Abstract

In this paper, we examine the performance of several modulation formats in more than four dimensions for coherent optical communications systems. We compare two high-dimensional modulation design methodologies based on spherical cutting of lattices and block coding of a ‘base constellation’ of binary phase shift keying (BPSK) on each dimension. The performances of modulation formats generated with these methodologies is analyzed in the asymptotic signal-to-noise ratio regime and for an additive white Gaussian noise (AWGN) channel. We then study the application of both types of high-dimensional modulation formats to standard single-mode fiber (SSMF) transmission systems. For modulation with spectral efficiencies comparable to dual-polarization (DP-) BPSK, polarization-switched quaternary phase shift keying (PS-QPSK) and DP-QPSK, we demonstrate SNR gains of up to 3 dB, 0.9 dB and 1 dB respectively, at a BER of 10−3.

© 2014 Optical Society of America

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  1. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
    [CrossRef] [PubMed]
  2. “Implementation Agreement for Integrated Dual Polarization Intradyne Coherent Receivers,” Optical Internetworking Forum (2010). http://www.oiforum.com/public/documents/OIF_DPC_RX-01.0.pdf .
  3. S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
    [CrossRef]
  4. M. Karlsson, E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17, 10814–10819 (2009).
    [CrossRef] [PubMed]
  5. E. Agrell, M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27, 5115–5126 (2009).
    [CrossRef]
  6. P. Poggiolini, G. Bosco, A. Carena, V. Curri, F. Forghieri, “Performance evaluation of coherent WDM PSQPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express 18, 11360–11371 (2010).
    [CrossRef] [PubMed]
  7. P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC, Th.10.E.2, (2010).
  8. D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
    [CrossRef] [PubMed]
  9. J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).
  10. L. D. Coelho, N. Hanik, “Global Optimization of Fiber-Optic Communication Systems using Four-Dimensional Modulation Formats,” Proc. ECOCMo.2.B.4, (2011).
  11. M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
    [CrossRef] [PubMed]
  12. H. Bülow, “Polarization QAM modulation (POL-QAM) for coherent detection schemes,” Proc. OFC/NFOECOWG.2, (2009).
  13. T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).
  14. S. Ishimura, K. Kikuchi, “Multi-dimensional Permutation Modulation Aiming at Both High Spectral Efficiency and High Power Efficiency,” Proc. OFC/NFOECM3A.2, (2014).
  15. D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).
  16. D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).
  17. T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).
  18. D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).
  19. D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).
  20. S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).
  21. T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).
  22. J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
    [CrossRef]
  23. I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
    [CrossRef]
  24. H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).
  25. M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
    [CrossRef]
  26. P. J. Winzer, “High-Spectral-Efficiency Optical Modulation Formats,” J. Lightwave Technol. 30, 3824–3835 (2012).
    [CrossRef]
  27. Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).
  28. G.-H. Gho, J. M. Kahn, “Rate-Adaptive Modulation and Coding for Optical Fiber Transmission Systems,” J. Lightwave Technol. 30, 1812–1818 (2012).
    [CrossRef]
  29. P. Poggiolini, “The GN Model of Non-Linear Propagation in Uncompensated Coherent Optical Systems,” J. Lightwave Technol. 30, 3857–3879 (2012).
    [CrossRef]
  30. T. Koike-Akino, V. Tarokh, “Sphere packing optimization and EXIT chart analysis for multi-dimensional QAM signaling,” Proc. IEEE ICC (2009).
  31. N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
    [CrossRef]
  32. J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, (Springer, 1998).
  33. C. D. Murphy, “High-order optimum hexagonal constellations,” IEEE PIMRC 1, 143–146 (2000).
  34. G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
    [CrossRef]
  35. G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
    [CrossRef]
  36. K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
    [CrossRef]
  37. J. H. van Lint, “A survey of perfect codes,” Rocky Mountain Journal of Mathematics 5, 199–224 (1975).
    [CrossRef]

2014

J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
[CrossRef]

I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
[CrossRef]

