Abstract

Optical performance monitoring covers a very wide range of measurements intended to help ensure network performance and is essential for service providers. We address the problem of solving the linearly accumulated end-to-end impairments of a special set of paths of interest in a reconfigurable all-optical network. This set of paths of interest may include all the paths between any two communicating nodes. The main focus is on the minimization of the number of monitoring devices that are required. A set of channels is injected into the network and monitored. By using the correlation in the channel quality between injected channels, a framework of algebraic performance monitoring is proposed to derive the channel quality of the paths of interest from the linear combination of the monitoring results of the injected channel. The upper bounds on the minimum number of monitoring devices required are derived and constructively achieved for a general network. For a special network in which all nodes are capable of initiating and dropping the monitoring channels, the fundamental limit on the minimum number of monitoring devices is also achieved. The proposed monitoring scheme for this kind of network can also locate at least one fault, even if multiple faults occur. We reduce the cost of monitoring by utilizing the information from the monitoring results and minimizing the number of monitoring devices.

© 2009 Optical Society of America

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  1. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol., vol. 22, pp. 294–304, 2004.
    [CrossRef]
  2. S. L. Woodward, “Monitors to ensure the performance of photonic networks,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OMM1.
  3. L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.
  4. L. K. Chen, M. H. Cheung, C. K. Chan, “From optical performance monitoring to optical network management: research progress and challenges,” presented at the 3rd Int. Conf. Optical Communications and Networks (ICOCN), Hong Kong, Nov. 30–Dec. 1, 2004.
  5. J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
    [CrossRef]
  6. M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
    [CrossRef]
  7. G. W. Lu, L. K. Chen, “Enhancing the monitoring sensitivity of DOP-based OSNR monitors in high OSNR region using off-center narrow-band optical filtering,” Opt. Express, vol. 15, pp. 823–828, 2007.
    [CrossRef] [PubMed]
  8. Y. C. Ku, C. K. Chan, L. K. Chen,“ A robust OSNR monitoring scheme using phase modulator embedded fiber loop mirror,” Opt. Lett., vol. 32, pp. 1752–1754, 2007.
    [CrossRef] [PubMed]
  9. X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
    [CrossRef]
  10. Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.
  11. G. W. Lu, K. T. Tsai, W. I. Way, L. K. Chen, “Experimental demonstration of resolution-enhanced residual chromatic-dispersion monitoring using half-bit delay-interferometer filtering for RZ-OOK system,” presented at 32nd European Conf. Optical Communication (ECOC 2006), Cannes, France, Sept. 24–28, 2006, paper We3.P.67.
  12. Y. Ku, C. Chan, L. Chan, “Chromatic dispersion monitoring technique using birefringent fiber loop,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., Technical Digest (CD), Washington, DC: Optical Society of America, 2006, paper OFN2.
  13. Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.
  14. G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
    [CrossRef]
  15. Y. Huang, J. P. Heritage, B. Mukherjee, “Connection provisioning with transmission impairment consideration in optical WDM networks with high-speed channels,” J. Lightwave Technol., vol. 23, pp. 982–993, 2005.
    [CrossRef]
  16. G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
    [CrossRef]
  17. C. Mas, I. Tomkos, O. K. Tonguz, “Failure location algorithm for transparent optical networks,” IEEE J. Sel. Areas Commun., vol. 23, pp. 1508–1519, 2005.
    [CrossRef]
  18. Y. Wen, W. S. Chan, L. Zheng, “Efficient fault-diagnosis algorithms for all-optical WDM networks with probabilistic link failures,” J. Lightwave Technol., vol. 23, pp. 3358–3371, 2005.
    [CrossRef]
  19. S. Ahuja, S. Ramasubramanian, M. Krunz, “SRLG failure localization in all-optical networks using monitoring cycles and paths,” in IEEE INFOCOM 2008. 27th Conf. Computer Communications, IEEE, 2008, pp. 700–708.

