Abstract

We propose a new modulation format providing 5 bits of information per recovered symbol while maintaining constant the total optical power. The proposed format applies a simple power constrain to the DP-8QAM format. This modulation format provides a passive way to mitigate nonlinear impairments due to Kerr effects occurring during propagation, and most specifically in the first 40 km. This report presents, to the authors’ knowledge, a new transmission format using solely phase and polarization as modulation methods. The performance of this format, named 8PolSK-QPSK, is experimentally compared with that of the DP-8QAM format as both require equal transmitter complexity and implementation penalty, at the expense of a 20% increase in signaling baud rate. The greater nonlinear tolerance of this format is experimentally demonstrated. Moreover, thorough analysis of the Manakov-PDM propagation equation applied to both formats provides analytic explanation of the 8PolSK-QPSK’s improved performance. The constant power property of the symbol set of the proposed format mitigates self- and cross-phase modulation (SPM, XPM) nonlinear effects and is experimentally validated over a long-haul transmission system in a WDM scenario. A total throughput of 7 × 129 Gbps is maintained for the transmission format comparison. Simulation of the same transmission system allows separate analysis of the strength of SPM, XPM and Cross-Polarization Modulation (XPolM) nonlinear effects and demonstrate reduced nonlinear impairments for the proposed format in the first span. We show an experimental reduction of the required OSNR for a BER threshold of 1.4 × 10−2 of 0.5 dB for 8PolSK-QPSK compared to DP-8QAM in back-to-back. After 1920 km of SMF fiber, we demonstrate a required OSNR (ROSNR) diminution for increasing launch power, allowing a ROSNR relief of 0.95 dB at optimal launch power of −1 dBm for the proposed format. Using the same threshold, we show an increased reach by more than 34%, or 975 km, at optimal launch power. We also demonstrate that the relative reach increase for 8PolSK-QPSK compared to DP-8QAM monotonically increases with increasing BER threshold and that the BER growth with distance, after the first span, is equal for both formats.

© 2013 Optical Society of America

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References

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  2. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
    [CrossRef]
  7. M. Chagnon, M. Osman, X. Xu, Q. Zhuge, and D. V. Plant, “Blind, fast and SOP independent polarization recovery for square dual polarization-MQAM formats and optical coherent receivers,” Opt. Express20(25), 27847–27865 (2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. E. Ip and J. M. Kahn, “Carrier synchronization for 3- and 4-bit-per-symbol optical transmission,” J. Lightwave Technol.23(12), 4110–4124 (2005).
    [CrossRef]
  13. M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, “A statistical treatment of cross-polarization modulation in DWDM systems,” J. Lightwave Technol.27(17), 3739–3751 (2009).
    [CrossRef]
  14. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
    [CrossRef]
  15. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci.97(9), 4541–4550 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. M. Winter, “A statistical treatment of cross-polarization modulation in DWDM systems & its application,” Techn. Univ, Berlin, Deutsche National Bibliothek, http://d-nb.info/1009105868 (2010).
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    [CrossRef]
  19. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol.22(3), 779–783 (2004).
    [CrossRef]
  20. S. Kumar, “Effect of dispersion on nonlinear phase noise in optical transmission systems,” Opt. Lett.30(24), 3278–3280 (2005).
    [CrossRef]
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    [CrossRef]
  23. M. Shtaif, “Analytical description of cross-phase modulation in dispersive optical fibers,” Opt. Lett.23(15), 1191–1193 (1998).
    [CrossRef]
  24. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
    [CrossRef]
  25. ITU-T Rec. G. 975.1, “Forward error correction for high bit-rate DWDM submarine systems,” (2004).
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    [CrossRef]
  27. D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.
  28. X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

2013 (2)

Z. Chen, L. Yan, W. Pan, B. Luo, Y. Guo, H. Jiang, A. Yi, Y. Sun, and X. Wu, “Transmission of multipolarization-multiplexed signals: another freedom to explore?” Opt. Express21(9), 11590–11605 (2013).
[CrossRef] [PubMed]

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

2012 (2)

2011 (2)

2009 (2)

2006 (1)

2005 (2)

2004 (1)

2003 (1)

2002 (1)

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

2000 (1)

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

1998 (1)

1997 (1)

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol.15(9), 1735–1746 (1997).
[CrossRef]

1996 (1)

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

1995 (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm.13(3), 531–542 (1995).
[CrossRef]

1992 (1)

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992).
[CrossRef]

1989 (1)

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Lightwave Technology Telecommunication Systems (Wiley-Interscience, 2005).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

Agrell, E.

