## Analytical results on channel capacity in uncompensated optical links with coherent detection |

Optics Express, Vol. 19, Issue 26, pp. B440-B451 (2011)

http://dx.doi.org/10.1364/OE.19.00B440

Acrobat PDF (806 KB)

### Abstract

Based on a recently introduced model of non-linear propagation, we propose analytical formulas for the capacity limit of polarization-multiplexed ultra-dense WDM uncompensated coherent optical systems at the Nyquist limit, assuming both lumped and ideally distributed amplification. According to these formulas, capacity fundamentally depends on the transmitted power spectral density and on the total optical WDM bandwidth, whereas it does not depend on symbol-rate. Also, capacity approximately decreases by 2 [bit/s/Hz] for every doubling of link length. We show examples of capacity calculations for specific ultra-long-haul links with different polarization-multiplexed (PM) constellations, i.e. ideal PM-Gaussian, PM-QPSK (quadrature-phase shift keying) and PM-QAM (quadrature amplitude modulation). We show that the launch power maximizing capacity is independent of link length and modulation format. We also discuss the usable range of PM-QAM systems and validate analysis with simulations.

© 2011 OSA

## 1. Introduction

1. A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM,” J. Lightw. Technol. **29**, 373–377 (2011). [CrossRef]

6. E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. La Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at baud-rate subcarrier spacing,” Proc. European Conference on Optical Communication (2010), paper We.7.C.2. [CrossRef]

13. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. **23**, 742–744 (2011). [CrossRef]

16. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, and V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express **15**, 15777–15810 (2008). [CrossRef]

18. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express **18**, 19039–19054 (2010). [CrossRef] [PubMed]

8. J. Tang, “A comparison study of the Shannon channel capacity of various nonlinear optical fibers,” J. Lightw. Technol. **24**, 2070–2075 (2006). [CrossRef]

19. H. Louchet, A. Hodzic, and K. Petermann, “Analytical model for the performance evaluation of DWDM transmission systems,” IEEE Photon. Technol. Lett. **15**, 1219–1221 (2003). [CrossRef]

13. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. **23**, 742–744 (2011). [CrossRef]

13. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. **23**, 742–744 (2011). [CrossRef]

## 2. Non-linear interference modeling

**23**, 742–744 (2011). [CrossRef]

23. A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” Proc. European Conference on Optical Communication (2010), paper P4.07. [CrossRef]

*non-linear interference*(NLI).

*P*

_{Tx,ch}is the average per-channel power and

*P*

_{ASE}is the dual-polarization ASE noise power within the OSNR noise bandwidth

*B*. The NLI noise power

_{n}*P*

_{NLI}can be written as: where

*G*

_{NLI}is the PSD of NLI. The above formula assumes that

*G*

_{NLI}is locally ‘white’. This is not true in general, but it is very well verified at the Nyquist limit, especially over the center channel of the WDM comb.

**23**, 742–744 (2011). [CrossRef]

*P*

_{NLI}at the Nyquist limit was provided for the case of lumped (EDFA) amplification: where

*N*is the number of spans,

_{s}*γ*is the fiber nonlinearity coefficient,

*N*

_{ch}is the number of WDM channels and

*β*

_{2}is fiber dispersion.

*L*

_{eff}is the effective length, defined as:

*L*

_{eff}= [1 – exp(−2

*αL*)]/(2

_{s}*α*), with

*α*the fiber loss coefficient and

*L*the span length.

_{s}**23**, 742–744 (2011). [CrossRef]

*L*

_{tot}is the total link length. Though approximations, both Eqs. (3)–(4) asymptotically converge to the exact NLI model prediction as the logarithm argument is increased.

*P*

_{ASE}in Eq. (1), the standard formulas: and can be used, where

*F*is the EDFA amplifiers noise figure,

*h*is the Plank’s constant,

*ν*is the center frequency of the WDM comb and

*K*≥ 1 is a constant which is approximately equal to 1.13 for realistic Raman amplification [12

_{T}12. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. **28**, 662–701 (2010). [CrossRef]

**23**, 742–744 (2011). [CrossRef]

*R*and three different fiber types. All these tests were performed using simulations based on direct error counting at the receiver. A very good agreement was found throughout. In particular, the model proved accurate for all the tested formats, confirming, as its derivation appears to imply [14], [15], that it should be valid with any coherent format of any cardinality. If so, it can then be used together with the ideally Gaussian constellation which provides the maximum achievable capacity [12

_{s}12. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. **28**, 662–701 (2010). [CrossRef]

## 3. Optical channel capacity with Gaussian constellation at the Nyquist limit

*C*= log

_{2}(1 + SNR) [bit/s/Hz], where SNR is the ratio between the average signal power and the noise variance at the Rx decision stage, it is then possible to derive a similar formula for the polarization-multiplexed (PM) optical channel: with: The relationship between SNR and OSNR

_{NL}assumes matched electrical filtering. Note that since typical Rx adaptive equalizers tend towards matched filtering, this condition is also a realistic one.

