Abstract

In this paper, we present a numerical, theoretical and experimental study on the mitigation of Polarization Dependent Loss (PDL) with Polarization-Time (PT) codes in long-haul coherent optical fiber transmissions using Orthogonal Frequency Division Multiplexing (OFDM). First, we review the scheme of a polarization-multiplexed (PolMux) optical transmission and the 2 × 2 MIMO model of the optical channel with PDL. Second, we introduce the Space-Time (ST) codes originally designed for wireless Rayleigh fading channels, and evaluate their performance, as PT codes, in mitigating PDL through numerical simulations. The obtained behaviors and coding gains are different from those observed on the wireless channel. In particular, the Silver code performs better than the Golden code and the coding gains offered by PT codes and forward-error-correction (FEC) codes aggregate. We investigate the numerical results through a theoretical analysis based on the computation of an upper bound of the error probability of the optical channel with PDL. The derived upper bound yields a design criterion for optimal PDL-mitigating codes. Furthermore, a transmission experiment of PDL-mitigation in a 1000km optical fiber link with inline PDL validates the numerical and theoretical findings. The results are shown in terms of Q-factor distributions. The mean Q-factor is improved with PT coding and the variance is also narrowed.

© 2013 OSA

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2013 (1)

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

2012 (2)

2011 (2)

2010 (1)

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (2)

2005 (1)

J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2×2 full-rate space-time code with nonvanishing determinants,” IEEE Transactions on Information Theory51(4), 1432–1436 (2005).
[CrossRef]

2003 (1)

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

2002 (1)

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photonics Technol. Lett.14(3), 313–315 (2002).
[CrossRef]

2000 (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

1999 (1)

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

1994 (1)

S. R. Desbruslais and P. R. Morkel, “Simulation of polarisation mode dispersion and its effects in long-haul optically amplified lightwave systems,” IEE Colloquium on International Transmission Systems, 6/1–6/6 (1994).

Adali, T.

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

Akasaka, Y.

Andrusier, A.

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

Antonelli, C.

Awwad, E.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, and E. Pincemin, “Polarization-Time Coded OFDM for PDL Mitigation in Long-Haul Optical Transmission Systems,” in proc. of ECOC’13, paper P3.4 (to be published).

E. Awwad, Y. Jaouën, and G. Rekaya-Ben Othman, “Improving PDL Tolerance of Long-Haul PDM-OFDM Systems Using Polarization-Time Coding,” in proc. of SPPCom’12, paper SpTu2A.5.

Baumert, W.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Belfiore, J.-C.

J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2×2 full-rate space-time code with nonvanishing determinants,” IEEE Transactions on Information Theory51(4), 1432–1436 (2005).
[CrossRef]

Ben Rayana, S.

S. Ben Rayana, H. Besbes, G. Rekaya-Ben Othman, and Y. Jaouën, “Joint equalization and polarization-time coding detection to mitigate PMD and PDL impairments,” in proc. of SPPCom’12, paper SpW2B.3.

Besbes, H.

S. Ben Rayana, H. Besbes, G. Rekaya-Ben Othman, and Y. Jaouën, “Joint equalization and polarization-time coding detection to mitigate PMD and PDL impairments,” in proc. of SPPCom’12, paper SpW2B.3.

Birk, M.

Bouda, M.

Buchali, F.

Bulow, H.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Bunge, C.

Calderbank, A.R.

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

Ciblat, P.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Delesques, P.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Desbruslais, S. R.

S. R. Desbruslais and P. R. Morkel, “Simulation of polarisation mode dispersion and its effects in long-haul optically amplified lightwave systems,” IEE Colloquium on International Transmission Systems, 6/1–6/6 (1994).

Duthel, T.

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK,” in proc. of OFC/NFOEC’08, 1–3.

Feder, M.

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

Fludger, C. R. S.

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK,” in proc. of OFC/NFOEC’08, 1–3.

Froc, G.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Geyer, J.

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK,” in proc. of OFC/NFOEC’08, 1–3.

Gisin, N.

N. Gisin, “Statistics of polarization dependent loss,” Optics Communications114, Elsevier (1995).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Jansen, S. L.

Jaouën, Y.

S. Mumtaz, G. Rekaya, and Y. Jaouën, “Space-Time codes for optical fiber communication with polarization multiplexing,” in proc. of ICC’10, 1–5.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Ben Rayana, H. Besbes, G. Rekaya-Ben Othman, and Y. Jaouën, “Joint equalization and polarization-time coding detection to mitigate PMD and PDL impairments,” in proc. of SPPCom’12, paper SpW2B.3.

E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, and E. Pincemin, “Polarization-Time Coded OFDM for PDL Mitigation in Long-Haul Optical Transmission Systems,” in proc. of ECOC’13, paper P3.4 (to be published).