Baney, D. M.

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

Bayvel, P.

Behrens, C.

Benedetto, S.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm.13(3), 531–542 (1995).
[CrossRef]

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992).
[CrossRef]

Bosco, G.

Bunge, C.-A.

Carena, A.

Chagnon, M.

Chang, D.

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

Chen, Z.

Chung, Y. C.

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

Curri, V.

Cvijetic, M.

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

Djordjevic, I. B.

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

Forghieri, F.

Gaudino, R.

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm.13(3), 531–542 (1995).
[CrossRef]

Gordon, J. P.

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

Guo, Y.

Ho, K.-P.

Ip, E.

Isaac, R.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Jiang, H.

Jovanovic, A. Z.

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

Kahn, J. M.

Karlsson, M.

Kim, C. H.

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

Kogelnik, H.

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

Kumar, S.

Lavery, D.

Lee, J. H.

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

Li, Y.

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

Luo, B.

Magill, P.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Makovejs, S.

Marcuse, D.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol.15(9), 1735–1746 (1997).
[CrossRef]

Menyuk, C. R.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol.15(9), 1735–1746 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

Millar, D. S.

Nazarathy, M.

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

Nelson, L.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Newton, S. A.

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

Osman, M.

Pan, W.

Park, K. J.

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

Peckham, D.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Peric, Z.

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

Petermann, K.

Plant, D. V.

Poggiolini, P.

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
[CrossRef]

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm.13(3), 531–542 (1995).
[CrossRef]

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992).
[CrossRef]

Proakis, J.

J. Proakis, Digital Communications, 4th ed. (McGraw-Hill Science, 2000).

Savory, S. J.

Setti, D.

Shtaif, M.

Sorin, W. V.

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

Stojanovic, N.

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

Sun, Y.

Sunnerud, H.

Thomsen, B. C.

Wai, P. K. A.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol.15(9), 1735–1746 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

Winter, M.

Wu, X.

Xiao, Z.

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

Xu, X.

Yan, L.

Yi, A.

Yu, F.

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

Zhou, X.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Zhu, B.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

Zhuge, Q.

IEEE J. Sel. Areas Comm. (1)

S. Benedetto, R. Gaudino, and P. Poggiolini, “Direct detection of optical digital transmission based on polarization shift keying modulation,” IEEE J. Sel. Areas Comm.13(3), 531–542 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. H. Lee, K. J. Park, C. H. Kim, and Y. C. Chung, “Effects of nonlinear crosstalk in optical PMD compensation,” IEEE Photon. Technol. Lett.14(8), 1082–1084 (2002).
[CrossRef]

IEEE Photonics J. (1)

I. B. Djordjevic, A. Z. Jovanovic, M. Cvijetic, and Z. Peric, “Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks,” IEEE Photonics J.5(4), 7901312 (2013).
[CrossRef]

IEEE Trans. Commun. (1)

S. Benedetto and P. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992).
[CrossRef]

J. Lightwave Technol. (9)

E. Ip and J. M. Kahn, “Carrier synchronization for 3- and 4-bit-per-symbol optical transmission,” J. Lightwave Technol.23(12), 4110–4124 (2005).
[CrossRef]

M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, “A statistical treatment of cross-polarization modulation in DWDM systems,” J. Lightwave Technol.27(17), 3739–3751 (2009).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol.14(2), 148–157 (1996).
[CrossRef]

M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol.24(11), 4127–4137 (2006).
[CrossRef]

K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol.22(3), 779–783 (2004).
[CrossRef]

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol.15(9), 1735–1746 (1997).
[CrossRef]

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol.27(22), 5115–5126 (2009).
[CrossRef]

M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, D. M. Baney, and S. A. Newton, “Spectral analysis of optical mixing measurements,” J. Lightwave Technol.7(7), 1083–1096 (1989).
[CrossRef]

A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol.30(10), 1524–1539 (2012).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. (1)

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

Other (7)

J. Proakis, Digital Communications, 4th ed. (McGraw-Hill Science, 2000).

G. P. Agrawal, Lightwave Technology Telecommunication Systems (Wiley-Interscience, 2005).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

M. Winter, “A statistical treatment of cross-polarization modulation in DWDM systems & its application,” Techn. Univ, Berlin, Deutsche National Bibliothek, http://d-nb.info/1009105868 (2010).

