” Quantum Inf. Comput. 15(5), 419–434 (2013).
  36. J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).
  37. W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
    [Crossref]
  38. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).
  39. F. Zhang and H. D. Pfister, “Verification decoding of high-rate LDPC codes with applications in compressed sensing,” IEEE Trans. Inf. Theory 58(8), 5042–5058 (2012).
    [Crossref]
  40. I. B. Djordjevic, M. Arabaci, and Y. Zhang, “Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks,” Opt. Express 20(8), 9296–9301 (2012).
    [Crossref] [PubMed]
  41. M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
    [Crossref]
  42. N. Miladinovic and M. Fossorier, “Systematic recursive construction of LDPC codes,” IEEE Commun. Lett. 8(5), 302–304 (2004).
    [Crossref]
  43. M. Fossorier, “Quasicyclic low density parity check codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2003), pp. 150–154.
  44. X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Progressive edge-growth tanner graphs,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2001), pp. 995–1001.
    [Crossref]
  45. X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Regular and irregular progressive edge-growth tanner graphs,” IEEE Trans. Inf. Theory 51(1), 386–398 (2005).
    [Crossref]

2018 (1)

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

2017 (3)

C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
[Crossref]

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

2013 (2)

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

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

2012 (3)

F. Zhang and H. D. Pfister, “Verification decoding of high-rate LDPC codes with applications in compressed sensing,” IEEE Trans. Inf. Theory 58(8), 5042–5058 (2012).
[Crossref]

I. B. Djordjevic, M. Arabaci, and Y. Zhang, “Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks,” Opt. Express 20(8), 9296–9301 (2012).
[Crossref] [PubMed]

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
[Crossref]

2011 (2)

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

2010 (2)

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
[Crossref]

2009 (1)

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

2007 (1)

E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
[Crossref]

2005 (3)

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

H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref] [PubMed]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005).
[Crossref] [PubMed]

2004 (3)

N. Miladinovic and M. Fossorier, “Systematic recursive construction of LDPC codes,” IEEE Commun. Lett. 8(5), 302–304 (2004).
[Crossref]

M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
[Crossref]

J. Zhang and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes,” IEEE Commun. Lett. 8(3), 165–167 (2004).
[Crossref]

2003 (1)

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

2001 (5)

S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
[Crossref]

Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
[Crossref]

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47(2), 599–618 (2001).
[Crossref]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
[Crossref]

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

1995 (1)

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

1988 (1)

C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
[Crossref]

1981 (1)

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27(5), 533–547 (1981).
[Crossref]

1962 (1)

R. G. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).
[Crossref]

Alléaume, R.

D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.

Anufriev, M.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Arabaci, M.

Arnold, D.-M.

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

X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Progressive edge-growth tanner graphs,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2001), pp. 995–1001.
[Crossref]

Aslam, C. A.

C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
[Crossref]

Ayutaya, T. S. N.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Banihashemi, A. H.

M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Bennet, C. H.

C. H. Bennet and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
[Crossref]

Boutros, J.

D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.

Bozhedarov, A.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
[Crossref]

C. H. Bennet and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers Systems and Signal Processing (IEEE, 1984), pp. 175–179.

Buttler, W. T.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Cai, K.

C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
[Crossref]

Cai, W.-Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Cao, Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Casado, A. I. V.

A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
[Crossref]

A. I. V. Casado, M. Griot, and R. D. Wesel, “Informed dynamic scheduling for belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2007), pp. 932–937.

Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.

Cerf, N. J.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Chang, M. C. F.

Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.

Chang, Y. M.

Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.

Chen, K.

H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref] [PubMed]

Chen, W.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Chen, X.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Chen, Y.-A.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Chung, S.

S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
[Crossref]

Ciurana, A.

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

Cormen, T. H.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).

Crepeau, C.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

Curty, M.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
[Crossref]

Deng, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Djordjevic, I. B.

Donahue, C.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Dušek, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Eleftheriou, E.

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

X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Progressive edge-growth tanner graphs,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2001), pp. 995–1001.
[Crossref]

Elkouss, D.

D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.

Elser, D.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Fedorov, A.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Fedorov, A. K.

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Fossorier, M.

