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Channel Coding for Optical Channels

  • Ivan Djordjevic
  • William Ryan
  • Bane Vasic
Chapter

Abstract

In this chapter, we describe different forward error correction (FEC) schemes currently in use or suitable for use in optical communication systems. We start with the description of standard block codes. The state-of-the-art in optical communication systems standardized by the ITU employ concatenated Bose–Chaudhuri–Hocquenghem (BCH)/RS codes [1, 2]. The RS(255,239), in particular, has been used in a broad range of long-haul communication systems [1, 2], and it is commonly considered as the first-generation of FEC [3, 4]. The elementary FEC schemes (BCH, RS, or convolutional codes) may be combined to design more powerful FEC schemes, e.g., RS(255,239) + RS(255,233). Several classes of concatenation codes are listed in ITU-T G975.1. Different concatenation schemes, such as the concatenation of two RS codes or the concatenation of RS and convolutional codes, are commonly considered as second generation of FEC [3, 4].

Keywords

Forward Error Correction LDPC Code Code Word Turbo Code Cyclic Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Forward error correction for submarine systems. Telecommunication Standardization Sector, International Telecommunication Union, Technical Recommendation G.975/G709Google Scholar
  2. 2.
    Forward error correction for high bit rate DWDM submarine systems. Telecommunication Standardization Sector, International Telecommunication Union, G.975.1, Feb. 2004Google Scholar
  3. 3.
    Mizuochi T et al (2004) Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems. IEEE/LEOS J Sel Top Quantum Electron 10(2):376–386CrossRefGoogle Scholar
  4. 4.
    Mizuochi T et al (2003) Next generation FEC for optical transmission systems. In: Proceedings of the optical fiber communication conference (OFC 2003), vol 2, pp 527–528Google Scholar
  5. 5.
    Sab OA (2001) FEC techniques in submarine transmission systems. In: Proceedings of the optical fiber communication conference, vol 2, pp TuF1-1–TuF1-3Google Scholar
  6. 6.
    Berrou C, Glavieux A, Thitimajshima P (1993) Near Shannon limit error-correcting coding and decoding: Turbo codes. In: Proc 1993 international conference on communication (ICC 1993), vol 2, pp 1064–1070Google Scholar
  7. 7.
    Berrou C, Glavieux A (1996) Near optimum error correcting coding and decoding: turbo codes. IEEE Trans Commun 44(10):1261–1271CrossRefGoogle Scholar
  8. 8.
    Pyndiah RM (1998) Near optimum decoding of product codes. IEEE Trans Commun 46: 1003–1010MATHCrossRefGoogle Scholar
  9. 9.
    Sab OA, Lemarie V (2001) Block turbo code performances for long-haul DWDM optical transmission systems. In: Proceedings of the optical fiber communication conference, vol 3, pp 280–282Google Scholar
  10. 10.
    Mizuochi T (2006) Recent progress in forward error correction and its interplay with transmission impairments. IEEE/LEOS J Sel Top Quantum Electron 12(4):544–554CrossRefGoogle Scholar
  11. 11.
    Gallager RG (1963) Low density parity check codes. MIT Press, Cambridge, MAGoogle Scholar
  12. 12.
    Djordjevic IB, Sankaranarayanan S, Chilappagari SK, Vasic B (2006) Low-density parity-check codes for 40 Gb/s optical transmission systems. IEEE/LEOS J Sel Top Quantum Electron 12(4):555–562CrossRefGoogle Scholar
  13. 13.
    Djordjevic IB, Milenkovic O, Vasic B (2005) Generalized low-density parity-check codes for optical communication systems. IEEE/OSA J Lightwave Technol 23:1939–1946CrossRefGoogle Scholar
  14. 14.
    Vasic B, Djordjevic IB, Kostuk R (2003) Low-density parity check codes and iterative decoding for long haul optical communication systems IEEE/OSA J Lightwave Technol 21:438–446Google Scholar
  15. 15.
    Djordjevic IB et al (2004) Projective plane iteratively decodable block codes for WDM high-speed long-haul transmission systems. IEEE/OSA J Lightwave Technol 22:695–702CrossRefGoogle Scholar
  16. 16.