2007

2005

G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
[CrossRef]

Y. Huang, J. P. Heritage, B. Mukherjee, “Connection provisioning with transmission impairment consideration in optical WDM networks with high-speed channels,” J. Lightwave Technol., vol. 23, pp. 982–993, 2005.
[CrossRef]

C. Mas, I. Tomkos, O. K. Tonguz, “Failure location algorithm for transparent optical networks,” IEEE J. Sel. Areas Commun., vol. 23, pp. 1508–1519, 2005.
[CrossRef]

Y. Wen, W. S. Chan, L. Zheng, “Efficient fault-diagnosis algorithms for all-optical WDM networks with probabilistic link failures,” J. Lightwave Technol., vol. 23, pp. 3358–3371, 2005.
[CrossRef]

2004

D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol., vol. 22, pp. 294–304, 2004.
[CrossRef]

M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
[CrossRef]

2001

J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
[CrossRef]

1991

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Ahuja, S.

S. Ahuja, S. Ramasubramanian, M. Krunz, “SRLG failure localization in all-optical networks using monitoring cycles and paths,” in IEEE INFOCOM 2008. 27th Conf. Computer Communications, IEEE, 2008, pp. 700–708.

Bach, R.

Bayvel, P.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Blumenthal, D. J.

Bollenz, B.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Brain, M. C.

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Buhl, L. L.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Cabot, S.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Chan, C.

Y. Ku, C. Chan, L. Chan, “Chromatic dispersion monitoring technique using birefringent fiber loop,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., Technical Digest (CD), Washington, DC: Optical Society of America, 2006, paper OFN2.

Chan, C. K.

Y. C. Ku, C. K. Chan, L. K. Chen,“ A robust OSNR monitoring scheme using phase modulator embedded fiber loop mirror,” Opt. Lett., vol. 32, pp. 1752–1754, 2007.
[CrossRef] [PubMed]

G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
[CrossRef]

L. K. Chen, M. H. Cheung, C. K. Chan, “From optical performance monitoring to optical network management: research progress and challenges,” presented at the 3rd Int. Conf. Optical Communications and Networks (ICOCN), Hong Kong, Nov. 30–Dec. 1, 2004.

Chan, L.

Y. Ku, C. Chan, L. Chan, “Chromatic dispersion monitoring technique using birefringent fiber loop,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., Technical Digest (CD), Washington, DC: Optical Society of America, 2006, paper OFN2.

Chan, W. S.

Chandrasekhar, S.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Chen, L. K.

Y. C. Ku, C. K. Chan, L. K. Chen,“ A robust OSNR monitoring scheme using phase modulator embedded fiber loop mirror,” Opt. Lett., vol. 32, pp. 1752–1754, 2007.
[CrossRef] [PubMed]

G. W. Lu, L. K. Chen, “Enhancing the monitoring sensitivity of DOP-based OSNR monitors in high OSNR region using off-center narrow-band optical filtering,” Opt. Express, vol. 15, pp. 823–828, 2007.
[CrossRef] [PubMed]

G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
[CrossRef]

L. K. Chen, M. H. Cheung, C. K. Chan, “From optical performance monitoring to optical network management: research progress and challenges,” presented at the 3rd Int. Conf. Optical Communications and Networks (ICOCN), Hong Kong, Nov. 30–Dec. 1, 2004.

G. W. Lu, K. T. Tsai, W. I. Way, L. K. Chen, “Experimental demonstration of resolution-enhanced residual chromatic-dispersion monitoring using half-bit delay-interferometer filtering for RZ-OOK system,” presented at 32nd European Conf. Optical Communication (ECOC 2006), Cannes, France, Sept. 24–28, 2006, paper We3.P.67.

Cheung, M. H.

G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
[CrossRef]

L. K. Chen, M. H. Cheung, C. K. Chan, “From optical performance monitoring to optical network management: research progress and challenges,” presented at the 3rd Int. Conf. Optical Communications and Networks (ICOCN), Hong Kong, Nov. 30–Dec. 1, 2004.

Christen, L. C.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Chung, Y. C.

J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
[CrossRef]

Creaner, M. J.

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Einstein, D.

Feinberg, J.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Havstad, S. A.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Heritage, J. P.

Huang, Y.

Jung, D. K.

J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
[CrossRef]

Kang, I.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Kao, Y. H.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Karlsson, M.

M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
[CrossRef]

Kashyap, R.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Kilper, D. C.

Kim, C. H.

J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
[CrossRef]

Krunz, M.