N. Miladinovic and M. Fossorier, “Systematic recursive construction of LDPC codes,” IEEE Commun. Lett. 8(5), 302–304 (2004).
[Crossref]

M. Fossorier, “Quasicyclic low density parity check codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2003), pp. 150–154.

J. Zhang and M. Fossorier, “Shuffled belief propagation decoding,” in Proceedings of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers (IEEE, 2002), pp. 8–15.
[Crossref]

Fossorier, M. P. C.

J. Zhang and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes,” IEEE Commun. Lett. 8(3), 165–167 (2004).
[Crossref]

Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
[Crossref]

Fuerst, M.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Gallager, R. G.

R. G. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).
[Crossref]

Gerhardt, I.

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Goldberger, J.

E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
[Crossref]

E. Sharon, S. Litsyn, and J. Goldberger, “An efficient message-passing schedule for LDPC decoding,” in Proceedings of IEEE Convention of Electrical and Electronics Engineers (IEEE, 2004), pp. 223–226.

Griot, M.

A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
[Crossref]

A. I. V. Casado, M. Griot, and R. D. Wesel, “Informed dynamic scheduling for belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2007), pp. 932–937.

Guan, Y. L.

C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
[Crossref]

Han, Z.-F.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Hemati, S.

M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
[Crossref]

Hocevar, D. E.

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

Hu, T.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Hu, X.-Y.

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

X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Progressive edge-growth tanner graphs,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2001), pp. 995–1001.
[Crossref]

Huang, Y.-M.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Ingkavet, C.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Jain, N.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Jia, J.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Jiang, X.

S. Wu, X. Jiang, and Z. Nie, “Alternate iteration of shuffled belief propagation decoding,” in Proceedings of International Conference on Communications and Mobile Computing (IEEE, 2010), pp. 278–281.

Jiang, X.-J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Kiktenko, E.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Kiktenko, E. O.

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Kou, Y.

Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
[Crossref]

Krauss, H.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Kurochkin, Y. V.

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Kurtsiefer, C.

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Lamas-Linares, A.

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Lamoreaux, S. K.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Lee, S.

S. Park, S. Lee, and K. Whang, “Shuffled BP decoding for punctured LDPC codes,” in Proceedings of 14th Asia-Pacific Conference on Communications (IEEE, 2008), pp. 1–5.

Leiserson, C. E.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).

Leuchs, G.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Leverrier, A.

D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.

Li, F.-Z.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Li, M.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Li, Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Li, Z.-P.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Liao, S.-K.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Lim, C. C. W.

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Lin, S.

Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
[Crossref]

Litsyn, S.

E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
[Crossref]

E. Sharon, S. Litsyn, and J. Goldberger, “An efficient message-passing schedule for LDPC decoding,” in Proceedings of IEEE Convention of Electrical and Electronics Engineers (IEEE, 2004), pp. 223–226.

Liu, N.-L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Liu, Q.

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Liu, W.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Lo, H.-K.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
[Crossref]

H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref] [PubMed]

Lu, C.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Luby, M. G.

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

Lütkenhaus, N.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Lydersen, L.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Ma, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Ma, X.-F.

H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref] [PubMed]

Makarov, V.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Malyshev, A.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Marquardt, C.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Martin, V.

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

Martinezmateo, J.

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

Maurer, U. M.

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

Miladinovic, N.

N. Miladinovic and M. Fossorier, “Systematic recursive construction of LDPC codes,” IEEE Commun. Lett. 8(5), 302–304 (2004).
[Crossref]

Mitzenmacher, M.

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

Nauerth, S.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Nickel, G.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Nie, Z.

S. Wu, X. Jiang, and Z. Nie, “Alternate iteration of shuffled belief propagation decoding,” in Proceedings of International Conference on Communications and Mobile Computing (IEEE, 2010), pp. 278–281.

Pacher, C.

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

Pan, J.-W.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Park, S.

S. Park, S. Lee, and K. Whang, “Shuffled BP decoding for punctured LDPC codes,” in Proceedings of 14th Asia-Pacific Conference on Communications (IEEE, 2008), pp. 1–5.

Pedersen, T. B.

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

Peev, M.

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Peng, C.-Z.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Peterson, C. G.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Pfister, H. D.

