Abstract

Soft-decision forward error correction (SD-FEC) schemes are typically designed for additive white Gaussian noise (AWGN) channels. In a fiber-optic communication system, noise may be neither circularly symmetric nor Gaussian, thus violating an important assumption underlying SD-FEC design. This paper quantifies the impact of non-AWGN noise on SD-FEC performance for such optical channels. We use a conditionally bivariate Gaussian noise model (CBGN) to analyze the impact of correlations among the signal’s two quadrature components, and assess the effect of CBGN on SD-FEC performance using the density evolution of low-density parity-check (LDPC) codes. On a CBGN channel generating severely elliptic noise clouds, it is shown that more than 3 dB of coding gain are attainable by utilizing correlation information. Our analyses also give insights into potential improvements of the detection performance for fiber-optic transmission systems assisted by SD-FEC.

© 2012 OSA

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References

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  1. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
    [CrossRef]
  2. T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).
  3. P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
    [CrossRef]
  4. ITU-T Recommendation G.975.1, 2004, Appendix I.9.
  5. A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
    [CrossRef]
  6. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of nonlinear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23, 742–744 (2011).
    [CrossRef]
  7. X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
    [CrossRef]
  8. X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).
  9. C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Sel. Top. Quantum Electron. 12, 843–8582006.
    [CrossRef]
  10. C. Xie, “Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators,” in Proc. European Conference on Optical Communication (ECOC’09), P4.08 (2009).
  11. C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol. 29, 536–5412011.
    [CrossRef]
  12. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28, 547–5562010.
    [CrossRef]
  13. A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).
  14. C. Xie and R.-J. Essiambre, “Electronic nonlinearity compensation in 112-Gb/s PDM-QPSK optical coherent transmission systems,” in Proc. European Conference on Optical Communication (ECOC’10), Mo.1.C.1 (2010).
    [CrossRef]
  15. C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in Proc. European Conference on Optical Communication (ECOC’11), We.8.B.1 (2011).
  16. J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).
  17. A. Leon-Garcia, Probability and random processes for electrical engineering, 2nd ed. (Addison-Wesley, 1993).
  18. N. A. Ahmed and D. V. Gokhale, “Entropy expressions and their estimators for multivariate distributions,” IEEE. Trans. Inf. Theory 35, 688–692 (1989).
    [CrossRef]
  19. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, 2005).
    [CrossRef]
  20. S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
    [CrossRef]
  21. R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inf. Theory IT-8, 21–28 (1962).
    [CrossRef]
  22. T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
    [CrossRef]
  23. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
    [CrossRef]
  24. F. R. Kschischang, B. J. Frey, and H-A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
    [CrossRef]
  25. R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory IT-27, 533–547 (1981).
    [CrossRef]

2011 (5)

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

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

C. R. Doerr, L. Zhang, and P. J. Winzer, “Monolithic InP multiwavelength coherent receiver using a chirped arrayed waveguide grating,” J. Lightwave Technol. 29, 536–5412011.
[CrossRef]

C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in Proc. European Conference on Optical Communication (ECOC’11), We.8.B.1 (2011).

J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).

2010 (5)

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28, 547–5562010.
[CrossRef]

C. Xie and R.-J. Essiambre, “Electronic nonlinearity compensation in 112-Gb/s PDM-QPSK optical coherent transmission systems,” in Proc. European Conference on Optical Communication (ECOC’10), Mo.1.C.1 (2010).
[CrossRef]

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
[CrossRef]

2009 (1)

C. Xie, “Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators,” in Proc. European Conference on Optical Communication (ECOC’09), P4.08 (2009).

2006 (1)

C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Sel. Top. Quantum Electron. 12, 843–8582006.
[CrossRef]

2005 (1)

P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
[CrossRef]

2001 (4)

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

F. R. Kschischang, B. J. Frey, and H-A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

1989 (1)

N. A. Ahmed and D. V. Gokhale, “Entropy expressions and their estimators for multivariate distributions,” IEEE. Trans. Inf. Theory 35, 688–692 (1989).
[CrossRef]

1981 (1)

R. M. Tanner, “A recursive approach to low complexity codes,” IEEE Trans. Inf. Theory IT-27, 533–547 (1981).
[CrossRef]

1962 (1)

R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inf. Theory IT-8, 21–28 (1962).
[CrossRef]

Ahmed, N. A.

