Abstract

We propose new coded modulation schemes for ultra-high-speed optical transmission (e.g., 100 Gb/s and above) using component concatenated zigzag codes in combination with high-order digital modulation and coherent detection. In particular, we propose single-level coded modulation and multi-level coded modulation using concatenated zigzag codes. For single-level coded modulation, only one concatenated zigzag code is employed to encode the information bits, and Gray mapping is employed to map the coded bits to channel symbols. For multi-level coded modulation, the mapping bits are divided into several layers, and one component concatenated zigzag code is employed at each layer; the layers are decoded successively, and the decoded layers are used to assist the decoding of the subsequent layers. Furthermore, we propose a rate allocation scheme for the component concatenated zigzag codes and a parameter selection scheme for multi-level coded modulation. Simulation results demonstrate that single-level and multi-level coded systems with zigzag codes show up to 0.5 dB performance gain over structured low-density parity check codes.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.
  2. E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.
  3. M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.
  4. H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.
  5. S. Bigo, “Coherent detection: A key enabler for next-generation optical transmission systems,” in 9th Int. Conf. on Proc. 2007 Transparent Optical Networks, ICTON ’07, July 2007, pp. 332–335.
  6. J. Renaudier, G. Charlet, M. Salsi, O. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol., vol. 26, no. 1, pp. 36–42, Jan.2008.
    [CrossRef]
  7. C. Zhang, Y. Mori, K. Igarashi, K. Katoh, and K. Kikuchi, “Ultrafast operation of digital coherent receivers using their time-division demultiplexing function,” J. Lightwave Technol., vol. 27, no. 3, pp. 224–232, Feb.2009.
    [CrossRef]
  8. O. A. Sab and V. Lemaire, “Block turbo code performance for long-haul DWDM optical transmission systems,” in Proc. 2000 Optical Fiber Communication Conf., Mar. 2000.
  9. M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.
  10. C.-J. Ahn, S. Takahashi, H. Fujisaka, T. Kamio, and K. Haeiwa, “Power consumption for coherent optical orthogonal frequency division multiplexing with punctured LDPC codes and variable amplitude block codes,” J. Lightwave Technol., vol. 26, no. 14, pp. 2227–2234, July2008.
    [CrossRef]
  11. I. Djordjevic and B. Vasic, “Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection,” J. Lightwave Technol., vol. 24, no. 1, pp. 420–428, Jan.2006.
    [CrossRef]
  12. B. Vasic, I. Djordjevic, and R. Kostuk, “Low-density parity check codes and iterative decoding for long-haul optical communication systems,” J. Lightwave Technol., vol. 21, no. 2, pp. 438–446, Feb.2003.
    [CrossRef]
  13. I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol., vol. 27, no. 16, pp. 3518–3530, Aug.2009.
    [CrossRef]
  14. Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
    [CrossRef]
  15. L. Ping and K. Y. Wu, “Concatenated tree codes: A low-complexity, high-performance approach,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 791–799, Feb.2001.
    [CrossRef]
  16. L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
    [CrossRef]
  17. M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788–1793, Aug.2004.
    [CrossRef]
  18. L. Ping, S. Chan, and K. Yeung, “Iterative decoding of multi-dimensional concatenated single parity check codes,” in Proc. IEEE ICC-98, June1998, pp. 131–135.
  19. C. Gong and X. Wang, “Multilevel LDPC-coded high-speed optical systems: Efficient hard decoding and code optimization,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1268–1279, Sept./Oct.2010.
    [CrossRef]
  20. G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
    [CrossRef]
  21. R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
    [CrossRef]
  22. I. B. Djordjevic and B. Vasic, “Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection,” J. Lightwave Technol., vol. 24, no. 1, pp. 420–428, Jan.2006.
    [CrossRef]

2010 (1)

C. Gong and X. Wang, “Multilevel LDPC-coded high-speed optical systems: Efficient hard decoding and code optimization,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1268–1279, Sept./Oct.2010.
[CrossRef]

2009 (2)

2008 (2)

2006 (3)

2004 (1)

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788–1793, Aug.2004.
[CrossRef]

2003 (1)

2001 (2)

L. Ping and K. Y. Wu, “Concatenated tree codes: A low-complexity, high-performance approach,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 791–799, Feb.2001.
[CrossRef]

L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
[CrossRef]

2000 (1)

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

1998 (1)

G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
[CrossRef]

Ahn, C.-J.

Akita, M.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Arabaci, M.

Biglieri, E.

G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
[CrossRef]

Bigo, S.

