Abstract

Low-density parity-check (LDPC) codes are excellent candidates for optical network applications due to their inherent low complexity of both encoders and decoders. A cyclic or quasi-cyclic form of finite geometry LDPC codes simplifies the encoding procedure. In addition, the complexity of an iterative decoder for such codes, namely the min-sum algorithm, is lower than the complexity of a turbo or Reed-Solomon decoder. In fact, simple hard-decoding algorithms such as the bit-flipping algorithm perform very well on codes from projective planes. In this paper, the authors consider LDPC codes from affine planes,projective planes, oval designs, and unitals. The bit-error-rate (BER) performance of these codes is significantly better than that of any other known foward-error correction techniques for optical communications. A coding gain of 9-10 dB at a BER of 10^-9, depending on the code rate, demonstrated here is the best result reported so far. In order to assess the performance of the proposed coding schemes, a very realistic simulation model is used that takes into account in a natural way all major impairments in long-haul optical transmission such as amplified spontaneous emission noise,pulse distortion due to fiber nonlinearities, chromatic dispersion, crosstalk effects, and intersymbol interferencec. This approach gives a much better estimate of the code's performance than the commonly used additive white Gaussian noise channel model.

© 2004 IEEE

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  1. J. X. Cai, M. Nissov, C. R. Davidson, A. N. Pilipetskii, G. Mohs, H. Li, Y. Cai, E. A. Golovchenko, A. J. Lucero, D. G. Foursa and N. S. Bergano, "Long-haul 40 Gb/s DWDM transmission with aggregate capacities exceeding 1Tb/s", J. Lightwave Technol., vol. 20, pp. 2247-2258, Dec. 2002.
  2. B. Vasic and I. B. Djordjevic, "Low-density parity check codes for long haul optical communications systems", IEEE Photon. Technol. Lett., vol. 14, pp. 1208-1210, Aug. 2002.
  3. O. Ait Sab, "FEC techniques in submarine transmission systems", in Proc. Optical Fiber Communication Conf., vol. 2, 2001, pp. TuF1-1-TuF1-3.
  4. O. A. Sab and V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems", in Proc. Optical Fiber Communication Conf., vol. 3, 2001, pp. 280-282.
  5. 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 Tech. Dig. Optical Fiber Communication Exhibit, 2002, pp. 289-290.
  6. B. Vasic, I. B. Djordjevic and R. Kostuk, "Low-density parity check codes and iterative decoding for long haul optical communication systems", J. Lightwave Technol., vol. 21, pp. 438-446, Feb. 2003.
  7. T. Richardson, A. Shokrollahi and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes", IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
  8. D. MacKay and M. Davey, "Evaluation of Gallager Codes for Short Block Length and High Rate Applications", [Online]. Available: http://www.cs.toronto.edu/~mackay/CodesRegular.html
  9. J. Hagenauer, M. Moerz and E. Offer, "Analog turbo-networks in VLSI: The next step in turbo decoding and equalization", presented at the 2nd Int. Symp. Turbo Codes, Brest, France,Sept. 4-7 , 2000.
  10. I. Andersen, "Combinatorial designs: Construction methods," in Mathematics and Its Applications, Chichester: U.K.: Ellis Horwood, 1990.
  11. C. J. Colbourn, and J. H. Dinitz, Eds. "The Handbook of Combinatorial Designs", CRC, Boca Raton, FL, 1996.
  12. J. A. Thas, Handbook of Incidence Geometry: Buildings and Foundations, F. Buekenhout, Ed. Amsterdam: The Netherlands: Elsevier Science, 1996, ch. 7.
