Abstract

A novel polar coded coherent optical orthogonal frequency division multiplexing (CO-OFDM) system is proposed and demonstrated through experiment for the first time. The principle of a polar coded CO-OFDM signal is illustrated theoretically and the suitable polar decoding method is discussed. Results show that the polar coded CO-OFDM signal achieves a net coding gain (NCG) of more than 10 dB at bit error rate (BER) of 10−3 over 25-Gb/s 480-km transmission in comparison with conventional CO-OFDM. Also, compared to the 25-Gb/s low-density parity-check (LDPC) coded CO-OFDM 160-km system, the polar code provides a NCG of 0.88 dB @BER = 10−3. Moreover, the polar code can relieve the laser linewidth requirement massively to get a more cost-effective CO-OFDM system.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  4. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of European Conference on Optical Communications (2009), paper PD 2.6.
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    [Crossref] [PubMed]
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    [Crossref]
  7. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
    [Crossref]
  8. X. Hong, X. Hong, and S. He, “Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system,” Opt. Express 23(4), 4691–4702 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  11. Z. Wu, J. K. Fischer, and B. Lankl, “Experimental investigation of polar code performance for coherent UDWDM PONs,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th3E.7.
    [Crossref]
  12. E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
    [Crossref]
  13. I. Tal and A. Vardy, “How to construct polar codes,” IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013).
    [Crossref]
  14. Z. Ye, “Chinese firms gain ground in 5G battle,” http://www.globaltimes.cn/content/1019126.shtml .
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    [Crossref]
  16. A. Bravo-Santos, “Polar codes for the Rayleigh fading channel,” IEEE Commun. Lett. 17(12), 2352–2355 (2013).
    [Crossref]
  17. W. Shieh and I. B. Djordjevic, OFDM for Optical Communications (Academic, 2009).
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    [Crossref]
  19. I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
    [Crossref]
  20. W. Shieh, “Maximum-likelihood phase and channel estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 20(8), 605–607 (2008).
    [Crossref]
  21. I. B. Djordjevic, W. Ryan, and B. Vasic, Coding for Optical Channels (Springer Science & Business Media, 2010).
  22. ITU-T Recommendation G.975.1, Appendix I.9 (2004).
  23. B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
    [Crossref]
  24. J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

2016 (1)

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

2015 (2)

2014 (1)

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

2013 (2)

A. Bravo-Santos, “Polar codes for the Rayleigh fading channel,” IEEE Commun. Lett. 17(12), 2352–2355 (2013).
[Crossref]

I. Tal and A. Vardy, “How to construct polar codes,” IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013).
[Crossref]

2012 (2)

P. Trifonov, “Efficient design and decoding of polar codes,” IEEE Trans. Commun. 60(11), 3221–3227 (2012).
[Crossref]

B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
[Crossref]

2010 (2)

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

2009 (3)

2008 (2)

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[Crossref] [PubMed]

W. Shieh, “Maximum-likelihood phase and channel estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 20(8), 605–607 (2008).
[Crossref]

2006 (1)

Arikan, E.

E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

Armstrong, J.

Bao, H.

Bi, M.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Bosco, G.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

Bravo-Santos, A.

A. Bravo-Santos, “Polar codes for the Rayleigh fading channel,” IEEE Commun. Lett. 17(12), 2352–2355 (2013).
[Crossref]

Buchali, F.

Carena, A.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

Chang, F.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Curri, V.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

Forghieri, F.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

He, H.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

He, S.

Hong, X.

Hu, W.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Li, B.

B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
[Crossref]

Li, J.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Liu, B.

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Liu, L.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Liu, X.

Lowery, A.

Mizuochi, T.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Onohara, K.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

Poggiolini, P.

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

Shen, H.

B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
[Crossref]

Shieh, W.

W. Shieh, “Maximum-likelihood phase and channel estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 20(8), 605–607 (2008).
[Crossref]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[Crossref] [PubMed]

Tal, I.

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

I. Tal and A. Vardy, “How to construct polar codes,” IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013).
[Crossref]

Tang, Y.

Tkach, R. W.

Trifonov, P.

P. Trifonov, “Efficient design and decoding of polar codes,” IEEE Trans. Commun. 60(11), 3221–3227 (2012).
[Crossref]

Tse, D.

B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
[Crossref]

Vardy, A.

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

I. Tal and A. Vardy, “How to construct polar codes,” IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013).
[Crossref]

Xiao, S.

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

Xin, X.

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Yang, J.

J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

You, X.

J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

Yu, J.

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Zhang, C.

J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

Zhang, L.

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

Zhou, H.