J. Renaudier, G. Charlet, M. Salsi, O. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol., vol. 26, no. 1, pp. 36–42, Jan.2008.
[CrossRef]

S. Bigo, “Coherent detection: A key enabler for next-generation optical transmission systems,” in 9th Int. Conf. on Proc. 2007 Transparent Optical Networks, ICTON ’07, July 2007, pp. 332–335.

Cadiou, J.

E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.

Caire, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
[CrossRef]

Carenco, A.

E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.

Chan, S.

L. Ping, S. Chan, and K. Yeung, “Iterative decoding of multi-dimensional concatenated single parity check codes,” in Proc. IEEE ICC-98, June1998, pp. 131–135.

Charlet, G.

Chen, L.

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

Dexter, J.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

Djordjevic, I.

Djordjevic, I. B.

Fong, W. H.

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

Fossorier, M. P. C.

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788–1793, Aug.2004.
[CrossRef]

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

Fujisaka, H.

Fujita, H.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Funk, E.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

Gong, C.

C. Gong and X. Wang, “Multilevel LDPC-coded high-speed optical systems: Efficient hard decoding and code optimization,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1268–1279, Sept./Oct.2010.
[CrossRef]

Goto, H.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

Haeiwa, K.

Huang, X. L.

L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
[CrossRef]

Igarashi, K.

Imai, H.

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

Jumpei, H.

H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.

Kamio, T.

Kasai, K.

H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

Katoh, K.

Kazmierski, C.

E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.

Kikuchi, K.

Kostuk, R.

Kubo, K.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Kuno, K.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Kurahashi, S.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Lemaire, V.

O. A. Sab and V. Lemaire, “Block turbo code performance for long-haul DWDM optical transmission systems,” in Proc. 2000 Optical Fiber Communication Conf., Mar. 2000.

Li, Z.

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

Lin, S.

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

Mardoyan, H.

Minkov, L. L.

Mizuochi, T.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Morelos-Zaragoza, R. H.

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

Mori, Y.

Nakazawa, M.

H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

Omiya, T.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

Pardo, O.

Phamdo, N.

L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
[CrossRef]

Ping, L.

L. Ping and K. Y. Wu, “Concatenated tree codes: A low-complexity, high-performance approach,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 791–799, Feb.2001.
[CrossRef]

L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
[CrossRef]

L. Ping, S. Chan, and K. Yeung, “Iterative decoding of multi-dimensional concatenated single parity check codes,” in Proc. IEEE ICC-98, June1998, pp. 131–135.

Renaudier, J.

Sab, O. A.

O. A. Sab and V. Lemaire, “Block turbo code performance for long-haul DWDM optical transmission systems,” in Proc. 2000 Optical Fiber Communication Conf., Mar. 2000.

Salsi, M.

Strutz, S.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

Takahashi, S.

Taricco, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
[CrossRef]

Tran, P.

Urick, V.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

Vasic, B.

Vergnol, E.

E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.

Wang, X.

C. Gong and X. Wang, “Multilevel LDPC-coded high-speed optical systems: Efficient hard decoding and code optimization,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1268–1279, Sept./Oct.2010.
[CrossRef]

Williams, K.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

Wu, K. Y.

L. Ping and K. Y. Wu, “Concatenated tree codes: A low-complexity, high-performance approach,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 791–799, Feb.2001.
[CrossRef]

Yeung, K.

L. Ping, S. Chan, and K. Yeung, “Iterative decoding of multi-dimensional concatenated single parity check codes,” in Proc. IEEE ICC-98, June1998, pp. 131–135.

Yoshida, H.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

Yoshida, M.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.

Zeng, L.

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

Zhang, C.

IEEE J. Sel. Top. Quantum Electron. (1)

C. Gong and X. Wang, “Multilevel LDPC-coded high-speed optical systems: Efficient hard decoding and code optimization,” IEEE J. Sel. Top. Quantum Electron., vol. 16, no. 5, pp. 1268–1279, Sept./Oct.2010.
[CrossRef]

IEEE Trans. Commun. (2)

R. H. Morelos-Zaragoza, M. P. C. Fossorier, S. Lin, and H. Imai, “Multilevel coded modulation for unequal error protection and multistage decoding—part I: Symmetric constellations,” IEEE Trans. Commun., vol. 48, no. 2, pp. 204–213, Feb.2000.
[CrossRef]

Z. Li, L. Chen, L. Zeng, S. Lin, and W. H. Fong, “Efficient encoding of quasi-cyclic low-density parity-check codes,” IEEE Trans. Commun., vol. 54, no. 1, pp. 71–81, Jan.2006.
[CrossRef]