N. A. Ahmed and D. V. Gokhale, “Entropy expressions and their estimators for multivariate distributions,” IEEE. Trans. Inf. Theory 35, 688–692 (1989).
[CrossRef]

Bosco, G.

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

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Buhl, L. L.

Carena, A.

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

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
[CrossRef]

Charlet, G.

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Cho, J.

J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).

Chung, S. -Y.

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, 2005).
[CrossRef]

Curri, V.

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

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Doerr, C. R.

Dorrer, C.

C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Sel. Top. Quantum Electron. 12, 843–8582006.
[CrossRef]

Draving, S.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

Dupuy, J.-Y.

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Essiambre, R.-J.

C. Xie and R.-J. Essiambre, “Electronic nonlinearity compensation in 112-Gb/s PDM-QPSK optical coherent transmission systems,” in Proc. European Conference on Optical Communication (ECOC’10), Mo.1.C.1 (2010).
[CrossRef]

P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
[CrossRef]

Evangelista, J.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

Forghieri, F.

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

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Forney, J. G. D.

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

Frey, B. J.

F. R. Kschischang, B. J. Frey, and H-A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Gallager, R. G.

R. G. Gallager, “Low-density parity-check codes,” IRE Trans. Inf. Theory IT-8, 21–28 (1962).
[CrossRef]

Gnauck, A. H.

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28, 547–5562010.
[CrossRef]

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Gokhale, D. V.

N. A. Ahmed and D. V. Gokhale, “Entropy expressions and their estimators for multivariate distributions,” IEEE. Trans. Inf. Theory 35, 688–692 (1989).
[CrossRef]

Hoffman, N.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

Jorge, F.

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Konczykowska, A.

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Kschischang, F. R.

F. R. Kschischang, B. J. Frey, and H-A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Kubo, K.

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Kwon, Y. H.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

Leon-Garcia, A.

A. Leon-Garcia, Probability and random processes for electrical engineering, 2nd ed. (Addison-Wesley, 1993).

Liu, X.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

Loeliger, H-A.

F. R. Kschischang, B. J. Frey, and H-A. Loeliger, “Factor graphs and the sumproduct algorithm,” IEEE Trans. Inf. Theory 47, 498–519 (2001).
[CrossRef]

Magarini, M.

Miyata, Y.

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Mizuochi, T.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
[CrossRef]

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Nam, E. S.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

Onohara, K.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
[CrossRef]

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Peckham, D. W.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Pfennigbauer, M.

P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
[CrossRef]

Poggiolini, P.

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

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Richardson, T.

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

Richardson, T. J.

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
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T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
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Riet, M.

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Shokrollahi, M. A.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
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Sugihara, T.

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Taiba, M. T.

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
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[CrossRef]

Urbanke, R.

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

Urbanke, R. L.

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

Winzer, P. J.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).

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P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28, 547–5562010.
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X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
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P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
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A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

Xie, C.

J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).

C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in Proc. European Conference on Optical Communication (ECOC’11), We.8.B.1 (2011).

C. Xie and R.-J. Essiambre, “Electronic nonlinearity compensation in 112-Gb/s PDM-QPSK optical coherent transmission systems,” in Proc. European Conference on Optical Communication (ECOC’10), Mo.1.C.1 (2010).
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C. Xie, “Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators,” in Proc. European Conference on Optical Communication (ECOC’09), P4.08 (2009).

Yoshida, H.

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

Youn, C. J.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

Zhang, L.

Zhu, B.

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

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F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Comm. Mag. 48, S48–S55 (2010).
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IEEE Commun. Lett. (1)

S. -Y. Chung, J. G. D. Forney, T. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5, 58–60 (2001).
[CrossRef]

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P. J. Winzer, M. Pfennigbauer, and R.-J. Essiambre, “Coherent crosstalk in ultra-dense WDM systems,” IEEE J. Lightwave Technol. 23, 1734–1744 (2005).
[CrossRef]

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

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T. J. Richardson and R. L. Urbanke, “The capacity of low-density parity-check codes under message-passing decoding,” IEEE Trans. Inf. Theory 47, 599–618 (2001).
[CrossRef]

T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity-approaching irregular low-density parity-check codes,” IEEE Trans. Inf. Theory 47, 619–637 (2001).
[CrossRef]

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J. Lightwave Technol (1)

A. H. Gnauck, P. J. Winzer, A. Konczykowska, F. Jorge, J.-Y. Dupuy, M. Riet, G. Charlet, B. Zhu, and D. W. Peckham, “Generation and transmission of 21.4-Gbaud PDM 64-QAM using a novel high-power DAC driving a single I/Q modulator,” J. Lightwave Technol. (to be published).

