Abstract

In this paper, we first describe an optimum signal constellation design algorithm, which is optimum in MMSE-sense, called MMSE-OSCD, for channel capacity achieving source distribution. Secondly, we introduce a feedback channel capacity inspired optimum signal constellation design (FCC-OSCD) to further improve the performance of MMSE-OSCD, inspired by the fact that feedback channel capacity is higher than that of systems without feedback. The constellations obtained by FCC-OSCD are, however, OSNR dependent. The optimization is jointly performed together with regular quasi-cyclic low-density parity-check (LDPC) code design. Such obtained coded-modulation scheme, in combination with polarization-multiplexing, is suitable as both 400 Gb/s and multi-Tb/s optical transport enabling technology. Using large girth LDPC code, we demonstrate by Monte Carlo simulations that a 32-ary signal constellation, obtained by FCC-OSCD, outperforms previously proposed optimized 32-ary CIPQ signal constellation by 0.8 dB at BER of 10-7. On the other hand, the LDPC-coded 16-ary FCC-OSCD outperforms 16-QAM by 1.15 dB at the same BER.

© 2012 OSA

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  1. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423, 623–656 (1948).
  2. P. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
    [CrossRef]
  3. J. McDonough, “Moving standards to 100GbE and beyond,” IEEE Appl. Prac.45, 6–9 (2007).
  4. T. Xia, G. Wellbrock, Y. Huang, E. Ip, M. Huang, Y. Shao, T. Wang, Y. Aono, T. Tajima, S. Murakami, and M. Cvijetic, “Field experiment with mixed line-rate transmission (112-Gb/s, 450-Gb/s, and 1.15-Tb/s) over 3,560 km of installed fiber using filterless coherent receiver and EDFAs only,” in Proc. Postdeadline Papers, OFC/NFOEC 2011, paper PDPA3, Los Angeles Convention Center, Los Angeles, CA, USA, March 6–10, 2011.
  5. T. Cover and J. Tomas, Elements of Information Theory (Wiley, 1991).
  6. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (2010).
    [CrossRef]
  7. Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, “Design of signal constellations for Gaussian channel by iterative polar quantization,” in Proc. 9th Mediterranean Electrotech. Conf. 2, Tel-Aviv, Israel, 866–869 (1998).
  8. I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw.1(6), 555–564 (2009).
    [CrossRef]
  9. X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, and B. Zhu, “Generation and FEC-decoding of a 231.5-Gb/s PDM-OFDM signal with 256-Iterative-Polar-Modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Proc. OFC/NFOEC, Postdeadline Papers (OSA, 2012), Paper PDP5B.3.
  10. C. Chang and L. D. Davisson, “On calculating the capacity of an infinite-input finite (infinite)-output channel,” IEEE Trans. Inf. Theory34(5), 1004–1010 (1988).
    [CrossRef]
  11. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol.28(4), 662–701 (2010).
    [CrossRef]
  12. G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
    [CrossRef]
  13. G. Proakis, Digital Communications (McGraw-Hill, 2001).
  14. I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol.27(16), 3518–3530 (2009).
    [CrossRef]
  15. J. Zhang and I. B. Djordjevic, “Optimized four-dimensional mapping for high-speed optical communication systems,” in Proc. OFC/NFOEC 2012, Paper no. OW1H.2, March 6–8, 2012, Los Angeles, CA, USA.

2010

P. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
[CrossRef]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (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(4), 662–701 (2010).
[CrossRef]

2009

2007

J. McDonough, “Moving standards to 100GbE and beyond,” IEEE Appl. Prac.45, 6–9 (2007).

1988

C. Chang and L. D. Davisson, “On calculating the capacity of an infinite-input finite (infinite)-output channel,” IEEE Trans. Inf. Theory34(5), 1004–1010 (1988).
[CrossRef]

1974

G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
[CrossRef]

1948

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423, 623–656 (1948).

Arabaci, M.

Batshon, H. G.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (2010).
[CrossRef]

Chang, C.

C. Chang and L. D. Davisson, “On calculating the capacity of an infinite-input finite (infinite)-output channel,” IEEE Trans. Inf. Theory34(5), 1004–1010 (1988).
[CrossRef]

Davisson, L. D.

C. Chang and L. D. Davisson, “On calculating the capacity of an infinite-input finite (infinite)-output channel,” IEEE Trans. Inf. Theory34(5), 1004–1010 (1988).
[CrossRef]

Djordjevic, I. B.

Essiambre, R.-J.

Foschini, G.