D. Chang, F. Yu, Z. Xiao, Y. Li, and N. Stojanovic, “FPGA verification of a single QC-LDPC code for 100 Gb/s optical systems without error floor down to BER of 10−15,” Proc. OFC 2011, Paper OTuN2, March2012.

X. Zhou, L. Nelson, R. Isaac, P. Magill, B. Zhu, and D. Peckham, “1200km transmission of 50GHz spaced, 5×504-Gb/s PDM-32-64 hybrid QAM using electrical and optical spectral shaping,” Proc. OFC 2012, Paper OM2A.2, March2012.

ITU-T Rec. G. 975.1, “Forward error correction for high bit-rate DWDM submarine systems,” (2004).

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Figures (8)

Fig. 1
Fig. 1

Star-8QAM format. In DP-8QAM, the 2 polarizations can both independently be at amplitude a or b. For 8PolSK-QPSK format, that independence is removed.

Fig. 2
Fig. 2

Stokes space representation of the a) 8PolSK-QPSK and b) DP-8QAM format, both with added noise giving 16 dB of SNR. The axis of both figures are equal. The higher power variations from symbol to symbol is clearly observed for DP-8QAM.

Fig. 3
Fig. 3

Temporal variance of SPM, XPM and XPolM, normalized by mean power squared, for 8PolSK-QPSK (solid lines: –––) and DP-8QAM (circled solid lines: –○–) a) Main figure showing all NL strengths for first two spans b) Zoom-in from 0 to 40 km showing SPM and XPolM strengths. c) SPM only, from 3rd to 9th span. d) XPM only between 400 and 650 km

Fig. 4
Fig. 4

Experiental testbed.

Fig. 5
Fig. 5

Launch Power per channel against maximum reach [km] for a BER = 1.4 × 10−2. The optimum launch power is −1dBm for 8PolSK-QPSK and around −1.4 dBm for DP-8QAM. 8PolSK-QPSK format propagates 34% more than DP-8QAM, or 975 km more.

Fig. 6
Fig. 6

BER against OSNR in 0.1 nm for both 8PolSK-QPSK and DP-8QAM formats. Inset a): Theoretical OSNR (in 0.1 nm) difference between formats as a function of BER threshold.

Fig. 7
Fig. 7

Required OSNR in 0.1 nm [dB] for BER = 1.4 × 10−2 after 1920 km.

Fig. 8
Fig. 8

BER against Distance [km] for both 8PolSK-QPSK and DP-8QAM. Aslo shown in inset (b) is the reach difference of the two formats as a function of BER in linear scale.

Equations (12)

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| S i = [ S i x S i y ] ,
min i ( Pol | | R | S i | 2 ) ,
max i ( Re { R | S i } ) .
min i ( R | R 2 Re { R | S i } + S i | S i ) .
| u z = α 2 | u ATT . i Δ β 0 2 ( b ^ σ ) | u BIREF . Δ β 1 ( b ^ σ ) | u t PMD + i β 2 2 2 | u t 2 CD + i 8 9 γ u | u | u NL ,
u | u | u NL = u n | u n | u n + m n ( u m | u m | u n + u m | u n | u m ) = u n | u n | u n SPM + m n ( 3 2 u m | u m | u n XPM + 1 2 ( u m σ ) | u n ) XPolM ,
SPM : σ S P M 2 = ( u n | u n 2 ¯ u n | u n ¯ 2 ) / u n | u n ¯ 2 .
XPM : σ X P M 2 = ( ( m n 3 2 u m | u m ) 2 ¯ ( m n 3 2 u m | u m ) ¯ 2 ) / u n | u n ¯ 2 .
XPolM : σ XPolM 2 = ( | m n u m | 2 ¯ | m n u m | ¯ 2 ) / u n | u n ¯ 2 .
u n | u n 2 ¯ = m = n = k = l = u m | u n u k | u l g * ( t m T ) g ( t n T ) g * ( t k T ) g ( t l T ) . ¯
u i | u i 2 ¯ = ( u k | u k u l | u l ¯ + u k | u l u l | u k ¯ ) 1 T m = | g ( t ) | 2 | g ( t m T ) | 2 d t + ( u k | u k 2 ¯ u k | u k u l | u l ¯ u k | u l u l | u k ¯ ) 1 T | g ( t m T ) | 4 d t .
BER ( α , β , SNR ) = α erfc ( β SNR ) ,

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