E. Awwad, Y. Jaouën, and G. Rekaya-Ben Othman, “Improving PDL Tolerance of Long-Haul PDM-OFDM Systems Using Polarization-Time Coding,” in proc. of SPPCom’12, paper SpTu2A.5.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Juarez, A.

Kim, I.

Koenig, S.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Kuppers, F.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Leuthold, J.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

Li, J.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

Lima, A.

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

Lima, I.

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

Liu, X.

Ma, Y.

Magill, P.

Mecozzi, A.

L. Nelson, C. Antonelli, A. Mecozzi, M. Birk, P. Magill, A. Schex, and L. Rapp, “Statistics of polarization dependent loss in an installed long-haul WDM system,” Opt. Express19(7), 6790–6796 (2011).
[CrossRef] [PubMed]

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photonics Technol. Lett.14(3), 313–315 (2002).
[CrossRef]

Menyuk, C.

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

Meron, E.

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

Mohr, F.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Morita, I.

Morkel, P. R.

S. R. Desbruslais and P. R. Morkel, “Simulation of polarisation mode dispersion and its effects in long-haul optically amplified lightwave systems,” IEE Colloquium on International Transmission Systems, 6/1–6/6 (1994).

Mumtaz, S.

S. Mumtaz, G. Rekaya, and Y. Jaouën, “Space-Time codes for optical fiber communication with polarization multiplexing,” in proc. of ICC’10, 1–5.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Naguib, A.

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

Nelson, L.

Petermann, K.

Pincemin, E.

E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, and E. Pincemin, “Polarization-Time Coded OFDM for PDL Mitigation in Long-Haul Optical Transmission Systems,” in proc. of ECOC’13, paper P3.4 (to be published).

Proakis, J.

J. Proakis and M. Salehi, Digital Communications, Fifth Edition. Mc Graw - Hill International Edition (2008).

Rapp, L.

Rekaya, G.

J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2×2 full-rate space-time code with nonvanishing determinants,” IEEE Transactions on Information Theory51(4), 1432–1436 (2005).
[CrossRef]

S. Mumtaz, G. Rekaya, and Y. Jaouën, “Space-Time codes for optical fiber communication with polarization multiplexing,” in proc. of ICC’10, 1–5.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Rekaya-Ben Othman, G.

E. Awwad, Y. Jaouën, and G. Rekaya-Ben Othman, “Improving PDL Tolerance of Long-Haul PDM-OFDM Systems Using Polarization-Time Coding,” in proc. of SPPCom’12, paper SpTu2A.5.

E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, and E. Pincemin, “Polarization-Time Coded OFDM for PDL Mitigation in Long-Haul Optical Transmission Systems,” in proc. of ECOC’13, paper P3.4 (to be published).

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

S. Ben Rayana, H. Besbes, G. Rekaya-Ben Othman, and Y. Jaouën, “Joint equalization and polarization-time coding detection to mitigate PMD and PDL impairments,” in proc. of SPPCom’12, paper SpW2B.3.

Salehi, M.

J. Proakis and M. Salehi, Digital Communications, Fifth Edition. Mc Graw - Hill International Edition (2008).

Savory, S.

Schenk, T. C. W.

Schex, A.

Schmogrow, R.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

Schmuck, H.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Schulien, C.

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK,” in proc. of OFC/NFOEC’08, 1–3.

Schulz, T.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Sekiya, M.

Seshadri, N.

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

Shieh, W.

Shtaif, M.

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express16(18), 13918–13932 (2008).
[CrossRef] [PubMed]

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photonics Technol. Lett.14(3), 313–315 (2002).
[CrossRef]

Tanaka, H.

Tang, Y.

Tarokh, V.

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

Vassilieva, O.

Viterbo, E.

J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2×2 full-rate space-time code with nonvanishing determinants,” IEEE Transactions on Information Theory51(4), 1432–1436 (2005).
[CrossRef]

Ware, C.

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

Warm, S.

Weiershausen, W.

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Winzer, P. J.

Xie, C.

C. Xie, “Polarization-dependent loss induced penalties in PDM-QPSK coherent optical communication systems,” in proc. of OFC/NFOEC’10, 1–3.

Yi, X.

IEE Colloquium on International Transmission Systems (1)

S. R. Desbruslais and P. R. Morkel, “Simulation of polarisation mode dispersion and its effects in long-haul optically amplified lightwave systems,” IEE Colloquium on International Transmission Systems, 6/1–6/6 (1994).