2012

2011

2010

P. Poggiolini, G. Bosco, A. Carena, V. Curri, F. Forghieri, “Performance evaluation of coherent WDM PSQPSK (HEXA) accounting for non-linear fiber propagation effects,” Opt. Express 18, 11360–11371 (2010).
[CrossRef] [PubMed]

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

2009

2008

2000

C. D. Murphy, “High-order optimum hexagonal constellations,” IEEE PIMRC 1, 143–146 (2000).

1995

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

1990

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

1989

G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
[CrossRef]

1984

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

1975

J. H. van Lint, “A survey of perfect codes,” Rocky Mountain Journal of Mathematics 5, 199–224 (1975).
[CrossRef]

Agrell, E.

M. Karlsson, E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17, 10814–10819 (2009).
[CrossRef] [PubMed]

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

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

Andekson, P. A.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

Andrekson, P. A.

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

Anguita, J. A.

J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
[CrossRef]

Arik, S. Ö.

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

Batshon, H. G.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Bayvel, P.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
[CrossRef] [PubMed]

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

Behrens, C.

Bergano, N. S.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Bertran-Pardo, O.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Betti, S.

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

Bigo, S.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Bononi, A.

P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC, Th.10.E.2, (2010).

Bosco, G.

Buchali, F.

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

Bülow, H.

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

H. Bülow, “Polarization QAM modulation (POL-QAM) for coherent detection schemes,” Proc. OFC/NFOECOWG.2, (2009).

Cai, J.-X.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Carena, A.

Chagnon, M.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Charlet, G.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Coelho, L. D.

L. D. Coelho, N. Hanik, “Global Optimization of Fiber-Optic Communication Systems using Four-Dimensional Modulation Formats,” Proc. ECOCMo.2.B.4, (2011).

Conway, J. H.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, (Springer, 1998).

Curri, V.

Curti, F.

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

Cvijetic, M.

I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
[CrossRef]

David, G.

G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
[CrossRef]

De Marchis, G.

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

Djordjevic, I. B.

J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
[CrossRef]

I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
[CrossRef]

Duff, T. D. S.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

Eriksson, T. A.

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

Forghieri, F.

Forney, G.

G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
[CrossRef]

Forney, G. D.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

Foursa, D. G.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Gallager, R. G.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

Gho, G.-H.

G.-H. Gho, J. M. Kahn, “Rate-Adaptive Modulation and Coding for Optical Fiber Transmission Systems,” J. Lightwave Technol. 30, 1812–1818 (2012).
[CrossRef]

Hanik, N.

L. D. Coelho, N. Hanik, “Global Optimization of Fiber-Optic Communication Systems using Four-Dimensional Modulation Formats,” Proc. ECOCMo.2.B.4, (2011).

Hardin, R. H.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

Herreros, J.

J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
[CrossRef]

Hirooka, T.

M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
[CrossRef]

Iannone, E.

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

Idler, W.

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

Inoue, T.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Ishimura, S.

S. Ishimura, K. Kikuchi, “Multi-dimensional Permutation Modulation Aiming at Both High Spectral Efficiency and High Power Efficiency,” Proc. OFC/NFOECM3A.2, (2014).

Johannisson, P.

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

Kahn, J. M.

G.-H. Gho, J. M. Kahn, “Rate-Adaptive Modulation and Coding for Optical Fiber Transmission Systems,” J. Lightwave Technol. 30, 1812–1818 (2012).
[CrossRef]

Kametani, S.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Karlsson, M.

M. Karlsson, E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17, 10814–10819 (2009).
[CrossRef] [PubMed]

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

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

Kasai, K.

M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
[CrossRef]

Kikuchi, K.

S. Ishimura, K. Kikuchi, “Multi-dimensional Permutation Modulation Aiming at Both High Spectral Efficiency and High Power Efficiency,” Proc. OFC/NFOECM3A.2, (2014).

Koike-Akino, T.

D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

T. Koike-Akino, V. Tarokh, “Sphere packing optimization and EXIT chart analysis for multi-dimensional QAM signaling,” Proc. IEEE ICC (2009).

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).

Kojima, K.