G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
[CrossRef]

Foschini, G. J.

Gitlin, R.

G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
[CrossRef]

Goebel, B.

Kramer, G.

McDonough, J.

J. McDonough, “Moving standards to 100GbE and beyond,” IEEE Appl. Prac.45, 6–9 (2007).

Minkov, L.

Minkov, L. L.

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423, 623–656 (1948).

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (2010).
[CrossRef]

I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw.1(6), 555–564 (2009).
[CrossRef]

Weinstein, S.

G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
[CrossRef]

Winzer, P.

P. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
[CrossRef]

Winzer, P. J.

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (2010).
[CrossRef]

I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw.1(6), 555–564 (2009).
[CrossRef]

Bell Syst. Tech. J.

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J.27, 379–423, 623–656 (1948).

IEEE Appl. Prac.

J. McDonough, “Moving standards to 100GbE and beyond,” IEEE Appl. Prac.45, 6–9 (2007).

IEEE Commun. Mag.

P. Winzer, “Beyond 100G Ethernet,” IEEE Commun. Mag.48(7), 26–30 (2010).
[CrossRef]

IEEE Photon. J.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Iterative polar quantization based modulation to achieve channel capacity in ultra-high-speed optical communication systems,” IEEE Photon. J.2(4), 593–599 (2010).
[CrossRef]

IEEE Trans. Commun.

G. Foschini, R. Gitlin, and S. Weinstein, “Optimization of two-dimensional signal constellations in the presence of Gaussian noise,” IEEE Trans. Commun.22(1), 28–38 (1974).
[CrossRef]

IEEE Trans. Inf. Theory

C. Chang and L. D. Davisson, “On calculating the capacity of an infinite-input finite (infinite)-output channel,” IEEE Trans. Inf. Theory34(5), 1004–1010 (1988).
[CrossRef]

J. Lightwave Technol.

J. Opt. Commun. Netw.

Other

G. Proakis, Digital Communications (McGraw-Hill, 2001).

J. Zhang and I. B. Djordjevic, “Optimized four-dimensional mapping for high-speed optical communication systems,” in Proc. OFC/NFOEC 2012, Paper no. OW1H.2, March 6–8, 2012, Los Angeles, CA, USA.

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, “Design of signal constellations for Gaussian channel by iterative polar quantization,” in Proc. 9th Mediterranean Electrotech. Conf. 2, Tel-Aviv, Israel, 866–869 (1998).

X. Liu, S. Chandrasekhar, T. Lotz, P. Winzer, H. Haunstein, S. Randel, S. Corteselli, and B. Zhu, “Generation and FEC-decoding of a 231.5-Gb/s PDM-OFDM signal with 256-Iterative-Polar-Modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach,” in Proc. OFC/NFOEC, Postdeadline Papers (OSA, 2012), Paper PDP5B.3.

T. Xia, G. Wellbrock, Y. Huang, E. Ip, M. Huang, Y. Shao, T. Wang, Y. Aono, T. Tajima, S. Murakami, and M. Cvijetic, “Field experiment with mixed line-rate transmission (112-Gb/s, 450-Gb/s, and 1.15-Tb/s) over 3,560 km of installed fiber using filterless coherent receiver and EDFAs only,” in Proc. Postdeadline Papers, OFC/NFOEC 2011, paper PDPA3, Los Angeles Convention Center, Los Angeles, CA, USA, March 6–10, 2011.

T. Cover and J. Tomas, Elements of Information Theory (Wiley, 1991).

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Figures (9)

Fig. 1
Fig. 1

MMSE-OSCD algorithm illustration.

Fig. 2
Fig. 2

MMSE-OSCD algorithm based signal constellations.

Fig. 3
Fig. 3

BER performance of 16-FCC-OSCD constellations for different OSNRs. Insets show how the optimized constellations look like for different OSNR ranges.

Fig. 4
Fig. 4

Polarization-division multiplexed LDPC-coded modulation scheme based on FCC-OSCD signal constellations.

Fig. 5
Fig. 5

Information capacities of FCC-OSCD-based signal constellation against QAM and CIPQ.

Fig. 9
Fig. 9

BER performance for different number of inner and outer iterations.

Fig. 6
Fig. 6

BER performance of MMSE-OSCD constellations.

Fig. 7
Fig. 7

BER performance of FCC-OSCD constellations.

Fig. 8
Fig. 8

BER performance for FCC and MMSE-OSCDs.

Equations (1)

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OSN R b = OSNR log 2 M = R s,info 2 B ref SN R b ,

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