S. Ahuja, S. Ramasubramanian, M. Krunz, “SRLG failure localization in all-optical networks using monitoring cycles and paths,” in IEEE INFOCOM 2008. 27th Conf. Computer Communications, IEEE, 2008, pp. 700–708.

Ku, Y.

Y. Ku, C. Chan, L. Chan, “Chromatic dispersion monitoring technique using birefringent fiber loop,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., Technical Digest (CD), Washington, DC: Optical Society of America, 2006, paper OFN2.

Ku, Y. C.

Landolsi, T.

Lee, J. H.

J. H. Lee, D. K. Jung, C. H. Kim, Y. C. Chung, “OSNR monitoring technique using polarization-nulling method,” IEEE Photon. Technol. Lett., vol. 13, pp. 88–90, 2001.
[CrossRef]

Lehmann, G.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Liu, X.

X. Liu, Y. H. Kao, S. Chandrasekhar, I. Kang, S. Cabot, L. L. Buhl, “OSNR monitoring method for OOK and DPSK based on optical delay interferometer,” IEEE Photon. Technol. Lett., vol. 19, pp. 1172–1174, 2007.
[CrossRef]

Lizé, Y. K.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Lu, G. W.

G. W. Lu, L. K. Chen, “Enhancing the monitoring sensitivity of DOP-based OSNR monitors in high OSNR region using off-center narrow-band optical filtering,” Opt. Express, vol. 15, pp. 823–828, 2007.
[CrossRef] [PubMed]

G. W. Lu, M. H. Cheung, L. K. Chen, C. K. Chan, “Simultaneous PMD and OSNR monitoring by enhanced RF spectral dip analysis assisted with a local large-DGD element,” IEEE Photon. Technol. Lett., vol. 17, pp. 2790–2792, 2005.
[CrossRef]

G. W. Lu, K. T. Tsai, W. I. Way, L. K. Chen, “Experimental demonstration of resolution-enhanced residual chromatic-dispersion monitoring using half-bit delay-interferometer filtering for RZ-OOK system,” presented at 32nd European Conf. Optical Communication (ECOC 2006), Cannes, France, Sept. 24–28, 2006, paper We3.P.67.

Mas, C.

C. Mas, I. Tomkos, O. K. Tonguz, “Failure location algorithm for transparent optical networks,” IEEE J. Sel. Areas Commun., vol. 23, pp. 1508–1519, 2005.
[CrossRef]

Meflah, L.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Mitchell, J.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Mukherjee, B.

Nuccio, S.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Olsson, B. E.

M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
[CrossRef]

Ostar, L.

Pan, Z.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Petersson, M.

M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
[CrossRef]

Preiss, M.

Ramasubramanian, S.

S. Ahuja, S. Ramasubramanian, M. Krunz, “SRLG failure localization in all-optical networks using monitoring cycles and paths,” in IEEE INFOCOM 2008. 27th Conf. Computer Communications, IEEE, 2008, pp. 700–708.

Santoni, S.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Séguin, F.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Starodubov, D. S.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Steele, R. C.

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Sunnerud, H.

M. Petersson, H. Sunnerud, M. Karlsson, B. E. Olsson, “Performance monitoring in optical networks using Stokes parameters,” IEEE Photon. Technol. Lett., vol. 16, pp. 686–688, 2004.
[CrossRef]

Thomsen, B.

L. Meflah, B. Thomsen, J. Mitchell, P. Bayvel, G. Lehmann, S. Santoni, B. Bollenz, “Advanced optical performance monitoring for dynamically reconfigurable networks,” in Proc. Conf. Networks and Optical Communication (NOC), Calgary, Canada: International Association of Science and Technology for Development, 2005, pp. 554.

Tomkos, I.

C. Mas, I. Tomkos, O. K. Tonguz, “Failure location algorithm for transparent optical networks,” IEEE J. Sel. Areas Commun., vol. 23, pp. 1508–1519, 2005.
[CrossRef]

Tonguz, O. K.

C. Mas, I. Tomkos, O. K. Tonguz, “Failure location algorithm for transparent optical networks,” IEEE J. Sel. Areas Commun., vol. 23, pp. 1508–1519, 2005.
[CrossRef]

Tsai, K. T.