*B*

_{WDM}is increased, though weakly due to the logarithm. This behavior is characteristic not only of the PM-Gaussian constellation which yields the ultimate capacity limits, but it can be shown to hold for any PM coherent format with UT. For instance, for PM-QPSK at the Nyquist limit a similar performance invariance vs. the symbol-rate was found in [13

**23**, 742–744 (2011). [CrossRef]

*K*= 1 (Fig. 1a) or EDFA amplification with

_{T}*F*=5 dB and

*L*=100 km (Fig. 1b). 125 channels at 32 GBaud each are considered, covering a total optical bandwidth

_{span}*B*

_{WDM}of 4 THz (approximately the C band). Each curve refers to a different system length, from 500 to 8000 km for DA and from 100 to 1600 km for EDFA amplification. The fiber is standard single-mode (SSMF) with same parameters as in [12

12. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. **28**, 662–701 (2010). [CrossRef]

*γ*= 1.27 1/W/km,

*α*= 0.22 dB/km,

*β*

_{2}= −21.7 ps

^{2}/km.

*L*within the inner logarithmic term in Eq. (13), it is easy to derive approximate laws for the peak capacity which confirm the decrease of about 2 bits/symbol for every doubling of distance for both EDFA and distributed amplification: Note that the previous relationships hold in general for capacity at any channel power, as can be easily derived from Eqs.(9)–(10).

_{tot}*P*

_{Tx,ch}(≃ −0.9 dBm for the EDFA case and ≃ −9.0 dBm for distributed amplification), independently of link length. We will further discuss this aspect in Sect. 4. Note also that, as shown in [26,27

27. A. Bononi and E. Grellier, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express **19**, 12781–12788 (2011). [CrossRef] [PubMed]

*P*

_{ASE}and

*P*

_{NLI}corresponding to the optimum launch power of −0.9 dBm in Fig. 1b can be evaluated using Eqs.(3) and (5), obtaining, at 1600 km,

*P*

_{ASE}≃−18.9 dBm and

*P*

_{NLI}≃−21.9 dBm over a 0.1 nm bandwidth.

**28**, 662–701 (2010). [CrossRef]

**28**, 662–701 (2010). [CrossRef]

**28**, 662–701 (2010). [CrossRef]

**28**, 662–701 (2010). [CrossRef]

## 4. Optical channel capacity for realistic constellations

*M*is the number of constellation points,

*X*= {

*x*

_{1},...,

*x*} is the set of possible transmitted symbols,

_{M}*Y*= {

*y*

_{1},...,

*y*} is set of the output symbols after hard-decision,

_{M}*P*(

_{Y|X}*b|a*) is the probability of receiving the symbol

*b*when the symbol

*a*has been transmitted,

*P*(

_{Y}*b*) is the probability of receiving the symbol

*b*.

*y*is the soft value at the output of the channel,

*p*(

_{Y|X}*y*|

*a*) is the probability density function of the random variable

*y*,

*p*(

_{Y}*y*), conditioned to the transmission of the symbol

*a*.

*f*is equal to the symbol-rate

*R*, the amount of

_{s}*P*

_{NLI}, required to estimate the OSNR

_{NL}, is evaluated using Eqs. (3)–(4). If Δ

*f*>

*R*,

_{s}*P*

_{NLI}can be obtained by resorting to the integral formula provided in [13

**23**, 742–744 (2011). [CrossRef]

## 5. Examples of application of the capacity formulas

### 5.1. Terrestrial link with EDFA amplification - Nyquist limit

### 5.2. Terrestrial link with EDFA amplification - 32 Gbaud with 50 GHz spacing

**23**, 742–744 (2011). [CrossRef]

*P*when the spacing is different from the symbol-rate, and requires numerical integration. Note that the plateau values of channel capacity in Fig. 4 are lower than ideal due to the loss of spectral efficiency induced by the channel spacing being larger than the symbol-rate (

_{NLI}*R*/Δ

_{s}*f*= 32/50 = 0.64). The simulation dots were obtained by estimating the capacity from BER values [12

**28**, 662–701 (2010). [CrossRef]

**23**, 742–744 (2011). [CrossRef]

### 5.3. Submarine link with EDFA amplification and PSCF fiber - Nyquist limit

*γ*= 0.9 1/W/km,

*α*= 0.18 dB/km,

*β*

_{2}= −26.3 ps

^{2}/km.

