Abstract

We characterize the effect of polarization dependent loss (PDL) on the information capacity of fiber-optic channels. The reduction in the outage capacity owing to the PDL is quantified as well as the signal-to-noise ratio margin that needs to be allocated for the PDL in order to avoid loss of capacity.

© 2009 Optical Society of America

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References

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  1. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
  2. M. Yoshida, H. Goto, K. Kasai, and M. Nakazawa, Opt. Express 16, 829 (2008).
    [CrossRef] [PubMed]
  3. See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
    [CrossRef] [PubMed]
  4. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, J. Lightwave Technol. 26, 36 (2008).
    [CrossRef]
  5. M. Shtaif, Opt. Express 16, 13918 (2008).
    [CrossRef] [PubMed]
  6. A. Andrusier and M. Shtaif, Opt. Express 17, 8173 (2009).
    [CrossRef] [PubMed]
  7. Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
    [CrossRef]
  8. A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
    [CrossRef]
  9. C. Antonelli and A. Mecozzi, IEEE J. Lightwave Technol. 24, 4064 (2006).
    [CrossRef]
  10. The notation O(Γ) or O(Γ2) refers to the general dependence of the considered quantity on the fundamental (local) PDL vector contributions, not necessarily on a particular vector such as Γ⃗0 or Γ⃗′.

2009

2008

2006

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

2003

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

1998

Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

1948

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Andrusier, A.

Antonelli, C.

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

Bigo, S.

Calderbank, A. R.

Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Charlet, G.

Essiambre, R. J.

See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Foschini, G. J.

See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Goldsmith, A.

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

Goto, H.

Jafar, S. A.

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

Jindal, N.

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

Kasai, K.

Kramer, G.

See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Mardoyan, H.

Mecozzi, A.

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

Nakazawa, M.

Pardo, O. B.

Renaudier, J.

Salsi, M.

Seshadri, N.

Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Shtaif, M.

Tarokh, V.

Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

Tran, P.

Vishwanath, S.

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

Winzer, P.

See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Yoshida, M.

Bell Syst. Tech. J.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

IEEE J. Lightwave Technol.

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

IEEE J. Sel. Areas Commun.

A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, IEEE J. Sel. Areas Commun. 21, 684 (2003).
[CrossRef]

IEEE Trans. Inf. Theory

Such codes are commonly used now in wireless MIMO systems. A good reference is V. Tarokh, N. Seshadri, and A. R. Calderbank, IEEE Trans. Inf. Theory 44, 744 (1998).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Phys. Rev. Lett.

See, for example, R. J. Essiambre, G. J. Foschini, G. Kramer, and P. Winzer, Phys. Rev. Lett. 101, 163901 (2008).
[CrossRef] [PubMed]

Other

The notation O(Γ) or O(Γ2) refers to the general dependence of the considered quantity on the fundamental (local) PDL vector contributions, not necessarily on a particular vector such as Γ⃗0 or Γ⃗′.

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Figures (2)

Fig. 1
Fig. 1

Cumulative distributions of (a) the instantaneous capacity loss C C 0 and (b) the instantaneous SNR penalty η in decibels. Dashed, solid, and dashed–dotted curves correspond to SNR = 20 , 10, and 7 dB, respectively, and the respective values of C 0 are 13.3, 6.9, and 5.2 bits per symbol. The dashed horizontal line indicates the outage probability of p o u t = 4 × 10 5 .

Fig. 2
Fig. 2

(a) Loss in outage capacity and (b) the required SNR margin as functions of the link average PDL. The SNR values are 20 (dashed–dotted curve), 10 (solid curve), and 7 (dashed curve) dB. The thin solid curve in (b) represents the BER-based result of [5].

Equations (9)

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r ̱ = T 0 x ̱ + n ̱ ,
Λ n = S 0 1 g ( I + Γ σ ) ,
r ̃ = H x ̱ + n ̃ ,
C = log 2 [ det ( I + H H ) ] ,
H H = S 0 g ( 1 Γ 2 ) T 0 ( I Γ σ ) T 0 .
η = S 0 det ( I + H H ) 1 ,
η S 0 det ( H H ) = g 1 Γ 2 1 Γ 0 2 ,
g = 1 N s j = 1 N s 1 Γ j Γ 0 1 Γ j 2 ,
η = 1 + O ( Γ 2 ) .

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