IEEE Photonics Technol. Lett. (2)

A. Mecozzi and M. Shtaif, “The statistics of polarization-dependent loss in optical communication systems,” IEEE Photonics Technol. Lett.14(3), 313–315 (2002).
[CrossRef]

W. Shieh, “PMD-Supported Coherent Optical OFDM Systems,” IEEE Photonics Technol. Lett.19(3), 134–136 (2007).
[CrossRef]

IEEE Transactions on Communications (1)

V. Tarokh, A. Naguib, N. Seshadri, and A.R. Calderbank, “Space-time codes for high data rate wireless communication: performance criteria in the presence of channel estimation errors, mobility, and multiple paths,” IEEE Transactions on Communications47(2), 199–207 (1999).
[CrossRef]

IEEE Transactions on Information Theory (1)

J.-C. Belfiore, G. Rekaya, and E. Viterbo, “The golden code: a 2×2 full-rate space-time code with nonvanishing determinants,” IEEE Transactions on Information Theory51(4), 1432–1436 (2005).
[CrossRef]

J. Lightwave Technol. (2)

OFC/IOOC’99 (1)

H. Bulow, W. Baumert, H. Schmuck, F. Mohr, T. Schulz, F. Kuppers, and W. Weiershausen, “Measurement of the maximum speed of PMD fluctuation in installed field fiber,” OFC/IOOC’992, 83–85.

Opt. Express (7)

Opt. Letters (3)

A. Lima, I. Lima, C. Menyuk, and T. Adali, “Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems,” Opt. Letters28(5), 310–312 (2003).
[CrossRef]

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, “Use of space-time coding in coherent polarization-multiplexed systems suffering from polarization-dependent loss,” Opt. Letters35(21), 3547–3549 (2010).
[CrossRef]

A. Andrusier, E. Meron, M. Feder, and M. Shtaif, “An optical implementation of a space-time-trellis code for enhancing the tolerance of systems to polarization-dependent loss,” Opt. Letters38(2), 118–120 (2013).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” in Proc. Natl. Acad. Sci. U.S.A.97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

proc. of ICC’10 (1)

S. Mumtaz, G. Rekaya, and Y. Jaouën, “Space-Time codes for optical fiber communication with polarization multiplexing,” in proc. of ICC’10, 1–5.

proc. of OFC/NFOEC’08 (1)

T. Duthel, C. R. S. Fludger, J. Geyer, and C. Schulien, “Impact of polarization dependent loss on coherent POLMUX-NRZ-DQPSK,” in proc. of OFC/NFOEC’08, 1–3.

proc. of OFC/NFOEC’10 (1)

C. Xie, “Polarization-dependent loss induced penalties in PDM-QPSK coherent optical communication systems,” in proc. of OFC/NFOEC’10, 1–3.

Other (8)

E. Awwad, Y. Jaouën, G. Rekaya-Ben Othman, and E. Pincemin, “Polarization-Time Coded OFDM for PDL Mitigation in Long-Haul Optical Transmission Systems,” in proc. of ECOC’13, paper P3.4 (to be published).

E. Awwad, Y. Jaouën, and G. Rekaya-Ben Othman, “Improving PDL Tolerance of Long-Haul PDM-OFDM Systems Using Polarization-Time Coding,” in proc. of SPPCom’12, paper SpTu2A.5.

N. Gisin, “Statistics of polarization dependent loss,” Optics Communications114, Elsevier (1995).
[CrossRef]

J. Proakis and M. Salehi, Digital Communications, Fifth Edition. Mc Graw - Hill International Edition (2008).

P. Delesques, E. Awwad, S. Mumtaz, G. Froc, P. Ciblat, Y. Jaouën, G. Rekaya, and C. Ware, “Mitigation of PDL in coherent optical communications: How close to the fundamental limit?,” in proc. of ECOC’12, paper P4.13.

S. Mumtaz, J. Li, S. Koenig, Y. Jaouën, R. Schmogrow, G. Rekaya-Ben Othman, and J. Leuthold, “Experimental demonstration of PDL mitigation using Polarization-Time coding in PDM-OFDM systems,” in proc. of SPPCom’11, paper SPWB6.

S. Mumtaz, G. Rekaya-Ben Othman, Y. Jaouën, J. Li, S. Koenig, R. Schmogrow, and J. Leuthold, “Alamouti code against PDL in polarization multiplexed systems,” in proc. of SPPCom’11, paper SPTuA2.

S. Ben Rayana, H. Besbes, G. Rekaya-Ben Othman, and Y. Jaouën, “Joint equalization and polarization-time coding detection to mitigate PMD and PDL impairments,” in proc. of SPPCom’12, paper SpW2B.3.

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Figures (8)

Fig. 1
Fig. 1

General scheme of a PolMux OFDM transmission with Polarization-Time coding.

Fig. 2
Fig. 2

Structure of the considered long-haul optical link.

Fig. 3
Fig. 3

Performance of PT codes obtained through Monte Carlo simulations.