  13. E. F. Assmus Jr. and J. D. Key, "Baer subplanes, ovals and unitals," in Coding Theory and Design Theory, Part I, D. Ray-Chaudhuri, Ed. New York: Springer-Verlag, 1990,vol. 20, pp. 1-8 .
  14. E. F. Assmus Jr. and J. D. Key, Designs and Their Codes, Cambridge: U.K.: Cambridge Univ. Press, 1992.
  15. E. F. Assmus Jr. and J. D. Key, "Designs and codes: An update", Designs, Codes Cryptography, vol. 9, pp. 7-27, 1996.
  16. Y. Kou, S. Lin and M. P. C. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results", IEEE Trans. Inform. Theory, vol. 47, pp. 2711-2736, Nov. 2001.
  17. S. R. Weller and S. J. Johnson, "Iterative decoding of codes from oval designs", presented at the Defense Applications Signal Processing, 2001 Workshop (DASP2001), South Australia, Sept. 16-20 , 2001.
  18. J. Hagenauer, E. Offer and L. Papke, "Iterative decoding of binary block and convolutional codes", IEEE Trans. Inform. Theory, pp. 429 -445, Mar. 1996.
  19. G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA: Academic, 2001.
  20. I. B. Djordjevic and B. Vasic, "An advanced direct detection receiver model", J. Opt. Commun., vol. 20, no. 1, Feb. 2004.
  21. N. S. Bergano and C. R. Davidson, "Circulating loop transmission experiments for the study long-transmission systems using erbium-doped fiber amplifiers", J. Lightwave Technol., vol. 13, pp. 879-888, May 1995.
  22. B. Vasic and O. Milenkovic, "Combinatorial constructions of structured low-density parity check codes for iterative decoding", IEEE Trans. Inform. Theory, to be published.
  23. E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball and V. J. Mazurczyk, "Modeling of transoceanic fiber-optic WDM communication systems", IEEE J. Select. Topics Quantum Electron., vol. 6, pp. 337-347, Mar.-Apr. 2000.
  24. W. E. Ryan, "An introduction to LDPC codes," in CRC Handbook for Coding and Signal Processing for Recording Systems, B. Vasic, Ed. Boca Raton, FL: CRC, 2004, to be published.
  25. I. B. Djordjevic and B. Vasic, "Projective geometry low-density parity-check codes for ultra-long haul WDM high-speed transmission", IEEE Photon. Technol. Lett., vol. 15, pp. 784-786, May 2003.
  26. E. Yeo, B. Nikolic and V. Anantharam, "Iterative decoder architectures", IEEE Commun. Mag., vol. 41, pp. 132-140, Aug. 2003.
  27. H. Xiao-Yu, E. Eleftheriou, D.-M. Arnold and A. Dholakia, "Efficient implementations of the sum-product algorithm for decoding LDPC codes", in Proc. IEEE GLOBECOM , vol. 2, Nov. 2001, pp. 1036-1036E.
  28. K. Azadet, E. F. Haratsch, H. Kim, F. Saibi, J. H. Saunders, M. Shaffer, L. Song and Y. MengLin, "Equalization and FEC techniques for optical transceivers", IEEE J. Solid-State Circuits, vol. 37, pp. 317-327, Mar. 2002.

J. Lightwave Technol. (3)

Other (25)

B. Vasic and I. B. Djordjevic, "Low-density parity check codes for long haul optical communications systems", IEEE Photon. Technol. Lett., vol. 14, pp. 1208-1210, Aug. 2002.

O. Ait Sab, "FEC techniques in submarine transmission systems", in Proc. Optical Fiber Communication Conf., vol. 2, 2001, pp. TuF1-1-TuF1-3.

O. A. Sab and V. Lemarie, "Block turbo code performances for long-haul DWDM optical transmission systems", in Proc. Optical Fiber Communication Conf., vol. 3, 2001, pp. 280-282.

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 Tech. Dig. Optical Fiber Communication Exhibit, 2002, pp. 289-290.

B. Vasic and O. Milenkovic, "Combinatorial constructions of structured low-density parity check codes for iterative decoding", IEEE Trans. Inform. Theory, to be published.

