Abstract

Fundamental information-density limits are evaluated for amplified systems, based on entropy analysis. It is shown that in-line amplification introduces information loss, which is more important in distributed than in lumped amplification. In the absence of any other degradation (such as that which comes from dispersion and nonlinearity), spectral efficiencies of 614 bits/s/Hz represent theoretical limits for medium- and long-haul amplified systems.

© 2000 Optical Society of America

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References

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  1. C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).
    [CrossRef]
  2. See Proceedings of the European Conference on Optical Communication (Société des Électriciens et des Électroniciens, Paris, 1999).
  3. J. Stark, Ref. 2, paper I-28.
  4. T. E. Stern, IRE Trans. Inf. Theory435 (1960).
    [CrossRef]
  5. J. P. Gordon, Proc. IRE1898 (1962).
    [CrossRef]
  6. From an industrial viewpoint, η is referred to as efficiency; however, there is no a priori reason to assume that it should be less than unity 1 bit/s/Hz; it is better conceived as representing spectral ID. The true ID efficiency is defined with respect to the unamplified reference system, as discussed in this Letter.
  7. E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

1962 (1)

J. P. Gordon, Proc. IRE1898 (1962).
[CrossRef]

1960 (1)

T. E. Stern, IRE Trans. Inf. Theory435 (1960).
[CrossRef]

1948 (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).
[CrossRef]

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

Gordon, J. P.

J. P. Gordon, Proc. IRE1898 (1962).
[CrossRef]

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).
[CrossRef]

Stern, T. E.

T. E. Stern, IRE Trans. Inf. Theory435 (1960).
[CrossRef]

Bell Syst. Tech. J. (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379, 623 (1948).
[CrossRef]

IRE Trans. Inf. Theory (1)

T. E. Stern, IRE Trans. Inf. Theory435 (1960).
[CrossRef]

Proc. IRE (1)

J. P. Gordon, Proc. IRE1898 (1962).
[CrossRef]

Other (4)

From an industrial viewpoint, η is referred to as efficiency; however, there is no a priori reason to assume that it should be less than unity 1 bit/s/Hz; it is better conceived as representing spectral ID. The true ID efficiency is defined with respect to the unamplified reference system, as discussed in this Letter.

E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications (Wiley, New York, 1994).

See Proceedings of the European Conference on Optical Communication (Société des Électriciens et des Électroniciens, Paris, 1999).

J. Stark, Ref. 2, paper I-28.

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Figures (2)

Fig. 1
Fig. 1

Maximum ID versus optical signal power for several bandwidths, assuming coherent light signals.

Fig. 2
Fig. 2

ID versus number of lumped–distributed amplifying elements with Za=50 and Za=100km spacings, assuming 0–10-dBm mean signal power in a 1–10-GHz bandwidth.

Tables (1)

Tables Icon

Table 1 ID’s η [(bits/s)/Hz] versus Input Photon Number n0 for Coherent (ηcoh) and Amplified Signals with G=10 dB (ηamp) and G1 (ηHG), Assuming m= 2 and nsp= 1a

Equations (11)

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C/B=log21+PS/PN,
px-pxlogpx-ξx-n2+λxpx+μpx=0,  px=expμ-1+λx-ξx-n2,
Hcc=-pxlog2pxdxlog2σ2πe.
σamp2=Gn0+mN+2Gn0N+mN2,
η=C/B=HPS+PN-HPN
η=log2σS+NσN=12 log21+Gn01+2NmNN+1+m/4,
ηcoh=12 log21+4mn012 log21+4P0mhνB.
ηamp=12 log21+4P0mhνB2neq+1/G4neqneq+1/G+1/G.
ηHG=12 log21+2P0mhνB.
ηlinek=12 log21+4P0mhνB11+2kneqelem=12 log21+4P0mhνBFk,
ηlinekηcoh-log2Fk=ηcoh-log21+2kneqelem1/2.

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