F. Zhang and H. D. Pfister, “Verification decoding of high-rate LDPC codes with applications in compressed sensing,” IEEE Trans. Inf. Theory 58(8), 5042–5058 (2012).
[Crossref]

Phromsa-ard, T.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Pozhar, N.

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Qi, B.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
[Crossref]

Rattanatamma,

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Rau, M.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Ren, J.-G.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Richardson, T. J.

S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
[Crossref]

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47(2), 599–618 (2001).
[Crossref]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
[Crossref]

Rivest, R. L.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).

Robert, J.-M.

C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
[Crossref]

Sangwongngam, P.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Sanor, W.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Sharon, E.

E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
[Crossref]

E. Sharon, S. Litsyn, and J. Goldberger, “An efficient message-passing schedule for LDPC decoding,” in Proceedings of IEEE Convention of Electrical and Electronics Engineers (IEEE, 2004), pp. 223–226.

Shen, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Shokrollahi, M. A.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
[Crossref]

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

Shu, R.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Skaar, J.

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Songneam, N.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Spielman, D. A.

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

Sripimanwat, K.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Stein, C.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).

Sun, L.-H.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Tanner, R. M.

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27(5), 533–547 (1981).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Torgerson, J. R.

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Toyran, M.

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

Treeviriyanupab, P.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Trushechkin, A. S.

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Urbanke, R. L.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
[Crossref]

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47(2), 599–618 (2001).
[Crossref]

S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
[Crossref]

Wang, J.-F.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Wang, J.-Y.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Wang, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Wang, X.-B.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005).
[Crossref] [PubMed]

Weier, H.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Weinfurter, H.

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Wesel, R. D.

A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
[Crossref]

A. I. V. Casado, M. Griot, and R. D. Wesel, “Informed dynamic scheduling for belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2007), pp. 932–937.

Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.

Whang, K.

S. Park, S. Lee, and K. Whang, “Shuffled BP decoding for punctured LDPC codes,” in Proceedings of 14th Asia-Pacific Conference on Communications (IEEE, 2008), pp. 1–5.

Wiechers, C.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Wittmann, C.

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

Wu, J.-C.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Wu, S.

S. Wu, X. Jiang, and Z. Nie, “Alternate iteration of shuffled belief propagation decoding,” in Proceedings of International Conference on Communications and Mobile Computing (IEEE, 2010), pp. 278–281.

Xi, T.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Yazdani, M. R.

M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
[Crossref]

Yin, J.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Zhang, C.-M.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

Zhang, F.

F. Zhang and H. D. Pfister, “Verification decoding of high-rate LDPC codes with applications in compressed sensing,” IEEE Trans. Inf. Theory 58(8), 5042–5058 (2012).
[Crossref]

Zhang, J.

J. Zhang and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes,” IEEE Commun. Lett. 8(3), 165–167 (2004).
[Crossref]

J. Zhang and M. Fossorier, “Shuffled belief propagation decoding,” in Proceedings of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers (IEEE, 2002), pp. 8–15.
[Crossref]

Zhang, L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Zhang, Q.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Zhang, Y.

Zhou, Y.-L.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

Zhu, Z.-C.

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

IEEE Commun. Lett. (3)

J. Zhang and M. P. C. Fossorier, “A modified weighted bit-flipping decoding of low-density parity-check codes,” IEEE Commun. Lett. 8(3), 165–167 (2004).
[Crossref]

M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. 8(1), 57–59 (2004).
[Crossref]

N. Miladinovic and M. Fossorier, “Systematic recursive construction of LDPC codes,” IEEE Commun. Lett. 8(5), 302–304 (2004).
[Crossref]

IEEE Trans. Commun. (2)

A. I. V. Casado, M. Griot, and R. D. Wesel, “LDPC decoders with informed dynamic scheduling,” IEEE Trans. Commun. 58(12), 3470–3479 (2010).
[Crossref]

C. A. Aslam, Y. L. Guan, and K. Cai, “Edge-based dynamic scheduling for belief-propagation decoding of LDPC and RS codes,” IEEE Trans. Commun. 65(2), 525–535 (2017).
[Crossref]

