Abstract

We present a new method, blind EVM minimization, for constellation recovery and transmitter impairment evaluation of dual polarization optical signals with complex modulation formats. Using simulated data, for which transmitter impairments are known exactly, the method is shown to be accurate and robust. In addition, the method is successfully tested on measured QPSK and QAM16 data. Because of its relatively long run-time, the method might best be used for defining and measuring transmitter impairments and for judging the performance of faster constellation recovery methods that rely on serial parameter evaluation rather than optimization.

© 2016 Optical Society of America

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References

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  1. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
    [Crossref]
  2. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008).
    [Crossref] [PubMed]
  3. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
    [Crossref]
  4. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
    [Crossref] [PubMed]
  5. B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).
    [Crossref]
  6. N. J. Muga and A. N. Pinto, “Adaptive 3-D Stokes space-based polarization demultiplexing algorithm,” J. Lightwave Technol. 32(19), 3290–3298 (2014).
    [Crossref]
  7. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
    [Crossref]
  8. W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM, and BER,” in 2012 14th International Conference on Transparent Optical Networks (IEEE, 2012), pp. 1–4.
    [Crossref]
  9. T. Jensen and T. Larsen, “Robust computation of error vector magnitude for wireless standards,” IEEE Trans. Commun. 61(2), 648–657 (2013).
    [Crossref]
  10. S. Amiralizadeh, A. T. Nguyen, and L. A. Rusch, “Error vector magnitude based parameter estimation for digital filter back-propagation mitigating SOA distortions in 16-QAM,” Opt. Express 21(17), 20376–20386 (2013).
    [Crossref] [PubMed]
  11. IEC Technical Report TR61282–10, “Fibre optic communication system design guides – Part 10: characterization of the quality of optical vector-modulated signals with the error vector magnitude,” Edition 1.0 (2013).
  12. S. Jacobs and R. Marsland, Tektronix, 455 Science Drive, Madison, WI 53711, are preparing a manuscript to be called “Constellation recovery and evaluation of transmitter impairments from coherent optical signals using numerical optimization.”
  13. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
    [Crossref]
  14. A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
    [Crossref]
  15. C. Tsallis and D. Stariolo, “Generalized simulated annealing,” Physica A 233(1-2), 395–406 (1996).
    [Crossref]
  16. A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Program. 50(1-3), 367–393 (1991).
    [Crossref]
  17. B. Nebendahl and R. Derksen, “Method for Carrier Phase Recovery,” ITU Contribution C, 1527 (2016).
  18. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2009).

2016 (1)

B. Nebendahl and R. Derksen, “Method for Carrier Phase Recovery,” ITU Contribution C, 1527 (2016).

2014 (1)

2013 (3)

2012 (1)

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

2010 (2)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref] [PubMed]

2008 (1)

2004 (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

1996 (1)

C. Tsallis and D. Stariolo, “Generalized simulated annealing,” Physica A 233(1-2), 395–406 (1996).
[Crossref]

1991 (1)

A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Program. 50(1-3), 367–393 (1991).
[Crossref]

1983 (1)

A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Aarts, E.

A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Program. 50(1-3), 367–393 (1991).
[Crossref]

Amiralizadeh, S.

Barros, D. J. F.

Becker, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Dekkers, A.

A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Program. 50(1-3), 367–393 (1991).
[Crossref]

Derksen, R.

B. Nebendahl and R. Derksen, “Method for Carrier Phase Recovery,” ITU Contribution C, 1527 (2016).

Dreschmann, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Freude, W.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Hillerkuss, D.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Huebner, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Ip, E.

Jensen, T.

T. Jensen and T. Larsen, “Robust computation of error vector magnitude for wireless standards,” IEEE Trans. Commun. 61(2), 648–657 (2013).
[Crossref]

Josten, A.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Kahn, J. M.

Koenig, S.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Koos, C.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

Larsen, T.

