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 (1)

2008 (4)

2006 (1)

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

2003 (1)

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

1998 (1)

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 (1)

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. (1)

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

IEEE J. Lightwave Technol. (1)

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

IEEE J. Sel. Areas Commun. (1)

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

IEEE Trans. Inf. Theory (1)

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. (1)

Opt. Express (3)

Phys. Rev. Lett. (1)

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

Other (1)

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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