IEEE Trans. Inf. Theory (11)

R. G. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).
[Crossref]

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory 27(5), 533–547 (1981).
[Crossref]

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47(2), 599–618 (2001).
[Crossref]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47(2), 619–637 (2001).
[Crossref]

E. Sharon, S. Litsyn, and J. Goldberger, “Efficient serial message-passing schedules for LDPC decoding,” IEEE Trans. Inf. Theory 53(11), 4076–4091 (2007).
[Crossref]

S. Chung, T. J. Richardson, and R. L. Urbanke, “Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation,” IEEE Trans. Inf. Theory 47(2), 657–670 (2001).
[Crossref]

Y. Kou, S. Lin, and M. P. C. Fossorier, “Low-density parity-check codes based on finite geometries: a rediscovery and new results,” IEEE Trans. Inf. Theory 47(7), 2711–2736 (2001).
[Crossref]

C. H. Bennett, G. Brassard, C. Crepeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995).
[Crossref]

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

F. Zhang and H. D. Pfister, “Verification decoding of high-rate LDPC codes with applications in compressed sensing,” IEEE Trans. Inf. Theory 58(8), 5042–5058 (2012).
[Crossref]

M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, “Improved low-density parity-check codes using irregular graphs,” IEEE Trans. Inf. Theory 47(2), 585–598 (2001).
[Crossref]

J. Russ. Laser Res. (1)

E. Kiktenko, A. Malyshev, A. Bozhedarov, N. Pozhar, M. Anufriev, and A. Fedorov, “Error estimation at the information reconciliation stage of quantum key distribution,” J. Russ. Laser Res. 39(6), 558–567 (2018).
[Crossref]

Nat. Commun. (1)

I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2010).
[Crossref]

Nature (1)

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549(7670), 43–47 (2017).
[Crossref] [PubMed]

New J. Phys. (1)

H. Weier, H. Krauss, M. Rau, M. Fuerst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

W. T. Buttler, S. K. Lamoreaux, J. R. Torgerson, G. Nickel, C. Donahue, and C. G. Peterson, “Fast, efficient error reconciliation for quantum cryptography,” Phys. Rev. A 67(5), 052303 (2003).
[Crossref]

Phys. Rev. Appl. (1)

E. O. Kiktenko, A. S. Trushechkin, C. C. W. Lim, Y. V. Kurochkin, and A. K. Fedorov, “Symmetric blind information reconciliation for quantum key distribution,” Phys. Rev. Appl. 8(4), 044017 (2017).
[Crossref]

Phys. Rev. Lett. (4)

N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, “Device calibration impacts security of quantum key distribution,” Phys. Rev. Lett. 107(11), 110501 (2011).
[Crossref] [PubMed]

H.-K. Lo, X.-F. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref] [PubMed]

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 103(18), 130503 (2012).
[Crossref]

X.-B. Wang, “Beating the photon-number-splitting attack in practical quantum cryptography,” Phys. Rev. Lett. 94(23), 230503 (2005).
[Crossref] [PubMed]

Quantum Inf. Comput. (2)

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

J. Martinezmateo, C. Pacher, M. Peev, A. Ciurana, and V. Martin, “Demystifying the information reconciliation protocol Cascade,” Quantum Inf. Comput. 15(5), 453–477 (2013).

Rev. Mod. Phys. (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

SIAM J. Comput. (1)

C. H. Bennett, G. Brassard, and J.-M. Robert, “Privacy amplification by public discussion,” SIAM J. Comput. 17(2), 210–229 (1988).
[Crossref]

Other (13)

C. H. Bennet and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers Systems and Signal Processing (IEEE, 1984), pp. 175–179.

J. Zhang and M. Fossorier, “Shuffled belief propagation decoding,” in Proceedings of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers (IEEE, 2002), pp. 8–15.
[Crossref]

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

E. Sharon, S. Litsyn, and J. Goldberger, “An efficient message-passing schedule for LDPC decoding,” in Proceedings of IEEE Convention of Electrical and Electronics Engineers (IEEE, 2004), pp. 223–226.