T. Jensen and T. Larsen, “Robust computation of error vector magnitude for wireless standards,” IEEE Trans. Commun. 61(2), 648–657 (2013).
[Crossref]

Lau, A. P. T.

Leuthold, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Marshall, T.

Marshall, T. S.

Meyer, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Muga, N. J.

Nebendahl, B.

B. Nebendahl and R. Derksen, “Method for Carrier Phase Recovery,” ITU Contribution C, 1527 (2016).

B. Szafraniec, T. S. Marshall, and B. Nebendahl, “Performance monitoring and measurement techniques for coherent optical systems,” J. Lightwave Technol. 31(4), 648–663 (2013).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010).
[Crossref] [PubMed]

Nguyen, A. T.

Pinto, A. N.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

Rusch, L. A.

Savory, S. J.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

Schmogrow, R.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Stariolo, D.

C. Tsallis and D. Stariolo, “Generalized simulated annealing,” Physica A 233(1-2), 395–406 (1996).
[Crossref]

Szafraniec, B.

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

Tsallis, C.

C. Tsallis and D. Stariolo, “Generalized simulated annealing,” Physica A 233(1-2), 395–406 (1996).
[Crossref]

Viterbi, A. J.

A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Viterbi, A. N.

A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

Winter, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (2)

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

IEEE Trans. Commun. (1)

T. Jensen and T. Larsen, “Robust computation of error vector magnitude for wireless standards,” IEEE Trans. Commun. 61(2), 648–657 (2013).
[Crossref]

IEEE Trans. Inf. Theory (1)

A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983).
[Crossref]

ITU Contribution (1)

B. Nebendahl and R. Derksen, “Method for Carrier Phase Recovery,” ITU Contribution C, 1527 (2016).

J. Lightwave Technol. (2)

Math. Program. (1)

A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Program. 50(1-3), 367–393 (1991).
[Crossref]

Opt. Express (3)

Physica A (1)

C. Tsallis and D. Stariolo, “Generalized simulated annealing,” Physica A 233(1-2), 395–406 (1996).
[Crossref]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[Crossref]

Other (4)

IEC Technical Report TR61282–10, “Fibre optic communication system design guides – Part 10: characterization of the quality of optical vector-modulated signals with the error vector magnitude,” Edition 1.0 (2013).

S. Jacobs and R. Marsland, Tektronix, 455 Science Drive, Madison, WI 53711, are preparing a manuscript to be called “Constellation recovery and evaluation of transmitter impairments from coherent optical signals using numerical optimization.”

W. Freude, R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, and J. Leuthold, “Quality metrics for optical signals: eye diagram, Q-factor, OSNR, EVM, and BER,” in 2012 14th International Conference on Transparent Optical Networks (IEEE, 2012), pp. 1–4.
[Crossref]

D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed. (American Mathematical Society, 2009).

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Figures (10)

Fig. 1
Fig. 1 The FFT amplitude versus frequency of the 4th power of typical symbol data. Left: QPSK. Right: QAM16.
Fig. 2
Fig. 2 Distorted QAM16 constellations at local minima of the blind IF-EVM (two left-hand panels) and the constellation at the global minimum (right).
Fig. 3
Fig. 3 The I-Q phase error (left) and blind IF-EVM (right) versus I-Q phase angle (y-pol) for simulated QPSK data.
Fig. 4
Fig. 4 Gain imbalance evaluated from blind IF-EVM minimization on measured QPSK data.
Fig. 5
Fig. 5 The blind IF-EVM obtained on measured QPSK data (left). The recovered constellation of the y-polarization on trial 26 (right).
Fig. 6
Fig. 6 Total run-time for processing simulated QPSK and QAM16 data versus number of symbols.
Fig. 7
Fig. 7 The I-Q phase error (left) and blind IF-EVM (right) versus I-Q phase angle (y-pol) for simulated QAM16 data.
Fig. 8
Fig. 8 The blind IF-EVM obtained in 20 trials of measured QAM16 transmission (left). The recovered constellation of the x-polarization in trial 10 (right).
Fig. 9
Fig. 9 The I-Q gain imbalance (a) and I-Q phase error (b) evaluated from blind IF-EVM minimization in twenty trials of measured QAM16 transmission.
Fig. 10
Fig. 10 Comparison between the blind IF-EVM of the y-polarization (a) and x-polarization (b) obtained from blind IF-EVM minimization and the blind EVM from the OMA. The latter was evaluated under the assumption that no transmitter impairments were present.