E. A. Golovchenko, A. N. Pilipetskii, N. S. Bergano, C. R. Davidson, F. I. Khatri, R. M. Kimball and V. J. Mazurczyk, "Modeling of transoceanic fiber-optic WDM communication systems", IEEE J. Select. Topics Quantum Electron., vol. 6, pp. 337-347, Mar.-Apr. 2000.

W. E. Ryan, "An introduction to LDPC codes," in CRC Handbook for Coding and Signal Processing for Recording Systems, B. Vasic, Ed. Boca Raton, FL: CRC, 2004, to be published.

I. B. Djordjevic and B. Vasic, "Projective geometry low-density parity-check codes for ultra-long haul WDM high-speed transmission", IEEE Photon. Technol. Lett., vol. 15, pp. 784-786, May 2003.

E. Yeo, B. Nikolic and V. Anantharam, "Iterative decoder architectures", IEEE Commun. Mag., vol. 41, pp. 132-140, Aug. 2003.

H. Xiao-Yu, E. Eleftheriou, D.-M. Arnold and A. Dholakia, "Efficient implementations of the sum-product algorithm for decoding LDPC codes", in Proc. IEEE GLOBECOM , vol. 2, Nov. 2001, pp. 1036-1036E.

K. Azadet, E. F. Haratsch, H. Kim, F. Saibi, J. H. Saunders, M. Shaffer, L. Song and Y. MengLin, "Equalization and FEC techniques for optical transceivers", IEEE J. Solid-State Circuits, vol. 37, pp. 317-327, Mar. 2002.

T. Richardson, A. Shokrollahi and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes", IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.

D. MacKay and M. Davey, "Evaluation of Gallager Codes for Short Block Length and High Rate Applications", [Online]. Available: http://www.cs.toronto.edu/~mackay/CodesRegular.html

J. Hagenauer, M. Moerz and E. Offer, "Analog turbo-networks in VLSI: The next step in turbo decoding and equalization", presented at the 2nd Int. Symp. Turbo Codes, Brest, France,Sept. 4-7 , 2000.

I. Andersen, "Combinatorial designs: Construction methods," in Mathematics and Its Applications, Chichester: U.K.: Ellis Horwood, 1990.

C. J. Colbourn, and J. H. Dinitz, Eds. "The Handbook of Combinatorial Designs", CRC, Boca Raton, FL, 1996.

J. A. Thas, Handbook of Incidence Geometry: Buildings and Foundations, F. Buekenhout, Ed. Amsterdam: The Netherlands: Elsevier Science, 1996, ch. 7.

E. F. Assmus Jr. and J. D. Key, "Baer subplanes, ovals and unitals," in Coding Theory and Design Theory, Part I, D. Ray-Chaudhuri, Ed. New York: Springer-Verlag, 1990,vol. 20, pp. 1-8 .

E. F. Assmus Jr. and J. D. Key, Designs and Their Codes, Cambridge: U.K.: Cambridge Univ. Press, 1992.

E. F. Assmus Jr. and J. D. Key, "Designs and codes: An update", Designs, Codes Cryptography, vol. 9, pp. 7-27, 1996.

Y. Kou, S. Lin and M. P. C. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results", IEEE Trans. Inform. Theory, vol. 47, pp. 2711-2736, Nov. 2001.

S. R. Weller and S. J. Johnson, "Iterative decoding of codes from oval designs", presented at the Defense Applications Signal Processing, 2001 Workshop (DASP2001), South Australia, Sept. 16-20 , 2001.

J. Hagenauer, E. Offer and L. Papke, "Iterative decoding of binary block and convolutional codes", IEEE Trans. Inform. Theory, pp. 429 -445, Mar. 1996.

G. P. Agrawal, Nonlinear Fiber Optics, San Diego, CA: Academic, 2001.

I. B. Djordjevic and B. Vasic, "An advanced direct detection receiver model", J. Opt. Commun., vol. 20, no. 1, Feb. 2004.

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