P. Treeviriyanupab, T. Phromsa-ard, C.-M. Zhang, M. Li, P. Sangwongngam, T. S. N. Ayutaya, N. Songneam, Rattanatamma, C. Ingkavet, W. Sanor, W. Chen, Z.-F. Han, and K. Sripimanwat, “Rate-adaptive reconciliation and its estimator for quantum bit error rate,” in Proceedings of International Symposium on Communications and Information Technologies (IEEE, 2014), pp. 351–355.

D. Elkouss, A. Leverrier, R. Alléaume, and J. Boutros, “Efficient reconciliation protocol for discrete-variable quantum key distribution,” in Proceedings of IEEE International Conference on Symposium on Information Theory (IEEE, 2009), pp. 1879–1883.

A. I. V. Casado, M. Griot, and R. D. Wesel, “Informed dynamic scheduling for belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2007), pp. 932–937.

Y. M. Chang, A. I. V. Casado, M. C. F. Chang, and R. D. Wesel, “Lower-complexity layered belief-propagation decoding of LDPC codes,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1155–1160.

S. Park, S. Lee, and K. Whang, “Shuffled BP decoding for punctured LDPC codes,” in Proceedings of 14th Asia-Pacific Conference on Communications (IEEE, 2008), pp. 1–5.

S. Wu, X. Jiang, and Z. Nie, “Alternate iteration of shuffled belief propagation decoding,” in Proceedings of International Conference on Communications and Mobile Computing (IEEE, 2010), pp. 278–281.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms (MIT, 2003).

M. Fossorier, “Quasicyclic low density parity check codes,” in Proceedings of IEEE International Symposium on Information Theory (IEEE, 2003), pp. 150–154.

X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, “Progressive edge-growth tanner graphs,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2001), pp. 995–1001.
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 A binary m × n LDPC matrix (a) and its corresponding TG (b).
Fig. 2
Fig. 2 (a) Update C2V information LCjVi. (b) Update V2C information LViCj.
Fig. 3
Fig. 3 Comparison of reconciliation efficiency f of the three most common reconciliation protocols (LDPC, Cascade and Winnow) at different BERpre.
Fig. 4
Fig. 4 Comparison of random sampling, single-syndrome and multi-syndrome for error estimation with 2000 sets of keys at the BERpre of 0.0068 (top), 0.0166 (middle), and 0.0267 (bottom), respectively. (a) Results of multi-syndrome error estimation (black lines) and random sampling method (magenta lines). (b) Results of multi-syndrome error estimation (black lines) and single-syndrome error estimation (red lines).
Fig. 5
Fig. 5 Comparison of convergence speed of 6 reconciliation algorithms by calculating their average numbers of iterations for different BERpre.
Fig. 6
Fig. 6 Relationship between the convergence speed and the number of matrices (1∼5) in reconciliation. The BERpre for data simulation is 0.0246.
Fig. 7
Fig. 7 The convergence speed of the multi-matrix algorithms relative to the number of waves. We generate 100 sets of keys at each BERpre, perform each algorithm on the keys using 5 matrices with compact and separated waves respectively, and calculate the average number of iterations.
Fig. 8
Fig. 8 Percentage increase in throughput of 2-matrix and 3-matrix reconciliation compared to single-matrix reconciliation at different BERpre.
Fig. 9
Fig. 9 A matrix with a 4-member cycle (a) and two additional matrices (b).
Fig. 10
Fig. 10 Reconciliation success rate for single-matrix and multi-matrix algorithms. 1000 sets of keys with BERpre of 0.0275 are generated for the comparison.
Fig. 11
Fig. 11 The valid number of corrected bits NcNm (Nc is the number of corrected bits; Nm is the number of misjudged bits) in each iteration for single- and multi-matrix algorithms. 100 sets of keys with BERpre of 0.0267 are considered.
Fig. 12
Fig. 12 The BERpost performances of the multi-matrix algorithms after 5 iterations. Five BERpre ranging from 0.0202 to 0.0256 are selected. For each BERpre, we generate 1000 sets of keys, and perform 5-matrix algorithms and single-matrix versions on these generated keys.