J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

IEEE Commun. Lett. (2)

A. Bravo-Santos, “Polar codes for the Rayleigh fading channel,” IEEE Commun. Lett. 17(12), 2352–2355 (2013).
[Crossref]

B. Li, H. Shen, and D. Tse, “An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Commun. Lett. 16(12), 2044–2047 (2012).
[Crossref]

IEEE Commun. Mag. (1)

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010).
[Crossref]

IEEE Photonics J. (2)

B. Liu, L. Zhang, X. Xin, and J. Yu, “Robust generalized filter bank multicarrier based optical access system with electrical polar coding,” IEEE Photonics J. 8(5), 1–7 (2016).
[Crossref]

M. Bi, S. Xiao, H. He, J. Li, L. Liu, and W. Hu, “Power budget improved symmetric 40-Gb/s long reach stacked WDM-OFDM-PON system based on single tunable optical filter,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (2)

G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photonics Technol. Lett. 22(15), 1129–1131 (2010).
[Crossref]

W. Shieh, “Maximum-likelihood phase and channel estimation for coherent optical OFDM,” IEEE Photonics Technol. Lett. 20(8), 605–607 (2008).
[Crossref]

IEEE Trans. Commun. (1)

P. Trifonov, “Efficient design and decoding of polar codes,” IEEE Trans. Commun. 60(11), 3221–3227 (2012).
[Crossref]

IEEE Trans. Inf. Theory (3)

E. Arikan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009).
[Crossref]

I. Tal and A. Vardy, “How to construct polar codes,” IEEE Trans. Inf. Theory 59(10), 6562–6582 (2013).
[Crossref]

I. Tal and A. Vardy, “List decoding of polar codes,” IEEE Trans. Inf. Theory 61(5), 2213–2226 (2015).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (3)

Other (8)

W. Ryan and S. Lin, Channel Codes: Classical and Modern (Cambridge University, 2009).

Z. Wu, J. K. Fischer, and B. Lankl, “Experimental investigation of polar code performance for coherent UDWDM PONs,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2015), paper Th3E.7.
[Crossref]

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of European Conference on Optical Communications (2009), paper PD 2.6.

W. Shieh and I. B. Djordjevic, OFDM for Optical Communications (Academic, 2009).

Z. Ye, “Chinese firms gain ground in 5G battle,” http://www.globaltimes.cn/content/1019126.shtml .

I. B. Djordjevic, W. Ryan, and B. Vasic, Coding for Optical Channels (Springer Science & Business Media, 2010).

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

J. Yang, C. Zhang, H. Zhou, and X. You, “Pipelined belief propagation polar decoders,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 2016), pp. 413–416.

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Figures (5)

Fig. 1
Fig. 1 Schematic diagrams of M-QAM polar coded CO-OFDM signal (a) generation and (b) post-processing.
Fig. 2
Fig. 2 Setup of the polar coded CO-OFDM system.
Fig. 3
Fig. 3 BER performances with SC decoder and SCL decoder of different list sizes in 160-km 25-Gb/s polar coded CO-OFDM system.
Fig. 4
Fig. 4 (a) Experiment and (b) simulation results of BER versus electrical SNR in 25-Gb/s CO-OFDM system with polar code and LDPC code over different transmission distances.
Fig. 5
Fig. 5 Receiver power penalty @BER = 3.8 × 10−3 versus laser linewidth in 25-Gb/s polar coded CO-OFDM system over different transmission distances.

Equations (6)

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

x = U G N = U B N [ 1 0 1 1 ] n
P ( y p | x m p m + q = 0 ) = k = 1 2 m 1 P ( y p , Re , x k , Re q , 0 ) P ( y p , Im , x k , Im q , 0 ) = k = 1 2 m 1 1 σ 2 π exp ( ( y p , Re x k , Re q , 0 ) 2 σ 2 ) 1 σ 2 π exp ( ( y p , Im x k , Im q , 0 ) 2 σ 2 )
P ( x m p m + q = 0 ) = P ( x m p m + q = 1 ) = 1 2
P ( y p ) = P ( y p | x m p m + q = 0 ) P ( x m p m + q = 0 ) + P ( y p | x m p m + q = 1 ) P ( x m p m + q = 1 )
Pr ( x m p m + q = 0 | y p ) = P ( y p | x m p m + q = 0 ) P ( x m p m + q = 0 ) P ( y p ) = P ( y p | x m p m + q = 0 ) 2 P ( y p ) = P ( y p | x m p m + q = 0 ) P ( y p | x m p m + q = 0 ) + P ( y p | x m p m + q = 1 )
Pr ( x m p m + q = 1 | y p ) = P ( y p | x m p m + q = 1 ) P ( y p | x m p m + q = 0 ) + P ( y p | x m p m + q = 1 )

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