IEEE Trans. Inf. Theory (3)

L. Ping and K. Y. Wu, “Concatenated tree codes: A low-complexity, high-performance approach,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 791–799, Feb.2001.
[CrossRef]

L. Ping, X. L. Huang, and N. Phamdo, “Zigzag codes and concatenated zigzag codes,” IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 800–807, Feb.2001.
[CrossRef]

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788–1793, Aug.2004.
[CrossRef]

IEEE Trans. Inform. Theory (1)

G. Caire, G. Taricco, and E. Biglieri, “Bit interleaved coded modulation,” IEEE Trans. Inform. Theory, vol. 44, pp. 927–946, May1998.
[CrossRef]

J. Lightwave Technol. (7)

I. B. Djordjevic and B. Vasic, “Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection,” J. Lightwave Technol., vol. 24, no. 1, pp. 420–428, Jan.2006.
[CrossRef]

C.-J. Ahn, S. Takahashi, H. Fujisaka, T. Kamio, and K. Haeiwa, “Power consumption for coherent optical orthogonal frequency division multiplexing with punctured LDPC codes and variable amplitude block codes,” J. Lightwave Technol., vol. 26, no. 14, pp. 2227–2234, July2008.
[CrossRef]

I. Djordjevic and B. Vasic, “Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection,” J. Lightwave Technol., vol. 24, no. 1, pp. 420–428, Jan.2006.
[CrossRef]

B. Vasic, I. Djordjevic, and R. Kostuk, “Low-density parity check codes and iterative decoding for long-haul optical communication systems,” J. Lightwave Technol., vol. 21, no. 2, pp. 438–446, Feb.2003.
[CrossRef]

I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol., vol. 27, no. 16, pp. 3518–3530, Aug.2009.
[CrossRef]

J. Renaudier, G. Charlet, M. Salsi, O. Pardo, H. Mardoyan, P. Tran, and S. Bigo, “Linear fiber impairments mitigation of 40-Gbit/s polarization-multiplexed QPSK by digital processing in a coherent receiver,” J. Lightwave Technol., vol. 26, no. 1, pp. 36–42, Jan.2008.
[CrossRef]

C. Zhang, Y. Mori, K. Igarashi, K. Katoh, and K. Kikuchi, “Ultrafast operation of digital coherent receivers using their time-division demultiplexing function,” J. Lightwave Technol., vol. 27, no. 3, pp. 224–232, Feb.2009.
[CrossRef]

Other (8)

O. A. Sab and V. Lemaire, “Block turbo code performance for long-haul DWDM optical transmission systems,” in Proc. 2000 Optical Fiber Communication Conf., Mar. 2000.

M. Akita, H. Fujita, T. Mizuochi, K. Kubo, H. Yoshida, K. Kuno, and S. Kurahashi, “Third generation FEC employing turbo product code for long-haul DWDM transmission systems,” in Proc. 2002 Optical Fiber Communication Conf., Mar. 2002.

E. Vergnol, J. Cadiou, A. Carenco, and C. Kazmierski, “New modulation scheme for integrated single side band lightwave source allowing fiber transport up to 256 QAM over 38 GHz carrier,” in Proc. OFC, 2000, pp. 134–136.

E. Funk, V. Urick, S. Strutz, J. Dexter, and K. Williams, “110 km 256-QAM digital microwave over fiber link,” in Proc. MTT-S, 2008, vol. 1, pp. 269–272.

M. Yoshida, H. Goto, T. Omiya, K. Kasai, and M. Nakazawa, “Frequency division multiplexed 1 Gsymbol/s, 64 QAM coherent optical transmission with a spectral efficiency of 8.6 bit/s/Hz,” in Proc. ECOC, 2008, pp. 1–4.

H. Jumpei, K. Kasai, M. Yoshida, and M. Nakazawa, “1 Gsymbol/s, 64 QAM coherent optical transmission over 150 km with a spectral efficiency of 3 bit/s/Hz,” in Proc. OFC/NFOEC, 2007, pp. 1–3.

S. Bigo, “Coherent detection: A key enabler for next-generation optical transmission systems,” in 9th Int. Conf. on Proc. 2007 Transparent Optical Networks, ICTON ’07, July 2007, pp. 332–335.

L. Ping, S. Chan, and K. Yeung, “Iterative decoding of multi-dimensional concatenated single parity check codes,” in Proc. IEEE ICC-98, June1998, pp. 131–135.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

The structures of zigzag and concatenated zigzag codes.