T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).

Konishi, Y.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Kubo, K.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Kuebart, W.

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

Lang, G.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

Lavery, D.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
[CrossRef] [PubMed]

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

Li, J.

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

Lin, C.

I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
[CrossRef]

Longstaff, F. M.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

Maher, R.

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

Makovejs, S.

Mazurczyk, M.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Millar, D. S.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
[CrossRef] [PubMed]

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).

T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).

Miyata, Y.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Mizuochi, T.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Mohs, G.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Morsy-Osman, M.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Murphy, C. D.

C. D. Murphy, “High-order optimum hexagonal constellations,” IEEE PIMRC 1, 143–146 (2000).

Nakazawa, M.

M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
[CrossRef]

Onohara, K.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Parsons, K.

T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).

D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

Paskov, M.

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

Pilipetskii, A.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Plant, D.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Poggiolini, P.

Qiu, M.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Qureshi, S. U.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

Rahman, T.

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

Renaudier, J.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Rival, O.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Savory, S. J.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
[CrossRef] [PubMed]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
[CrossRef] [PubMed]

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

Serena, P.

P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC, Th.10.E.2, (2010).

Sinkin, O.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Sjödin, M.

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

Sloane, N. J. A.

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, (Springer, 1998).

Sugihara, K.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Sugihara, T.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Tarokh, V.

T. Koike-Akino, V. Tarokh, “Sphere packing optimization and EXIT chart analysis for multi-dimensional QAM signaling,” Proc. IEEE ICC (2009).

Thomsen, B. C.

D. S. Millar, D. Lavery, S. Makovejs, C. Behrens, B. C. Thomsen, P. Bayvel, S. J. Savory, “Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s,” Opt. Express 19, 9296–9302 (2011).
[CrossRef] [PubMed]

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

van Lint, J. H.

J. H. van Lint, “A survey of perfect codes,” Rocky Mountain Journal of Mathematics 5, 199–224 (1975).
[CrossRef]

Vannucci, A.

P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC, Th.10.E.2, (2010).

Voicila, A.

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

Wei., L.-F.

G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
[CrossRef]

Winzer, P. J.

Xu, X.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Yoshida, H.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

Yoshida, M.

M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
[CrossRef]

Zhang, H.

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

Zhuge, Q.

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

Discrete & Computational Geometry

N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete & Computational Geometry 14, 237–259 (1995).
[CrossRef]

Electron. Lett.

S. Betti, F. Curti, G. De Marchis, E. Iannone, “Exploiting fibre optics transmission capacity: 4-quadrature multilevel signalling,” Electron. Lett. 26, 992–993 (1990).
[CrossRef]

IEEE J. Sel. Areas Commun.

G. D. Forney, R. G. Gallager, G. Lang, F. M. Longstaff, S. U. Qureshi, “Efficient modulation for band-limited channels,” IEEE J. Sel. Areas Commun. 2, 632–647 (1984).
[CrossRef]

G. Forney, G. David, L.-F. Wei., “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Commun. 7, 877–892 (1989).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, T. Mizuochi, “Soft-Decision-Based Forward Error Correction for 100 Gb/s Transport Systems,” IEEE J. Sel. Top. Quantum Electron. 16, 1258–1267 (2010).
[CrossRef]

IEEE Photonics J.

J. A. Anguita, J. Herreros, I. B. Djordjevic, “Coherent Multimode OAM Superpositions for Multidimensional Modulation,” IEEE Photonics J. 6, 1–11 (2014).
[CrossRef]

IEEE PIMRC

C. D. Murphy, “High-order optimum hexagonal constellations,” IEEE PIMRC 1, 143–146 (2000).

IEEE Sig. Proc. Mag.

I. B. Djordjevic, M. Cvijetic, C. Lin, “Multidimensional Signaling and Coding Enabling Multi-Tb/s Optical Transport and Networking: Multidimensional aspects of coded modulation,” IEEE Sig. Proc. Mag. 3122, 104–117 (2014).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Rocky Mountain Journal of Mathematics

J. H. van Lint, “A survey of perfect codes,” Rocky Mountain Journal of Mathematics 5, 199–224 (1975).
[CrossRef]

Other

J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, (Springer, 1998).