J. Lightwave Technol. (2)

Proc. European Conference on Optical Communication (6)

C. Xie and R.-J. Essiambre, “Electronic nonlinearity compensation in 112-Gb/s PDM-QPSK optical coherent transmission systems,” in Proc. European Conference on Optical Communication (ECOC’10), Mo.1.C.1 (2010).
[CrossRef]

C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in Proc. European Conference on Optical Communication (ECOC’11), We.8.B.1 (2011).

J. Cho, C. Xie, and P. J. Winzer, “Performance of soft-decision FEC in systems with bivariate Gaussian noise distributions,” in Proc. European Conference on Optical Communication (ECOC’11), to appear (2011).

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single coherent detection of a 606-Gb/s CO-OFDM signal with 32-QAM subcarrier modulation using 4×480-Gsamples/s ADCs,” in Proc. European Conference on Optical Communication (ECOC’10), PD2.06 (2010).
[CrossRef]

C. Xie, “Suppression of inter-channel nonlinearities in WDM coherent PDM-QPSK systems using periodic-group-delay dispersion compensators,” in Proc. European Conference on Optical Communication (ECOC’09), P4.08 (2009).

A. Carena, G. Bosco, V. Curri, P. Poggiolini, M. T. Taiba, and F. Forghieri, “Statistical characterization of PM-QPSK signals after propagation in uncompensated fiber links,” in Proc. European Conference on Optical Communication (ECOC’10), P4.07 (2010).
[CrossRef]

Proc. Optical Fiber Communication Conference (1)

X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3×485-Gb/s WDM transmission over 4800 km of ULAF and 12×4100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” in Proc. Optical Fiber Communication Conference (OFC’11), JThA37 (2011).

Other (4)

ITU-T Recommendation G.975.1, 2004, Appendix I.9.

T. Mizuochi, Y. Miyata, K. Kubo, T. Sugihara, K. Onohara, and H. Yoshida, “Progress in soft-decision FEC,” in Proc. Optical Fiber Communication Conference (OFC’11), NWC2 (2011).

A. Leon-Garcia, Probability and random processes for electrical engineering, 2nd ed. (Addison-Wesley, 1993).

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, 2005).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Simulated QPSK constellations after nonlinear transmission.

Fig. 2
Fig. 2

Parameters of the bivariate Gaussian noise (BGN) model. (a) Tilt angle α. (b) Eccentricity angle β.

Fig. 3
Fig. 3

Quantities of bivariate Gaussian noise evaluated on α-β plane. (a) Standard deviation σI. (b) Standard deviation σQ. (c) Correlation coefficient ρ. (d) Entropy h(f). All quantities are computed at Eb/N0 = 3 dB assuming rate-0.8 FEC encoding, where the relation between Eb/N0, code rate, and σ is addressed in Section 4.2 in detail.

Fig. 4
Fig. 4

Communication system model. (a) Odd and even codeword bits are mapped to a symbol in an interleaved manner. (b) Detailed view of the receiver, which is marked by the dashed box in (a).

Fig. 5
Fig. 5

Density evolution algorithm. (a) Iterative bit and check processing for density evolution. L denotes the LLR and f(L) is the pdf of the LLR. (b) Noise threshold calculation using density evolution.

Fig. 6
Fig. 6

(a) LLR as a function of the received signal’s amplitude I. (b) Pdf of the LLR. The LLR is calculated at Eb/N0 = 3 dB assuming rate-0.8 LDPC encoding, where the tilt angle α is fixed at 5.6°.

Fig. 7
Fig. 7

(a) Maximum noise standard deviation σ* for error-free transmission. (b) Minimum SNR per bit E b / N 0 * (in dB) for error-free transmission. The channel is rotationally-symmetric CBGN and the rate-0.8 (4, 20) regular LDPC code ensemble is used with BP decoding.

Fig. 8
Fig. 8

QPSK constellations with noise clouds used for Monte Carlo simulations. (a) Constant tilt α = 21°. (b) Constant eccentricity β = 21°.

Fig. 9
Fig. 9

Pre-FEC (dashed lines) and post-FEC (solid lines) BER performance of marginal pdf BP decoding. (a) Constant tilt α = 21°. (b) Constant eccentricity β = 21°.

