Abstract

Constellation modulation (CM) is introduced as a new degree of freedom to increase the spectral efficiency and to further approach the Shannon limit. Constellation modulation is the art of encoding information not only in the symbols within a constellation but also by encoding information by selecting a constellation from a set of constellations that are switched from time to time. The set of constellations is not limited to sets of partitions from a given constellation but can e.g., be obtained from an existing constellation by applying geometrical transformations such as rotations, translations, scaling, or even more abstract transformations. The architecture of the transmitter and the receiver allows for constellation modulation to be used on top of existing modulations with little penalties on the bit-error ratio (BER) or on the required signal-to-noise ratio (SNR). The spectral bandwidth used by this modulation scheme is identical to the original modulation. Simulations demonstrate a particular advantage of the scheme for low SNR situations. So, for instance, it is demonstrated by simulation that a spectral efficiency increases by up to 33% and 20% can be obtained at a BER of 10−3 and 2×10−2 for a regular BPSK modulation format, respectively. Applying constellation modulation, we derive a most power efficient 4D-CM-BPSK modulation format that provides a spectral efficiency of 0.7 bit/s/Hz for an SNR of 0.2 dB at a BER of 2 × 10−2.

© 2017 Optical Society of America

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2016 (3)

2014 (2)

2013 (2)

2012 (3)

2011 (1)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

2010 (2)

2009 (3)

E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

J. Armstrong, “OFDM for Optical Communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
[Crossref]

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

2002 (1)

S. Verdu, “Spectral efficiency in the wideband regime,” IEEE Trans. Inf. Theory 48(6), 1319–1343 (2002).
[Crossref]

1993 (1)

J. P. Aldis and A. G. Burr, “The channel capacity of discrete time phase modulation in AWGN,” IEEE Trans. Inf. Theory 39(1), 184–185 (1993).
[Crossref]

1984 (1)

C. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Commun. 2(1), 153–170 (1984).
[Crossref]

1982 (1)

G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inf. Theory 28(1), 55–67 (1982).
[Crossref]

Agrell, E.

Aldis, J. P.

J. P. Aldis and A. G. Burr, “The channel capacity of discrete time phase modulation in AWGN,” IEEE Trans. Inf. Theory 39(1), 184–185 (1993).
[Crossref]

Alreesh, S.

Alvarado, A.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6(1), 21278 (2016).
[Crossref] [PubMed]

Arik, S. Ö.

Arikan, E.

E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

Armstrong, J.

Baeuerle, B.

Bayvel, P.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6(1), 21278 (2016).
[Crossref] [PubMed]

Becker, J.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ben-Ezra, S.

Birk, M.

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Borel, P. I.

Burr, A. G.

J. P. Aldis and A. G. Burr, “The channel capacity of discrete time phase modulation in AWGN,” IEEE Trans. Inf. Theory 39(1), 184–185 (1993).
[Crossref]

Carlson, K.

Cotter, D.

Dreschmann, M.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ellis, A. D.

Elschner, R.

Essiambre, R. J.

Fini, J. M.

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
[Crossref]

Fischer, J. K.

Forchhammer, S.

Foschini, G. J.

Freude, W.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Frey, F.

J. K. Fischer, S. Alreesh, R. Elschner, F. Frey, M. Nölle, C. Schmidt-Langhorst, and C. Schubert, “Bandwidth-Variable Transceivers based on Four-Dimensional Modulation Formats,” J. Lightwave Technol. 32(16), 2886–2895 (2014).
[Crossref]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Galili, M.

Goebel, B.

Guan, P.

Guodong, Z.

Hillerkuss, D.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Hu, H.

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Huebner, M.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Isaac, R.

Jeruchim, C.

C. Jeruchim, “Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication Systems,” IEEE J. Sel. Areas Commun. 2(1), 153–170 (1984).
[Crossref]

Jian Zhao,

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Karlsson, M.

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koike-Akino, T.

Kojima, K.

Koos, C.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Kramer, G.

Larsen, K. J.

Lavery, D.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6(1), 21278 (2016).
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Leuthold, J.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Li, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Lillieholm, M.

Ludwig, A.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Lutz, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Magill, P.