## 6. Conclusion

**28**, 662–701 (2010). [CrossRef]

## Acknowledgments

## References and links

1. | A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM,” J. Lightw. Technol. |

2. | K. Schuh, F. Buchali, D. Roesener, E. Lach, O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, and P. Tran, “15.4 Tb/s transmission over 2400 km using polarization multiplexed 32-Gbaud 16-QAM modulation and coherent detection comprising digital signal processing,” Proc. European Conference on Optical Communication (2011), paper We.8.B.4. |

3. | A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100x120 Gb/s PDM 64 QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” Proc. European Conference on Optical Communication (2010), paper PD2.2 [CrossRef] |

4. | T. Kobayashi, A. Sano, A. Matsuura, M. Yoshida, T. Sakano, H. Kubota, Y. Miyamoto, K. Ishihara, M. Mizoguchi, and M. Nagatani, “45.2Tb/s C-band WDM transmission over 240km using 538Gb/s PDM-64QAM single carrier FDM signal with digital pilot tone,” Proc. European Conference on Optical Communication (2011), PD paper Th.13.C.6 |

5. | J.-X. Cai, Y. Cai, C. Davidson, A. Lucero, H. Zhang, D. Foursa, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s capacity transmission over 6,860 km,” Proc. Optical Fiber Communication Conference (2011), paper PDPB4. |

6. | E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. La Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at baud-rate subcarrier spacing,” Proc. European Conference on Optical Communication (2010), paper We.7.C.2. [CrossRef] |

7. | P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature |

8. | J. Tang, “A comparison study of the Shannon channel capacity of various nonlinear optical fibers,” J. Lightw. Technol. |

9. | M. H. Taghavi, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory |

10. | H. Haunstein and M. Mayrock, “OFDM spectral efficiency limits from fiber and system non-linearities,” Proc. Optical Fiber Communication Conference (2010), paper OThM7. |

11. | A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. |

12. | R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. |

13. | P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. |

14. | P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “A simple and accurate model for non-linear propagation effects in uncompensated coherent transmission links,” Proc. International Conference on Transparent Optical Networks (2011), paper We.B1.3 |

15. | A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of non-linear propagation effects in uncompensated optical coherent transmission links,” submitted to IEEE J. Lightwave Technol. |

16. | M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, and V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express |

17. | B. Goebel, B. Fesl, L.D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” Proc. Optical Fiber Communication Conference (2008), paper JWA58. |

18. | X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express |

19. | H. Louchet, A. Hodzic, and K. Petermann, “Analytical model for the performance evaluation of DWDM transmission systems,” IEEE Photon. Technol. Lett. |

20. | E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri,“Experimental validation of an analytical model for nonlinear propagation in uncompensated pptical links,” Proc. European Conference on Optical Communication (2011), paper We.7.B.2. |

21. | S. Benedetto and E. Biglieri, |

22. | G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Proc. European Conference on Optical Communication (2011), paper We.7.B.3. |

23. | A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” Proc. European Conference on Optical Communication (2010), paper P4.07. [CrossRef] |

24. | F. Vacondio, C. Simonneau1, L. Lorcy, J.-C. Antona, A. Bononi, and S. Bigo, “Experimental characterization of Gaussian-distributed nonlinear distortions,” Proc. European Conference on Optical Communication (2011), paper We.7.B.1. |

25. | C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. |

26. | G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri,“Performance prediction for WDM PM-QPSK transmission over uncompensated links,” Proc. Optical Fiber Communication Conference (2011), paper OThO7. |

27. | A. Bononi and E. Grellier, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Transmission Systems and Network Elements

**History**

Original Manuscript: September 30, 2011

Revised Manuscript: November 16, 2011

Manuscript Accepted: November 16, 2011

Published: November 22, 2011

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," Opt. Express **19**, B440-B451 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B440

