Abstract

We evaluate the advantage of using space–time coding in order to increase the tolerance of fiber-optic communications systems to polarization-dependent loss (PDL). Focusing on three particular codes, the Golden Code, the Silver Code (SC), and the Alamouti Code (AC), we calculate the amount of average PDL that can be tolerated for a given signal-to-noise ratio margin that is designed into the system. The SC is shown to be optimal in the case of low to moderate PDL, whereas, in the case of extreme PDL, the AC shows the best performance.

© 2010 Optical Society of America

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  1. See, for example, J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, J. Lightwave Technol. 26, 36 (2008).
    [CrossRef]
  2. A. Mecozzi and M. Shtaif, IEEE Photonics Technol. Lett. 14, 313 (2002).
    [CrossRef]
  3. C. Xie and L. F. Mollenauer, J. Lightwave Technol. 21, 1953 (2003).
    [CrossRef]
  4. M. Shtaif and A. Mecozzi, IEEE Photonics Technol. Lett. 16, 671 (2004).
    [CrossRef]
  5. Z. Wang, C. Xie, and X. Ren, Opt. Express 17, 7993 (2009).
    [CrossRef] [PubMed]
  6. J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
    [CrossRef]
  7. O. Tirkkonen and A. Hottinen, IEEE Trans. Inf. Theory 48, 384 (2002).
    [CrossRef]
  8. L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).
  9. S. Mumtaz, G. R. Othman, and Y. Jaouen, in Proceedings of Optical Fiber Communication Conference, paper JThA7 (2010).
  10. S. Mumtaz, G. R. Othman, and Y. Jaouen, in IEEE International Conference on Communications (ICC) (2010).
  11. V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
    [CrossRef]
  12. M. Shtaif, Opt. Express 16, 13918 (2008).
    [CrossRef] [PubMed]
  13. A. Galtarossa and L. Palmieri, IEEE Photonics Technol. Lett. 15, 57 (2003).
    [CrossRef]
  14. C. Antonelli and A. Mecozzi, J. Lightwave Technol. 24, 4064 (2006).
    [CrossRef]
  15. A. Andrusier and M. Shtaif, Opt. Express 17, 8173 (2009).
    [CrossRef] [PubMed]
  16. A. Nafta, E. Meron, and M. Shtaif, Opt. Lett. 34, 3613 (2009).
    [CrossRef] [PubMed]
  17. We note that since the time constants characterizing the temporal variations of the channel matrix are typically much longer than the FEC frame, other commonly used quantities such as the ergodic capacity are of no relevance in our case.

2009 (3)

2008 (2)

2006 (1)

2005 (1)

J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
[CrossRef]

2004 (1)

M. Shtaif and A. Mecozzi, IEEE Photonics Technol. Lett. 16, 671 (2004).
[CrossRef]

2003 (2)

A. Galtarossa and L. Palmieri, IEEE Photonics Technol. Lett. 15, 57 (2003).
[CrossRef]

C. Xie and L. F. Mollenauer, J. Lightwave Technol. 21, 1953 (2003).
[CrossRef]

2002 (2)

A. Mecozzi and M. Shtaif, IEEE Photonics Technol. Lett. 14, 313 (2002).
[CrossRef]

O. Tirkkonen and A. Hottinen, IEEE Trans. Inf. Theory 48, 384 (2002).
[CrossRef]

1998 (1)

V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Andrusier, A.

Antonelli, C.

Belfiore, J. C.

J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
[CrossRef]

Belfiore, J.-C.

L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).

Bigo, S.

Calderbank, A. R.

V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Charlet, G.

Galtarossa, A.

A. Galtarossa and L. Palmieri, IEEE Photonics Technol. Lett. 15, 57 (2003).
[CrossRef]

Hottinen, A.

O. Tirkkonen and A. Hottinen, IEEE Trans. Inf. Theory 48, 384 (2002).
[CrossRef]

Jaouen, Y.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in Proceedings of Optical Fiber Communication Conference, paper JThA7 (2010).