Maher, R.

R. Maher, A. Alvarado, D. Lavery, and P. Bayvel, “Increasing the information rates of optical communications via coded modulation: a study of transceiver performance,” Sci. Rep. 6(1), 21278 (2016).
[Crossref] [PubMed]

Marculescu, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Meyer, J.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Meyer, M.

Mikkelsen, B.

Millar, D. S.

Moeller, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

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Mulvad, H. C. H.

Narkiss, N.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Nebendahl, B.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
[Crossref] [PubMed]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Nelson, L. E.

Nölle, M.

Oehler, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Oxenløwe, L. K.

Pan, Y.

Parmigiani, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Peckham, D. W.

Pendock, G.

Petropoulos, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Resan, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Schmidt-Langhorst, C.

Schmogrow, R.

R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Figures (14)

Fig. 1
Fig. 1 Schematic representation of the symbol stream being transmitted in constellation modulation: the stream in constituted of meta-symbols. Each meta-symbol consists of a sequence of L consecutive symbols encoded with the same constellation.
Fig. 2
Fig. 2 Example of a constellation set generated by rotation of the 8 QAM constellation.
Fig. 3
Fig. 3 Schematic representation of the constellation modulation encoder. The input bit stream is segmented into blocks of k + (L × m) bits to be encoded onto a meta-symbol. In a first step, the first k bits are encoded by selecting one out of K constellations. Next the L × m bits are encoded by mapping the bits onto a consecutive sequence of L symbols each encoding m bits. Finally, the stream of meta-symbols comprising of bits encoded into constellations and symbols is transmitted.
Fig. 4
Fig. 4 Schematic representation of the decoder for constellation demodulation. The meta-symbol input stream is mapped onto all possible constellations within the set of K constellations. For each of the K possible constellations, the total square error of the received with respect to the ideal symbols of the constellations are determined. The constellation with the smallest total error is then selected as the constellation for demodulation of the meta-symbol. The demodulated bits of constellation modulation bit stream and symbol bit streams are then merged to form the output bit stream.
Fig. 5
Fig. 5 Representation of the transmitted symbols for (a) a regular 16 QAM signal, as well as for (b) a constellation modulated signal with a set of K = 2 constellations. The second constellation (in red) is obtained from the constellation (a) by a rotation of π/4 (right picture).
Fig. 6
Fig. 6 Spectral efficiency increase when working with sets of K rotated constellations for BPSK, 4 QAM, 8 QAM, 16 QAM, 32 QAM, and 64 QAM.
Fig. 7
Fig. 7 Polarization multiplexed BPSK (CM-PM-BPSK) encoded in two different sets of constellations. Each of the constellations c1 and c2 of the constellation set consists of two binary phase shift keying modulated signals multiplexed in two polarizations. To generate the second constellation c2, the initial constellation c1 is rotated by 90° in the complex plane.
Fig. 8
Fig. 8 Constellation modulation by relying on polarization switched BPSK (CM-PS-BPSK). Each of the constellations c1 and c2 of the constellation sets consists of a polarization switched binary phase shift keying modulated signal. To generate the second constellation c2, the initial constellation c1 is rotated by 90° in the complex plane.
Fig. 9
Fig. 9 Four-dimensional constellation modulation BPSK (4D-CM-BPSK). Each of the constellations c1, c2, c3 and c4 of the constellation set consists of a binary phase shift keying modulated signal. To generate the second constellation c2, the initial constellation c1 is rotated by 90° in the complex plane. The constellations c3 and c4 are then generated by switching the polarization of the constellations c1 and c2, respectively.
Fig. 10
Fig. 10 Spectral efficiency improvements through constellation modulation (red circle) for single polarization, (red square) for dual polarization 4D formats) compared to the original modulation (blue circle) for single polarization, (blue square) for dual polarization 4D formats)). These values are valid for a BER of 1 × 10−3 and are compared to the Shannon-Hartley limit (solid curve).
Fig. 11