Fig. 10
Fig. 10

Post-FEC BER performance of marginal pdf (dashed lines) and joint pdf (solid lines) BP decoding, as a function of Eb/N0. (a) Constant tilt α = 21°. (b) Constant eccentricity β = 21°.

Fig. 11
Fig. 11

Post-FEC BER performance of marginal pdf (dashed lines) and joint pdf (solid lines) BP decoding, as a function of Pre-FEC BER. (a) Constant tilt α = 21°. (b) Constant eccentricity β = 21°.

Equations (14)

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

f ( I , Q ) = 1 2 π σ I σ Q 1 ρ 2 exp [ 1 2 ( 1 ρ 2 ) { ( I μ I ) 2 σ I 2 2 ρ ( I μ I ) ( Q μ Q ) σ I σ Q + ( Q μ Q ) 2 σ Q 2 } ] ,
α = 1 2 arctan 2 ρ σ I σ Q σ I 2 σ Q 2 .
σ I 2 = σ u 2 sin 2 α + σ v 2 cos 2 α = σ 2 ( sin 2 α cos 2 β + cos 2 α sin 2 β ) , σ Q 2 = σ u 2 cos 2 α + σ v 2 sin 2 α = σ 2 ( cos 2 α cos 2 β + sin 2 α sin 2 β ) ,
ρ = σ I 2 σ Q 2 2 σ I σ Q tan 2 α = sin 2 α cos 2 β 1 cos 2 2 α cos 2 2 β ,
R 1 = ( I 1 , Q 1 ) 𝒩 ( 1 2 , 1 2 , ρ , σ 1 2 , σ 2 2 ) , R 2 = ( I 2 , Q 2 ) 𝒩 ( 1 2 , 1 2 , ρ , σ 2 2 , σ 1 2 ) , R 3 = ( I 3 , Q 3 ) 𝒩 ( 1 2 , 1 2 , ρ , σ 1 2 , σ 2 2 ) , and R 4 = ( I 4 , Q 4 ) 𝒩 ( 1 2 , 1 2 , ρ , σ 2 2 , σ 1 2 ) ,
h ( f ) = log ( 2 π e σ I σ Q 1 ρ 2 ) .
h ( f ) = log ( π e σ 2 | sin 2 β | ) .
( c | I ) = log [ f ( c = + 1 | I ) f ( c = 1 | I ) ] = log [ f ( I | c = + 1 ) f ( c = + 1 ) f ( I ) f ( I | c = 1 ) f ( c = 1 ) f ( I ) ] = log [ f ( I | c = + 1 ) f ( I | c = 1 ) ] .
( c | I ) = log [ f ( I ; 1 , σ 2 ) f ( I ; 1 , σ 2 ) ] = log [ e ( I 1 ) 2 / ( 2 σ 2 ) e ( I + 1 ) 2 / ( 2 σ 2 ) ] = log [ e 4 I / ( 2 σ 2 ) ] = 2 σ 2 I ,
( c | I ) = 2 σ I 2 I , and ( c | Q ) = 2 σ Q 2 Q .
( c odd | I ) log ( f 1 + f 4 ) ( I ) ( f 2 + f 3 ) ( I ) = log 1 σ 1 exp ( ( I 1 2 ) 2 2 σ 1 2 ) + 1 σ 2 exp ( ( I 1 2 ) 2 2 σ 2 2 ) 1 σ 1 exp ( ( I + 1 2 ) 2 2 σ 1 2 ) + 1 σ 2 exp ( ( I + 1 2 ) 2 2 σ 2 2 ) , and ( c even | Q ) log ( f 1 + f 2 ) ( Q ) ( f 3 + f 4 ) ( Q ) = log 1 σ 2 exp ( ( Q 1 2 ) 2 2 σ 2 2 ) + 1 σ 1 exp ( ( Q 1 2 ) 2 2 σ 1 2 ) 1 σ 2 exp ( ( Q + 1 2 ) 2 2 σ 2 2 ) + 1 σ 1 exp ( ( Q + 1 2 ) 2 2 σ 1 2 ) ,
( c odd | I , Q ) log ( f 1 + f 4 ) ( I , Q ) ( f 2 + f 3 ) ( I , Q ) , and ( c even | I , Q ) log ( f 1 + f 2 ) ( I , Q ) ( f 3 + f 4 ) ( I , Q ) ,
σ 2 = 1 2 R E b / N 0 .
f ( ( c | I ) ) = k f I ( I ) | d ( c | I ) / d I | | I = I k .

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