S. Mumtaz, G. R. Othman, and Y. Jaouen, in IEEE International Conference on Communications (ICC) (2010).

Mardoyan, H.

Mecozzi, A.

C. Antonelli and A. Mecozzi, J. Lightwave Technol. 24, 4064 (2006).
[CrossRef]

M. Shtaif and A. Mecozzi, IEEE Photonics Technol. Lett. 16, 671 (2004).
[CrossRef]

A. Mecozzi and M. Shtaif, IEEE Photonics Technol. Lett. 14, 313 (2002).
[CrossRef]

Meron, E.

Mollenauer, L. F.

Mroueh, L.

L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).

Mumtaz, S.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in Proceedings of Optical Fiber Communication Conference, paper JThA7 (2010).

S. Mumtaz, G. R. Othman, and Y. Jaouen, in IEEE International Conference on Communications (ICC) (2010).

Nafta, A.

Othman, G. R.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in IEEE International Conference on Communications (ICC) (2010).

S. Mumtaz, G. R. Othman, and Y. Jaouen, in Proceedings of Optical Fiber Communication Conference, paper JThA7 (2010).

L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).

Palmieri, L.

A. Galtarossa and L. Palmieri, IEEE Photonics Technol. Lett. 15, 57 (2003).
[CrossRef]

Pardo, O. B.

Rekaya, G.

J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
[CrossRef]

Ren, X.

Renaudier, J.

Rouquette-Leveil, S.

L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).

Salsi, M.

Seshadri, N.

V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Shtaif, M.

Tarokh, V

V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Tirkkonen, O.

O. Tirkkonen and A. Hottinen, IEEE Trans. Inf. Theory 48, 384 (2002).
[CrossRef]

Tran, P.

Viterbo, E.

J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
[CrossRef]

Wang, Z.

Xie, C.

IEEE Photonics Technol. Lett. (3)

A. Mecozzi and M. Shtaif, IEEE Photonics Technol. Lett. 14, 313 (2002).
[CrossRef]

M. Shtaif and A. Mecozzi, IEEE Photonics Technol. Lett. 16, 671 (2004).
[CrossRef]

A. Galtarossa and L. Palmieri, IEEE Photonics Technol. Lett. 15, 57 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (3)

V Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

J. C. Belfiore, G. Rekaya, and E. Viterbo, IEEE Trans. Inf. Theory 51, 1432 (2005).
[CrossRef]

O. Tirkkonen and A. Hottinen, IEEE Trans. Inf. Theory 48, 384 (2002).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Lett. (1)

Other (4)

L. Mroueh, S. Rouquette-Leveil, G. R. Othman, and J.-C. Belfiore, in Forty-First Asilomar Conference on Signals, Systems and Computers (2007).

S. Mumtaz, G. R. Othman, and Y. Jaouen, in Proceedings of Optical Fiber Communication Conference, paper JThA7 (2010).

S. Mumtaz, G. R. Othman, and Y. Jaouen, in IEEE International Conference on Communications (ICC) (2010).

We note that since the time constants characterizing the temporal variations of the channel matrix are typically much longer than the FEC frame, other commonly used quantities such as the ergodic capacity are of no relevance in our case.

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Figures (3)

Fig. 1
Fig. 1

Schematic of coding implementation. ST stands for space–time.

Fig. 2
Fig. 2

Complementary cumulated distribution of the PDL-induced SNR penalty for average PDL of (a) 3, (b) 5, (c) 8, and (d) 10 dB ; w/o refers to the calculation without space–time coding. Dotted horizontal line indicates the outage probability of 4 × 10 5 . The curve corresponding to the AC is not shown in the 3 dB case, as it is almost outside the range of plotted values. Similarly, the curve without ST coding is outside the range of displayed values in parts (c) and (d). All curves were obtained for QPSK constellations.

Fig. 3
Fig. 3

(a) SNR that is required to achieve a raw BER of 10 3 with probability 1 P outage . The curve labeled Cap. shows the SNR that is needed in order to guarantee that the channel capacity exceeds 2 bits per polarization with probability 1 P outage . (b) The SNR margin that needs to be allocated for the various codes.

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