In this paper, a new method of constructing three-dimensional modulation formats with constant power is introduced. Constellations designed by the method have slightly larger minimum Euclidean distances (MEDs) than the conventional ones. No repetitive algorithm to maximize MED is used so that the new method has little computational complexity. Since signal points in the new formats are distributed regularly and symmetrically, an error control coding with systematic set-partition is applicable. We also present theoretical symbol error probability (SEP) of the new constellations in an additive white Gaussian noise environment, and demonstrate that the theoretical results are accurate. As the new modulation formats have almost the same or slightly lower SEPs than the conventional ones, they are appropriate for implementing a highly reliable optical communication system.

© 2011 OSA

1. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Express17(13), 10814–10819 (2009). [CrossRef] [PubMed]
2. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett.21(16), 1139–1141 (2009). [CrossRef]
3. J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun.150(5), 317–323 (2003). [CrossRef]
4. S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992). [CrossRef]
5. S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol.8(7), 1127–1136 (1990). [CrossRef]
6. S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol.10(12), 1985–1997 (1992). [CrossRef]
7. S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun.43(2/3/4), 1591–1602 (1995). [CrossRef]
8. R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun.45(1), 95–102 (1997). [CrossRef]
9. N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry. 14(3), 237–259 (1995).
10. J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).
11. Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett.14(2), 112–114 (2010). [CrossRef]

IEE Proc.-Commun.

• J.-E. Porath and T. Aulin, “Design of multidimensional signal constellations,” IEE Proc.-Commun.150(5), 317–323 (2003). [CrossRef]

IEEE Commun. Lett.

• Z. Chen, E. C. Choi, and S. G. Kang, “Closed-form expressions for the symbol error probability of 3-D OFDM,” IEEE Commun. Lett.14(2), 112–114 (2010). [CrossRef]

IEEE Photon. Technol. Lett.

• H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett.21(16), 1139–1141 (2009). [CrossRef]

IEEE Trans. Commun.

• S. Benedetto and E. Poggiolini, “Theory of polarization shift keying modulation,” IEEE Trans. Commun.40(4), 708–721 (1992). [CrossRef]
• S. Benedetto, G. Olmo, and E. Poggiolini, “Trellis coded polarization shift keying modulation for digital optical communications,” IEEE Trans. Commun.43(2/3/4), 1591–1602 (1995). [CrossRef]
• R. J. Blaikie, D. P. Taylor, and P. T. Gough, “Multilevel differential polarization shift keying,” IEEE Trans. Commun.45(1), 95–102 (1997). [CrossRef]

J. Lightwave Technol.

• S. Betti, F. Curti, G. D. Marchis, and E. Iannone, “Multilevel coherent optical system based on Stokes parameters modulation,” J. Lightwave Technol.8(7), 1127–1136 (1990). [CrossRef]
• S. Betti, G. D. Marchis, and E. Iannone, “Polarization modulated direct detection optical transmission systems,” J. Lightwave Technol.10(12), 1985–1997 (1992). [CrossRef]

Opt. Express

• M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?,” Opt. Express17(13), 10814–10819 (2009). [CrossRef] [PubMed]

Other

• N. J. A. Sloane, R. H. Hardin, T. D. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” discrete and Computational Geometry. 14(3), 237–259 (1995).
• J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, Singapore, 2008).

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