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### References

- A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Spectrally efficient long-haul WDM transmission using 224-Gb/s polarization-multiplexed 16-QAM,” J. Lightw. Technol.29, 373–377 (2011). [CrossRef]
- K. Schuh, F. Buchali, D. Roesener, E. Lach, O. Bertran-Pardo, J. Renaudier, G. Charlet, H. Mardoyan, and P. Tran, “15.4 Tb/s transmission over 2400 km using polarization multiplexed 32-Gbaud 16-QAM modulation and coherent detection comprising digital signal processing,” Proc. European Conference on Optical Communication (2011), paper We.8.B.4.
- A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, and T. Mizuno, “100x120 Gb/s PDM 64 QAM transmission over 160 km using linewidth-tolerant pilotless digital coherent detection,” Proc. European Conference on Optical Communication (2010), paper PD2.2 [CrossRef]
- T. Kobayashi, A. Sano, A. Matsuura, M. Yoshida, T. Sakano, H. Kubota, Y. Miyamoto, K. Ishihara, M. Mizoguchi, and M. Nagatani, “45.2Tb/s C-band WDM transmission over 240km using 538Gb/s PDM-64QAM single carrier FDM signal with digital pilot tone,” Proc. European Conference on Optical Communication (2011), PD paper Th.13.C.6
- J.-X. Cai, Y. Cai, C. Davidson, A. Lucero, H. Zhang, D. Foursa, O. Sinkin, W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s capacity transmission over 6,860 km,” Proc. Optical Fiber Communication Conference (2011), paper PDPB4.
- E. Torrengo, R. Cigliutti, G. Bosco, G. Gavioli, A. Alaimo, A. Carena, V. Curri, F. Forghieri, S. Piciaccia, M. Belmonte, A. Brinciotti, A. La Porta, S. Abrate, and P. Poggiolini, “Transoceanic PM-QPSK Terabit superchannel transmission experiments at baud-rate subcarrier spacing,” Proc. European Conference on Optical Communication (2010), paper We.7.C.2. [CrossRef]
- P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411, 1027–1030 (2001). [CrossRef] [PubMed]
- J. Tang, “A comparison study of the Shannon channel capacity of various nonlinear optical fibers,” J. Lightw. Technol.24, 2070–2075 (2006). [CrossRef]
- M. H. Taghavi, “On the multiuser capacity of WDM in a nonlinear optical fiber: coherent communication,” IEEE Trans. Inf. Theory52, 5008–5022 (2006). [CrossRef]
- H. Haunstein and M. Mayrock, “OFDM spectral efficiency limits from fiber and system non-linearities,” Proc. Optical Fiber Communication Conference (2010), paper OThM7.
- A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol.28, 423–433 (2010). [CrossRef]
- R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol.28, 662–701 (2010). [CrossRef]
- P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett.23, 742–744 (2011). [CrossRef]
- P. Poggiolini, G. Bosco, A. Carena, V. Curri, and F. Forghieri, “A simple and accurate model for non-linear propagation effects in uncompensated coherent transmission links,” Proc. International Conference on Transparent Optical Networks (2011), paper We.B1.3
- A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of non-linear propagation effects in uncompensated optical coherent transmission links,” submitted to IEEE J. Lightwave Technol.
- M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, I. Shpantzer, and V. Karagodsky, “Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links,” Opt. Express15, 15777–15810 (2008). [CrossRef]
- B. Goebel, B. Fesl, L.D. Coelho, and N. Hanik, “On the effect of FWM in coherent optical OFDM systems,” Proc. Optical Fiber Communication Conference (2008), paper JWA58.
- X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express18, 19039–19054 (2010). [CrossRef] [PubMed]
- H. Louchet, A. Hodzic, and K. Petermann, “Analytical model for the performance evaluation of DWDM transmission systems,” IEEE Photon. Technol. Lett.15, 1219–1221 (2003). [CrossRef]
- E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri,“Experimental validation of an analytical model for nonlinear propagation in uncompensated pptical links,” Proc. European Conference on Optical Communication (2011), paper We.7.B.2.
- S. Benedetto and E. Biglieri, Principles of digital transmission: with wireless applications (New York: Kluwer, 1999).
- G. Bosco, P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Analytical results on channel capacity in uncompensated optical links with coherent detection,” Proc. European Conference on Optical Communication (2011), paper We.7.B.3.
- A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. Tapia Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” Proc. European Conference on Optical Communication (2010), paper P4.07. [CrossRef]
- F. Vacondio, C. Simonneau1, L. Lorcy, J.-C. Antona, A. Bononi, and S. Bigo, “Experimental characterization of Gaussian-distributed nonlinear distortions,” Proc. European Conference on Optical Communication (2011), paper We.7.B.1.
- C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423 (1948).
- G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri,“Performance prediction for WDM PM-QPSK transmission over uncompensated links,” Proc. Optical Fiber Communication Conference (2011), paper OThO7.
- A. Bononi and E. Grellier, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express19, 12781–12788 (2011). [CrossRef] [PubMed]

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