Abstract

We propose a space–time coding scheme designed to increase the tolerance of fiber-optic communications systems to polarization-dependent loss (PDL). A notable increase in the tolerable amount of average link PDL is achieved without affecting the complexity of the overall optical communications link. Other advantages include seamless integration with the broadly deployed blind equalization modules relying on the constant modulus algorithm.

© 2013 Optical Society of America

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References

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  1. V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
    [CrossRef]
  2. S. Mumtaz, G. R. Othman, and Y. Jaouen, in National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2010), paper JThA7.
  3. E. Meron, A. Andrusier, M. Feder, and M. Shtaif, Opt. Lett. 35, 3547 (2010).
    [CrossRef]
  4. S. J. Savory, Opt. Express 16, 804 (2008).
    [CrossRef]
  5. A. Viterbi, IEEE Trans. Inf. Theory 13, 260 (1967).
    [CrossRef]
  6. L. E. Nelson, C. Antonelli, A. Mecozzi, M. Birk, P. Magill, A. Schex, and L. Rapp, Opt. Express 19, 6790 (2011).
    [CrossRef]
  7. A. Andrusier and M. Shtaif, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2009), paper 4.0.1.
  8. M. Shtaif, Opt. Express 16, 13918 (2008).
    [CrossRef]
  9. A. Andrusier, M. Shtaif, and E. Meron, in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2012), paper OTu1A.1.
  10. A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
    [CrossRef]
  11. C. Antonelli, A. Mecozzi, L. E. Nelson, and P. Magill, Opt. Lett. 36, 4005 (2011).
    [CrossRef]

2011 (2)

2010 (1)

2008 (2)

2002 (1)

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

1998 (1)

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

1967 (1)

A. Viterbi, IEEE Trans. Inf. Theory 13, 260 (1967).
[CrossRef]

Andrusier, A.

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, Opt. Lett. 35, 3547 (2010).
[CrossRef]

A. Andrusier, M. Shtaif, and E. Meron, in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2012), paper OTu1A.1.

A. Andrusier and M. Shtaif, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2009), paper 4.0.1.

Antonelli, C.

Birk, M.

Calderbank, A. R.

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

Feder, M.

Jaouen, Y.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2010), paper JThA7.

Magill, P.

Mecozzi, A.

Meron, E.

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, Opt. Lett. 35, 3547 (2010).
[CrossRef]

A. Andrusier, M. Shtaif, and E. Meron, in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2012), paper OTu1A.1.

Mumtaz, S.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2010), paper JThA7.

Nelson, L. E.

Othman, G. R.

S. Mumtaz, G. R. Othman, and Y. Jaouen, in National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2010), paper JThA7.

Rapp, L.

Savory, S. J.

Schex, A.

Seshadri, N.

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

Shtaif, M.

E. Meron, A. Andrusier, M. Feder, and M. Shtaif, Opt. Lett. 35, 3547 (2010).
[CrossRef]

M. Shtaif, Opt. Express 16, 13918 (2008).
[CrossRef]

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

A. Andrusier and M. Shtaif, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2009), paper 4.0.1.

A. Andrusier, M. Shtaif, and E. Meron, in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2012), paper OTu1A.1.

Tarokh, V.

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

Viterbi, A.

A. Viterbi, IEEE Trans. Inf. Theory 13, 260 (1967).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

IEEE Trans. Inf. Theory (2)

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

A. Viterbi, IEEE Trans. Inf. Theory 13, 260 (1967).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Other (3)

S. Mumtaz, G. R. Othman, and Y. Jaouen, in National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2010), paper JThA7.

A. Andrusier, M. Shtaif, and E. Meron, in Optical Fiber Communication Conference, Technical Digest (Optical Society of America, 2012), paper OTu1A.1.

A. Andrusier and M. Shtaif, in Proceedings of the European Conference on Optical Communication (ECOC) (IEEE, 2009), paper 4.0.1.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Equivalent optical implementation contains a birefringent element introducing a differential delay τ between the polarization axes at 45° and 45° with respect to H and V. (b) Digital implementation as a space–time code. (c) The data transmitted over the H and V polarizations are smeared over a large circle on the Poincaré sphere, thereby averaging the effect of PDL. Tx, transmitter; Rx, receiver; MUX, optical multiplexer.

Fig. 2.
Fig. 2.

(a) Required link margin as a function of the coding delay. The solid curves correspond to the proposed scheme with a ZF receiver, and the stars indicate the CMA receiver results, shown only for integer values of τ/Ts. The dashed curves show the results that would be obtained if instead of the space–time code proposed here, PMD with average DGP equal to τ were distributed along the link as in [9]. (b) Required margin versus mean PDL with the Silver and Golden codes, the proposed code (with τ=Ts), and in the uncoded case. Silver and Golden code results were copied from [3].

Fig. 3.
Fig. 3.

Cumulated distributions of the SNR penalty when only the worst of the two polarization channels is transmitted (leftmost curve), the best of the two channels is transmitted (rightmost curve) and the cumulated distribution of the average SNR penalty (middle dashed curve). The circles and plus symbols on the middle curve represent the distribution of the SNR penalty with both channels transmitted and using the proposed coding scheme with τ=Ts. The overlap of the circles and plus symbols with the middle curve indicates the perfect averaging that takes place. The plot was produced under the assumption of a ZF receiver.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

EH(t)=sH(t)+sV(t)2+sH(tτ)sV(tτ)2,
EV(t)=sH(t)+sV(t)2sH(tτ)sV(tτ)2,
bH,k=aH,k+aV,k2+aH,kmaV,km2,
bV,k=aH,k+aV,k2aH,kmaV,km2,
aH,k=bH,k+bV,k2+bH,k+mbV,k+m2,
aV,k=bH,k+bV,k2bH,k+mbV,k+m2,

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