T. Koike-Akino, V. Tarokh, “Sphere packing optimization and EXIT chart analysis for multi-dimensional QAM signaling,” Proc. IEEE ICC (2009).

P. Serena, A. Vannucci, A. Bononi, “The performance of polarization switched-QPSK (PS-QPSK) in dispersion managed WDM transmissions,” Proc. ECOC, Th.10.E.2, (2010).

Q. Zhuge, X. Xu, M. Morsy-Osman, M. Chagnon, M. Qiu, D. Plant, “Time Domain Hybrid QAM Based Rate-Adaptive Optical Transmissions Using High Speed DACs,” Proc. OFC/NFOECOTh4E.6, (2013).

H. Bülow, T. Rahman, F. Buchali, W. Idler, W. Kuebart, “Transmission of 4-D Modulation Formats at 28-Gbaud,” Proc. OFC/NFOECJW2A.39, (2013).

M. Nakazawa, T. Hirooka, M. Yoshida, K. Kasai, “Extremely Higher-Order Modulation Formats,” in Optical Fiber Telecommunications VIB, I. Kaminow, T. Li, A. E. Willner, eds. (Elsevier, 2013), pp. 297–336.
[CrossRef]

“Implementation Agreement for Integrated Dual Polarization Intradyne Coherent Receivers,” Optical Internetworking Forum (2010). http://www.oiforum.com/public/documents/OIF_DPC_RX-01.0.pdf .

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” Proc. ECOCWe.1.C.5, (2010).

L. D. Coelho, N. Hanik, “Global Optimization of Fiber-Optic Communication Systems using Four-Dimensional Modulation Formats,” Proc. ECOCMo.2.B.4, (2011).

M. Sjödin, P. Johannisson, J. Li, E. Agrell, P. A. Andrekson, M. Karlsson, “Comparison of 128-SP-QAM with PM-16-QAM,” Opt. Express20, 8356–8366 (2012).
[CrossRef] [PubMed]

H. Bülow, “Polarization QAM modulation (POL-QAM) for coherent detection schemes,” Proc. OFC/NFOECOWG.2, (2009).

T. A. Eriksson, P. Johannisson, M. Sjödin, E. Agrell, P. A. Andrekson, M. Karlsson, “Frequency and Polarization Switched QPSK,” Proc. ECOCTh.2.D.4, (2013).

S. Ishimura, K. Kikuchi, “Multi-dimensional Permutation Modulation Aiming at Both High Spectral Efficiency and High Power Efficiency,” Proc. OFC/NFOECM3A.2, (2014).

D. G. Foursa, H. G. Batshon, H. Zhang, M. Mazurczyk, J.-X. Cai, O. Sinkin, A. Pilipetskii, G. Mohs, N. S. Bergano, “44.1 Tb/s transmission over 9,100 km using coded modulation based on 16QAM signals at 4.9 bits/s/Hz spectral efficiency,” Proc. ECOCPD3.E.1, (2013).

D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “A 24-Dimensional Modulation Format Achieving 6 dB Asymptotic Power Efficiency,” Proc. SPPCOMSPM3D.6, (2013).

T. Koike-Akino, D. S. Millar, K. Kojima, K. Parsons, “Eight-Dimensional Modulation for Coherent Optical Communications,” Proc. ECOCTu.3.C.3, (2013).

D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima, K. Parsons, B. C. Thomsen, S. J. Savory, P. Bayvel, “Experimental Demonstration of 24-Dimensional Extended Golay Coded Modulation with LDPC,” Proc. OFC/NFOECM3A.5, (2014).

D. S. Millar, T. Koike-Akino, S. Ö. Arık, K. Kojima, K. Parsons, “Comparison of Quaternary Block-Coding and Sphere-Cutting for High-Dimensional Modulation,” Proc. OFC/NFOECM3A.4, (2014).