Fig. 11 Spectral efficiency improvements through constellation modulation (red circle) for single polarization, (red square) for dual polarization 4D formats) compared to the original modulation (blue circle) for single polarization, (blue square) for dual polarization 4D formats)). These values are for a pre-FEC BER of 2 × 10−2 together with a SD-FEC overhead of 20%. The Shannon-Hartley limit (solid black curve) is plotted for reference.
Fig. 12
Fig. 12 Simulation results showing the bit-error ratio (in an AWGN Channel) as a function of SNR for the BPSK (blue circle) and CM-BPSK with constellation set size K of 2 and meta-symbol length L of 6 (red circle), PS-BPSK (blue trinagle) and CM-PS-BPSK with constellation set size K of 2 and meta-symbol length L of 6 (red triangle) and PS-QPSK (blue diamond), CM-PS-QPSK K of 2 and meta-symbol length L of 6 (red diamond) and finally the novel 4D-CM-BPSK for constellation set size K of 4 and meta-symbol length L of 4 (red square).
Fig. 13
Fig. 13 Experimental setup: Transmitter: An external cavity laser provides the optical carrier at 1550 nm to the IQ-modulator that encodes the 28 GBd signal generated by an arbitrary waveform generator operating at 56GSa/s. Inset (a) depicts the constellation of the QPSK signal with constellation modulation constellation points with (blue square) represents the standard QPSK constellation and the constellation points with (green square)) represents the π/4 rotated QPSK constellation (Ref [29].). Noise loading: The signal is then noise-loaded with an amplified spontaneous emission source (ASE). The OSNR and the relative ASE noise loading were adjusted with a variable optical attenuator (VOA). Receiver: The OSNR is measured by the optical spectrum analyzer (OSA). The signal is fed into a polarization controller to track the polarization and guarantee optimum power in the single polarization. A separate ECL is used as a local oscillator. The signal is then received with a coherent receiver. The real-time oscilloscope stores the signal for the offline processing (orange boxes). The received spectrum is the same, inset (b) depicts the spectrum of 28 GHz signal (‒ (blue dash)) with constellation modulation (meta-symbol length L of 8) and (‒ (red dash)) without constellation modulation. The processed constellation of the constellation modulated QPSK signal with meta-symbol length L = 10 after the constellation decision and correction.
Fig. 14
Fig. 14 Experimental results for meta-symbol lengths L of 6 (green square), 8 (blue square), 10 (turquoise square), 12 (pink square), and 14 (orange square) in comparison to QPSK (red square) and the theoretical limits (‒). (a) BER measurements for different signal to noise ratios for all meta-symbol lengths L. Theoretical limit (‒) and experimental results (red square, red dash) for QPSK serve as a reference, (b) BER for different L at the SNR required for a QPSK signal to reach a BER of 10−3. (c) Required SNR for different meta-symbol lengths L in comparison to QPSK (red ‒) to reach the BER of 10−3. (d) Spectral efficiency (SE) at a BER = 10−3 for all tested formats. A spectral efficiency increase of 6.25% is found for a constellation modulation format with meta-symbol length L = 8 (blue square).

Tables (5)

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Table 1 Summary of the performance of constellation modulation for transmission on a single polarization (2D) to reach total BER less than 1.2 × 10−3.

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Table 2 Summary of the performance of constellation modulation for transmission on a single polarization (2D) to reach a total BER of less than 2.2 × 10−2.

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Table 3 Descriptions of selected dual polarization constellation sets and their derivation from known modulation constellations.

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Table 4 Summary of the performance of constellation modulation in our 4D examples in order to reach a total BER less than 1.2 × 10−3.

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Table 5 Summary of the performance of constellation modulation in our 4D examples in order to reach a total BER less than 2.2 × 10−2.

Equations (8)

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E i = t=1 L | s t s t i | 2
Bitrate increase= lo g 2 ( K ) L×lo g 2 ( M i ) i
BE R 0 BE R 1 BE R 2 BE R K
d 1 min,s d 2 min,s d min,s
D i,j min,c = L × d i,j min,c for ij  
L> ( d i min d i,j min ) 2
BERBE R 0
BER= bit errors symbol stream +meta-symbol errors constellation stream N ο symbols symbol stream × log 2 ( M )+ N ο meta-symbol s constellation stream × log 2 ( K )

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