Fig. 4
Fig. 4

Bit Error Rate as a function of the SNR bit for the uncoded scheme and the Silver code, with or without FEC: (a) Hard decision decoding (HDD), (b) Soft decision decoding (SDD). The simulated FEC is a BCH(63,45) code.

Fig. 5
Fig. 5

Bit Error Rate as a function of the SNR bit for the Silver code, obtained through Monte Carlo simulations.

Fig. 6
Fig. 6

Experimental setup. (ECL: External Cavity Laser, AWG: Arbitrary Waveform Generator, MUX: Multiplexer, AO: Acousto-Optical Modulator, PS: Polarization Scrambler, OBPF: Optical Band-Pass Filter, ASE: Accumulated Spontaneous Emission source, LO: Local Oscillator, OSA: Optical Spectrum Analyzer, OSC: Tektronix 50GS/s Oscilloscope).

Fig. 7
Fig. 7

BER evolution versus launched input power after 5 × 200km for the Silver-coded and 4-QAM schemes, at three different PDL values at the transmitter: 0, 3 and 6dB.

Fig. 8
Fig. 8

Q-factor distribution after 5 × 200km at Pin = −3dBm (OSNR0.1 nm = 12dB). Inset: Experimental and theoretical probability distributions of PDL.

Tables (1)

Tables Icon

Table 1 d min 2 for different coding schemes at different PDL values

Equations (32)

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X = [ X Pol 1 , T 1 X Pol 1 , T 2 X Pol 2 , T 1 X Pol 2 , T 2 ]
Y k , i = H k ( ω k ) X k , i + N k , i
X = argmin X 𝒞 Y HX 2
H P D L = R α [ 1 0 0 ε ] R α 1 = 1 1 + γ R α [ 1 + γ 0 0 1 γ ] R α 1
𝒴 k = 1 N S 2 ( Tr ( 1 N S 1 N S ) ) 1 / 2 X k + j = 1 N S 1 j + 1 N S 2 ( Tr ( j + 1 N S j + 1 N S ) ) 1 / 2 N j = k X k + 𝒩 k + N N S
Y k = Q 1 / 2 𝒴 k = H k X k + N k
Y k = U [ λ max 0 0 λ min ] V X k + N k = a U [ 1 + γ eq 0 0 1 γ eq ] V X k + N k
H = R α [ 1 + γ eq 0 0 1 γ eq ] R α 1
X 𝒢 = 1 5 [ α ( S 1 + θ S 2 ) α ( S 3 + θ S 4 ) i α ¯ ( S 3 + θ ¯ S 4 ) α ¯ ( S 1 + θ ¯ S 2 ) ]
X 𝒮 = [ S 1 + Z 3 S 2 * Z 4 * S 2 Z 4 S 1 * Z 3 * ] [ Z 3 Z 4 ] = 1 7 [ 1 + i 1 + 2 i 1 + 2 i 1 i ] [ S 3 S 4 ]
X 𝒜 = [ S 1 S 2 * S 2 S 1 * ]
Y k = H X k + N k
R c = k n < 1
P error = Pr { X X } = X 𝒞 Pr { X } Pr { X X | X }
P error 1 card ( 𝒞 ) X , X 𝒞 , X X Pr ( X X )
Pr ( X X ) 𝔼 H [ exp ( H ( X X ) 2 8 σ 2 ) ]
Pr ( X X ) 𝔼 H [ exp ( H ( X X ) 2 8 σ 2 ) ]
Pr ( X X ) exp ( X Δ 2 8 σ 2 ) I 0 ( γ eq 8 σ 2 a 2 + b 2 )
a = x 2 2 x 1 2
b = 2 Re ( x 1 , x 2 )
Pr ( X X ) exp ( X Δ 2 γ eq a 2 + b 2 8 σ 2 )
p error , A W G N exp ( X Δ 2 8 σ 2 )
P e , H D D m = t + 1 n ( n m ) p m ( 1 p ) n m
P e , H D D ( n t + 1 ) p t + 1 = ( n d F E C , H D D ) p d F E C , H D D
P e , S D D ( 2 k 1 ) p d F E C , S D D
1 4 log 2 M Pr ( X X ) p Pr ( X X )
p A d P T exp ( d P T 2 8 σ 2 )
P e K ( A d P T ) d F E C exp ( d F E C d P T 2 SNR bit r P T R c log 2 M 4 )
G = SNR bit , F E C + P T SNR bit , N C = R c d F E C d P T 2 d N C 2
G d B = 10 log 10 ( R c d F E C ) + 10 log 10 ( d P T 2 d N C 2 ) = G d B , F E C + G d B , P T
BER = 0.5 e r f c ( Q / 2 ) and Q d B = 20 log 10 ( Q )
OSNR = R b 2 B ref SNR bit

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