G. W. Lu, K. T. Tsai, W. I. Way, L. K. Chen, “Experimental demonstration of resolution-enhanced residual chromatic-dispersion monitoring using half-bit delay-interferometer filtering for RZ-OOK system,” presented at 32nd European Conf. Optical Communication (ECOC 2006), Cannes, France, Sept. 24–28, 2006, paper We3.P.67.

Walker, G. R.

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Walker, N. G.

G. R. Walker, N. G. Walker, R. C. Steele, M. J. Creaner, M. C. Brain, “Erbium-doped fiber amplifier cascade for multichannel coherent optical transmission,” J. Lightwave Technol., vol. 9, pp. 182–193, 1991.
[CrossRef]

Way, W. I.

G. W. Lu, K. T. Tsai, W. I. Way, L. K. Chen, “Experimental demonstration of resolution-enhanced residual chromatic-dispersion monitoring using half-bit delay-interferometer filtering for RZ-OOK system,” presented at 32nd European Conf. Optical Communication (ECOC 2006), Cannes, France, Sept. 24–28, 2006, paper We3.P.67.

Wen, Y.

Willner, A. E.

D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol., vol. 22, pp. 294–304, 2004.
[CrossRef]

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Woodward, S. L.

S. L. Woodward, “Monitors to ensure the performance of photonic networks,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OMM1.

Wu, T.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Wu, X.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Xie, Y.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

Yang, J.

Y. K. Lizé, J. Yang, L. C. Christen, X. Wu, S. Nuccio, T. Wu, A. E. Willner, R. Kashyap, F. Séguin, “Simultaneous and independent monitoring of OSNR, chromatic and polarization mode dispersion for NRZ-OOK, DPSK and duobinary,” in Optical Fiber Communication Conf. and Exposition and Nat. Fiber Optic Engineers Conf., OSA Technical Digest Series (CD), Washington, DC: Optical Society of America, 2007, paper OThN2.

Yu, Q.

Z. Pan, Q. Yu, Y. Xie, S. A. Havstad, A. E. Willner, D. S. Starodubov, J. Feinberg, “Chromatic dispersion monitoring and automated compensation for NRZ and RZ data using clock regeneration and fading without adding signaling,” in Optical Fiber Communication Conf., 2001 OSA Technical Digest Series, Washington, DC: Optical Society of America, 2001, paper WH5.

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Figures (12)

Fig. 1
Fig. 1

Sample network for the illustration of the terminology in the paper.

Fig. 2
Fig. 2

The National Science Foundation (NSF) backbone network is a two-node-connected network without cut nodes and bridges.

Fig. 3
Fig. 3

(a) Impairment variables for a node with degree 2. (b) Impairment variables for a node with degree d = 4 .

Fig. 4
Fig. 4

Probing channels for four cases.

Fig. 5
Fig. 5

Contraction of link between nodes out of N. A short segment is a link between nodes in N. A long segment is the segment that contains multiple links, and the originating node and the terminating node of the segment are in N, while all intermediate nodes are out of N. The middle nodes in the long segment are contracted into a supernode; thus the long segment becomes a two-hop path after contraction.

Fig. 6
Fig. 6

Single two-link-connected network that can be decomposed into three two-node-connected networks.

Fig. 7
Fig. 7

Left, ring subnetwork in a two-node-connected network. Right, a Eulerian cycle in a two-link-connected network. If n a n b , the Eulerian cycle is a ring subnetwork.

Fig. 8
Fig. 8

Left, a figure for the proof of the Case 3 of Theorem 2. Important nodes and paths in the proof are labeled. Right, in the proof of Case 4 of Theorem 2, the merged node m can be restored into the two fully equipped nodes m a and m b .

Fig. 9
Fig. 9

(a) Paths to derive the accumulated impairment in the path p . (b) The accumulated impairment along the long segment p can be derived directly by Lemma 1.

Fig. 10
Fig. 10

Sample network to illustrate the application of Theorem 2.

Fig. 11
Fig. 11

Routing nodes contracted by contracting links between two routing nodes.

Fig. 12
Fig. 12

Sample network to illustrate application of Theorems 3 and 4.