S. Ö. Arık, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, “High-Dimensional Modulation for Mode-Division Multiplexing,” Proc. OFC/NFOECW4J.1, (2014).

T. A. Eriksson, P. Johannisson, E. Agrell, P. A. Andekson, M. Karlsson, “Biorthogonal Modulation in 8 Dimensions Experimentally Implemented as 2PPM-PS-QPSK,” Proc. OFC/NFOECW1A.5, (2014).

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Figures (11)

Fig. 1
Fig. 1

Block diagram to illustrate transmission of p-bit, N-dimensional block-coded symbols over a 4-dimensional optical fiber channel. Solid arrows indicate binary signals, dashed arrows are either binary or multi-level signals, block arrows are multi-level and non-instantaneous, while hollow block arrows are optical signals.

Fig. 2
Fig. 2

4b-8D constellation (N = 8 and M = 16) with an example reference point and corresponding minimum and maximum distance points shown.

Fig. 3
Fig. 3

Extended Hamming [8,4,4] code constellation (N = 8 and M = 16) with an example reference point and corresponding minimum and maximum distance points shown.

Fig. 4
Fig. 4

Spectral efficiency (bit/symbol/dimension) vs sensitivity penalty (dB) of optimized sphere-cut constellations (circles) and block-coded modulation (crosses) and commonly used optical modulation formats (stars).

Fig. 5
Fig. 5

BER vs SNR in an AWGN channel for high-dimensional modulation formats with (a) sphere-cutting (b) block coding for spectral efficiencies between 0.5 and 0.571 bit/symbol/dimension. DP-BPSK/DP-QPSK is included for comparison.

Fig. 6
Fig. 6

BER vs SNR in an AWGN channel for high-dimensional modulation formats with (a) sphere-cutting (b) block coding for spectral efficiencies between 0.687 and 0.75 bit/symbol/dimension. DP-BPSK/DP-QPSK is included for comparison.

Fig. 7
Fig. 7

BER vs SNR in an AWGN channel for high-dimensional modulation formats with (a) sphere-cutting (b) block coding for spectral efficiencies between 0.875 and 1 bit/symbol/dimension. DP-BPSK/DP-QPSK is included for comparison.

Fig. 8
Fig. 8

SMF transmission system employing modulation with p bits in N dimensions: (a) Transmitter (b) SMF channel (c) Receiver.

Fig. 9
Fig. 9

Span loss budget for low-spectral efficiency modulation format for (a) 7% FEC overhead and BER threshold of 10−3, (b) 20% FEC overhead and BER threshold of 10−2.

Fig. 10
Fig. 10

Span loss budget for intermediate spectral efficiency modulation format for (a) 7% FEC overhead and BER threshold of 10−3, (b) 20% FEC overhead and BER threshold of 10−2.

Fig. 11
Fig. 11

Span loss budget for high-spectral efficiency modulation format for (a) 7% FEC overhead and BER threshold of 10−3, (b) 20% FEC overhead and BER threshold of 10−2.

Tables (2)

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Table 1 Average number of neighbors/dimension within 1.01 · dmin distance for sphere-cut/block-coded p-bit N-dimensional modulation.

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Table 2 Simulated modulated formats

Equations (6)

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c = ( c 1 , , c p )
E = ( real ( E x ( 1 , , N 4 ) ) imag ( E x ( 1 , , N 4 ) ) real ( E y ( 1 , , N 4 ) ) imag ( E y ( 1 , , N 4 ) ) ) = ( s 1 s 5 s N 3 s 2 s 6 s N 2 s 3 s 7 s N 1 s 4 s 8 s N )
c = ( c 1 , , c p )
w = ( w 1 , , w N ) = c × G
s = ( s 1 , , s N ) , where s i = ( 1 ) w i
E = ( real ( E x ( 1 , , N 4 ) ) imag ( E x ( 1 , , N 4 ) ) real ( E y ( 1 , , N 4 ) ) imag ( E y ( 1 , , N 4 ) ) ) = ( s 1 s 5 s N 3 s 2 s 6 s N 2 s 3 s 7 s N 1 s 4 s 8 s N )

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