Tables (6)

Tables Icon

Table 1 Transmitter parameters used for simulated QPSK data

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Table 2 Recovery parameters and symbol period used for simulated QPSK data

Tables Icon

Table 3 Statistics for the run-time and blind IF-EVM for simulated QPSK data

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Table 4 Transmitter impairments from blind IF-EVM minimization of simulated QPSK data

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Table 5 Statistics for the run-time and blind IF-EVM for simulated QAM16 data

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Table 6 Transmitter impairments from blind IF-EVM minimization for simulated QAM16 data

Equations (18)

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( T k (x) T k (y) )=( S I (x) ( I k (x) μ I (x) )+ e i θ (x) S Q (x) ( Q k (x) μ Q (x) ) S I (y) ( I k (y) μ I (y) )+ e i θ (y) S Q (y) ( Q k (y) μ Q (y) ) )
( Z k (x) Z k (y) )=exp( 2πiν t k iϕ )U( T k (x) T k (y) )
U=( e i η 1 cosτ e i η 2 sinτ e i η 2 sinτ e i η 1 cosτ )
I k (x,y) = μ I (x,y) ( A k (x,y) cosτ+ B k (x,y) sinτ )/( S I (x,y) sin θ (x,y) )
Q k (x,y) = μ Q (x,y) +( C k (x,y) cosτ+ D k (x,y) sinτ )/( S Q (x,y) sin θ (x,y) )
A k (x,y) = Z kr (x,y) sin{ (k1)ψ+ϕ η 1 θ (x,y) }+ Z ki (x,y) cos{ (k1)ψ+ϕ η 1 θ (x,y) }
B k (x,y) =± Z kr (y,x) sin{ (k1)ψ+ϕ± η 2 θ (x,y) }± Z ki (y,x) cos{ (k1)ψ+ϕ± η 2 θ (x,y) }
C k (x,y) = Z kr (x,y) sin{ (k1)ψ+ϕ η 1 }+ Z ki (x,y) cos{ (k1)ψ+ϕ η 1 }
D k (x,y) =± Z kr (y,x) sin{ (k1)ψ+ϕ± η 2 }± Z ki (y,x) cos{ (k1)ψ+ϕ± η 2 }
EV M B = 1 2 [ ( EV M B (x) ) 2 + ( EV M B (y) ) 2 ]
EV M B (x,y) = { 1 N k=1 N [ min 1j M R ( I k (x,y) ± a j ) 2 + min 1m M R ( Q k (x,y) ± a m ) 2 ] } 1/2
EV M B (x,y) = { 1 N k=1 N [ min 1j M R ( | I k (x,y) | a j ) 2 + min 1m M R ( | Q k (x,y) | a m ) 2 ] } 1/2
σ (x,y) = 1 N k=1 N | Z k (x,y) | 2 .
( T k (x) T k (y) )=( S I (x) ( I k (x) μ I (x) )+ e i θ (x) S Q (x) ( Q k (x) μ Q (x) ) S I (y) ( I k (y) μ I (y) )+ e i θ (y) S Q (y) ( Q k (y) μ Q (y) ) )+σ( n k (x) n k (y) ).
ϕ k = 2πλP j=1 k B j 1kN
G (x,y) =max{ S I (x,y) / S Q (x,y) , S Q (x,y) / S I (x,y) },
M DC (x,y) = ( μ I (x,y) ) 2 + ( μ Q (x,y) ) 2 ,
Φ (x,y) =| 90° θ (x,y) |

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