Equations (70)

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accumulated impairment of a path p = l i is a link in p x i .
NF acc = NF 1 + NF 2 G 2 + NF 3 G 3 + + NF k G k ,
NF acc = NF 1 + NF 2 + NF 3 + + NF k .
Δ T CD Δ λ = ( Δ T 1 + Δ T 2 + Δ T 3 + + Δ T k ) Δ λ .
PMD acc 2 = PMD fiber 2 + PMD component 2 .
q 1 : a b c ,
q 2 : c b a ,
q 3 : a b d c ,
q 4 : c d b a ,
q 5 : a d b c ,
q 6 : c b d a ,
q 7 : a d c ,
q 8 : c d a ,
q 9 : a d ,
q 10 : d a ,
q 11 : c d ,
q 12 : d c .
p 1 : a b c ,
p 2 : d c ,
p 3 : a d ,
p 4 : a b d ,
p 5 : d b a d ,
p 6 : d b c ,
p 7 : d c b d ,
p 8 : a b c d ,
p 9 : d a b c .
Z = [ 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ] .
Y = [ 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 ] .
z 3 + z 8 : t 1 r m ,
z 7 + z 4 : m r t 1 t 2 r 4 m
  and t 1 t 2 r 4 m ( by Lemma 1 ) ,
z 7 + z 5 : m r 4 t 3 ,
z 6 + z 8 : t 4 r 4 t 3 t 2 r m
  and t 4 r 4 t 3 t 2 ( by Lemma 1 ) ,
z 3 + z 5 : t 1 r t 2 ,
z 6 + z 4 = ( z 6 + z 8 ) + ( z 7 + z 4 ) ( z 3 + z 8 ) ( z 3 + z 8 ) + ( z 3 + z 5 ) ( by Case 3 b of Theorem 2 ) .
z 18 + z 19 : t 4 r 4 m ,
z 20 + z 17 : m r 4 t 4 t 1 r m
  and t 4 t 1 r m ( by Lemma 1 ) ,
z 20 + z 16 : m r 4 t 2 ,
z 15 + z 19 : t 1 r t 2 t 3 r 4 m ,
  and t 1 r t 2 t 3 ( by Lemma 1 ) ,
z 18 + z 16 : t 4 r 4 t 3 ,
z 15 + z 17 = ( z 15 + z 19 ) + ( z 20 + z 17 ) ( z 18 + z 19 ) ( z 20 + z 16 ) + ( z 18 + z 16 ) ( by Case 3 b of Theorem 2 ) .
x 1 : t 4 t 1 r t 2 ( by the minimum - length path approach in Theorem 4 ) ,
x 2 : t 1 t 4 r 4 t 3 ( by the minimum - length path approach in Theorem 4 ) ,
x 13 : t 1 r t 2 t 3 ( by the minimum - length path approach in Theorem 4 ) ,
x 14 : t 2 r 4 t 3 t 2 ( by the minimum - length path approach in Theorem 4 ) .
x 1 : n 8 n 1 n 2 n 3 m ,
x 2 : n 1 n 8 n 7 m ,
x 3 : n 1 n 2 n 3 m ,
x 4 : n 2 n 1 n 8 n 7 m ,
x 5 : n 2 n 3 m ,
x 6 : n 3 n 2 n 1 n 8 n 7 m ,
x 7 : n 2 n 4 n 3 m ,
x 8 : n 4 n 2 n 3 m ,
x 9 : n 3 n 4 n 5 n 6 n 7 m ,
x 10 : n 4 n 3 m ,
x 11 : n 4 n 5 n 6 n 7 m ,
x 12 : n 5 n 4 n 3 m ,
x 13 : n 5 n 6 n 7 m ,
x 14 : n 6 n 5 n 4 n 3 m ,
x 15 : n 6 n 7 m ,
x 16 : n 7 n 6 n 5 n 4 n 3 m ,
x 17 : n 7 n 8 n 1 n 2 n 3 m ,
x 18 : n 8 n 7 m ,
x 19 : n 7 m ,
x 20 : m n 7 n 8 n 1 n 2 n 3 m ,
x 21 : m n 3 n 4 n 5 n 6 n 7 m ,
x 22 : n 3 m .