Fig. 2
Fig. 2

The iterative decoding structure of the concatenated zigzag codes.

Fig. 3
Fig. 3

Mappings for (a) 4-, 16-, 64-QAM and (b) 8-QAM and ring 16-array.

Fig. 4
Fig. 4

Multi-level encoding and multi-stage decoding with component zigzag codes.

Fig. 5
Fig. 5

Code rate chart of the component codes for 8-QAM.

Fig. 6
Fig. 6

Comparison of single-level zigzag-coded modulation with 4-, 16-, and 64-QAMs.

Fig. 7
Fig. 7

Performance of multi-level zigzag-coded modulation with 8-QAM and ring 16-array.

Tables (1)

Tables Icon

Table I The Component Codes Rates and the Average Code Rate of 8-QAM Obtained From Fig. 5.

Equations (36)

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

D=d(1,1)d(1,2)d(1,J)d(2,1)d(2,2)d(2,J)d(I,1)d(I,2)d(I,J)I×J
and p=p(1),p(2),,p(I)I×1T.
p(i)=(p(i1)+j=1Jd(i,j))mod 2,1iI,
P=p1(1)p2(1)pK(1)p1(2)p2(2)pK(2)p1(I)p2(I)pK(I)I×K.
a(d(i,j))=logP(d(i,j)=0|y)P(d(i,j)=1|y)+logP(d(i,j)=0)P(d(i,j)=1),1iI,1jJ,
a(pk(i))=logP(pk(i)=0|y)P(pk(i)=1|y),1iI,1kK.
Fk(i)=a(pk(i))+W(Fk(i1),ka(i,1),,ka(i,J)),i=1,2,,I;
Bk(i1)=a(pk(i1))+W(ka(i,1),ka(i,2),,ka(i,J),Bk(i)),i=I,I1,,2,
W(x1,x2,,xn)j=1nsign(xj)min1jn|xj|.
ko(i,j)=W(Fk(i1),ka(i,1),ka(i,2),,ka(i,j1),ka(i,j+1),,ca(i,J),Bk(i)).
1a(i,j)1=a(d(i,j)),
1a(i,j)n=Ko(i,j)n11e(i,j)n1,n=2,3,.
ka(i,j)n=k1o(i,j)nke(i,j)n1,n=1,2,.
bi=logP(bi=0|y)P(bi=1|y)=logxAi,0P(y|x)xAi,1P(y|x).
I(X1X2XL;Y)=i=1LI(Xi;Y|X1X2Xi1).
b1,1j,,b1,α1j,b2,1j,,b2,α2j,,bL,1j,,bL,αLj,
Ri=KiNαi,1iL.
RS=i=1LKiN=i=1LαiRi,
R̄=RSi=1Lαi=i=1LαiRii=1Lαi.
(ci,(j1)αi+m)=logxAj,m,0iP(y|x)xAj,m,1iP(y|x).
Ci(g)I(Xi;Y|X1X2Xi1),1iL.
min{Ri,gi}1iLmax1iLgis.t.Ci(gi)=αiRi,1iL,i=1LαiRi=RS.
C(gm)=i=1LCi(gm)i=1LCi(gi)=i=1LαiRi=RS;
gi=gS=C1(RS),andRi=Ci(gS)αi,1iL,
Ri(g)=Ci(g)αi,1iL.
R(g)=C(g)i=1Lαi=i=1LCi(g)i=1Lαi=i=1Lαii=1LαiRi(g),
C1(g)=I(X1;Y)=H(Y)H(Y|X1),C2(g)=I(X2;Y|X1)=H(Y|X1)H(Y|X1X2),
H(Y|X1,X2)=EY,b2b1b0{log1pY|X1X2(y|b2b1b0)}=Eb2b1b0{log(πeσ2)}=log(πeσ2).
pY(y)=18b2b1b0pY|X1X2(y|b2b1b0),andH(Y)=EY{log1pY(y)};
pY|X1(y|b0)=14b2b1pY|X1X2(y|b2b1b0),andH(Y|X1)=EY,b0{log1pY|X1(y|b0)}.
R(g)=13R1(g)+23R2(g).
Mij=sm,sn,smsndth1{bi(sm)bi(sn),bj(sm)bj(sn)},
XAXXXandbi,bjXMijMth.
i0=argmaxi,biXbjX,jiMij,
R={JJ+K,K3,J+KNm},
Ij(Jj+Kj)=Nαj,1jL,