Tables (7)

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Table 1 Space Complexities of Reconciliation Algorithms

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Table 2 Time Complexities of Reconciliation Algorithms

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Table 3 Soft-decision Values of V2 and V4

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Table 4 Soft-decision Values of V2 and V4 in 3-matrix Reconciliation

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Algorithm 1 MBP algorithm

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Algorithm 2 MSBP algorithm

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Algorithm 3 MLBP algorithm

Equations (39)

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BER = | { y i | y i x i , i { 1 , , n } } | n .
{ P i 0 = 1 e , P i 1 = e y i = 0 P i 0 = e , P i 1 = 1 e y i = 1 ,
L P i = log P i 0 P i 1 ,
L V i C j = L P i ,
L C j V i = sign ( z j ) 2 tan 1 ( V i N ( C j ) \ i tanh ( 1 2 L V i C j ) ) ,
sign ( z j ) = { + 1 z j = 0 1 z j = 1 .
L V i C j = L P i + C j N ( V i ) \ j L C j V i ,
L V i = L P i + C j N ( V i ) L C j V i ,
y i = { 0 L V i > 0 1 L V i < 0 .
Δ z k = z A | k z B | k , k { 1 , , u } ,
e = arg max e [ 0 , threshold ] M e | Δ Z ,
M e | Δ Z = k = 1 u j = 1 m [ 1 Δ z j k + ( 2 Δ z j k 1 ) p ( e , d C j k ) ] ,
p ( e , d C j k ) = Pr ( Δ z j k = 1 ) = i = 1 i mod 2 = 1 d C j k ( d C j k i ) e i ( 1 e ) d C j k i ,
( z k ) T = [ z 1 k , , z n k ] = H k x , k { 1 , , u } , z i k { 0 , 1 } ,
H k x = H x ( mod 2 ) .
L V i = L P i + k = 1 u C j N k ( V i ) L C j V i k ,
f = m n h ( e ) > 1 ,
h ( e ) = e log 2 e ( 1 e ) log 2 ( 1 e ) .
f = α m n h ( e ) > 1 , ( α 1 ) ,
BER post = N error N key * n ,
I ( x ; z ) m .
I ( x ; z ) = H ( z ) H ( z | x ) .
H ( z | x ) = 0 .
I ( x ; z ) = H ( z ) 1 2 m ( 1 2 m log 1 2 m ) = log 2 m = m .
P ( X = x ) = 1 2 n ,
H ( x | z ) t .
H ( x ) = 1 2 n ( 1 2 n log 1 2 n ) = log 2 n = n .
H ( x | z ) = H ( x ) H ( z ) = H ( x ) I ( x ; z ) n m = t .
H m × n = ( H m × t , E m ) ,
z = ( H m × t , E m ) x = H m × t [ x 1 x 2 x t ] [ x t + 1 x t + 2 x n ] = [ z 1 z 2 z m ] ,
H m × t [ x 1 x 2 x t ] = [ z 1 z 2 z m ] [ x t + 1 x t + 2 x n ] .
H m × n = A ( H m × t , E m ) B ,
z = ( H m × t , E m ) x = H m × t [ x 1 x 2 x t ] [ x t + 1 x t + 2 x n ] = [ z 1 z 2 z m ] .
H i = A i ( H i , E m ) B i ,
H j = A j ( H j , E m ) B j ,
z i = ( H i , E m ) x i = H i [ x 1 i x 2 i x t i ] [ x t + 1 i x t + 2 i x n i ] = [ z 1 i z 2 i z m i ] ,
z j = ( H i , E m ) x j = H j [ x 1 j x 2 j x t j ] [ x t + 1 j x t + 2 j x n j ] = [ z 1 j z 2 j z m j ] ,
H ( z i | z i 1 , , z 1 ) = 0 , z i { z 2 , , z u } ,
I ( x ; Z ) = I ( x ; z 1 ) + I ( x ; z 2 | z 1 ) + I ( x ; z 3 | z 2 z 1 ) + + I ( x ; z u | z u 1 z 1 ) = H ( z 1 ) H ( z 1 | x ) + H ( z 2 | z 1 ) H ( z 2 | x z 1 ) + + H ( z u | z u 1 + z 1 ) H ( z u | x z u 1 z 1 ) = H ( z 1 ) + H ( z 2 | z 1 ) + + H ( z u | z u 1 z 1 ) = H ( z 1 )

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