    Milenkovic O, Djordjevic IB, Vasic B (2004) Block-circulant low-density parity-check codes for optical communication systems IEEE/LEOS J Sel Top Quantum Electron 10:294–299Google Scholar
  17. 17.
    Vasic B, Djordjevic IB (2002) Low-density parity check codes for long haul optical communications systems. IEEE Photon Technol Lett 14:1208–1210CrossRefGoogle Scholar
  18. 18.
    Djordjevic IB, Arabaci M, Minkov L Next generation FEC for high-capacity communication in optical transport networks. IEEE/OSA J Lightwave Technol 27(16):3518–3530 (invited paper)Google Scholar
  19. 19.
    Chung S et al (2001) On the design of low-density parity-check codes within 0.0045 dB of the Shannon Limit. IEEE Commun Lett 5:58–60CrossRefGoogle Scholar
  20. 20.
    Djordjevic IB, Minkov LL, Batshon HG (2008) Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization. IEEE J Sel Areas Comm, Optical Commun Netw 26(6):73–83CrossRefGoogle Scholar
  21. 21.
    Ingels FM (1971) Information and coding theory. Intext Educational, Scranton, PAMATHGoogle Scholar
  22. 22.
    Haykin S (2004) Communication systems. Wiley, New YorkGoogle Scholar
  23. 23.
    Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New YorkMATHCrossRefGoogle Scholar
  24. 24.
    Lin S, Costello DJ (1983) Error control coding: fundamentals and applications. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  25. 25.
    Elias P (1954) Error-free coding. IRE Trans Inf Theory IT-4:29–37CrossRefMathSciNetGoogle Scholar
  26. 26.
    Anderson JB, Mohan S (1991) Source and channel coding: an algorithmic approach. Kluwer Academic, Boston, MAMATHGoogle Scholar
  27. 27.
    MacWilliams FJ, Sloane NJA (1977) The theory of error-correcting codes. North Holland, Amsterdam, the NetherlandsMATHGoogle Scholar
  28. 28.
    Wicker SB (1995) Error control systems for digital communication and storage. Prentice-Hall, Englewood Cliffs, NJMATHGoogle Scholar
  29. 29.
    Forney GD Jr (1966) Concatenated codes. MIT Press, Cambridge, MAGoogle Scholar
  30. 30.
    Morelos-Zaragoza RH (2002) The art of error correcting coding. Wiley, Boston, MACrossRefGoogle Scholar
  31. 31.
    Drajic DB (2004) (An introduction to information theory and coding, 2nd edn). Akademska Misao, Belgrade, Serbia (in Serbian)Google Scholar
  32. 32.
    Proakis JG (2001) Digital communications. McGaw-Hill, Boston, MAGoogle Scholar
  33. 33.
    Anderson I (1997) Combinatorial designs and tournaments. Oxford University Press, New YorkMATHGoogle Scholar
  34. 34.
    Raghavarao D (1988) Constructions and combinatorial problems in design of experiments. Dover, New York (reprint)MATHGoogle Scholar
  35. 35.
    Bosco G, Poggiolini P (2006) Long-distance effectiveness of MLSE IMDD receivers IEEE Photon Technol Lett 18(9):1037–1039Google Scholar
  36. 36.
    Bahl LR, Cocke J, Jelinek F, Raviv J (1974) Optimal decoding of linear codes for minimizing symbol error rate IEEE Trans Inf Theory IT-20(2):284–287MATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Ryan WE (2003) Concatenated convolutional codes and iterative decoding. In: Proakis JG (ed) Wiley encyclopedia in telecommunications. Wiley, New YorkGoogle Scholar
  38. 38.
    Reed IS, Solomon G (1960) Polynomial codes over certain finite fields. SIAM J Appl Math 8:300–304MATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Wicker SB, Bhargva VK (eds) (1994) Reed-Solomon codes and their applications. IEEE, New YorkMATHGoogle Scholar
  40. 40.
    Wolf JK (1978) Efficient maximum likelihood decoding of linear block codes using a trellis. IEEE Trans Inf Theory IT-24(1):76–80MATHCrossRefGoogle Scholar
  41. 41.
    Vucetic B, Yuan J (2000) Turbo codes-principles and applications. Kluwer Academic, BostonMATHGoogle Scholar
  42. 42.
    Ivkovic M, Djordjevic IB, Vasic B (2007) Calculation of achievable information rates of long-haul optical transmission systems using instanton approach. IEEE/OSA J Lightwave Technol 25:1163–1168CrossRefGoogle Scholar
  43. 43.
    van Valkenburg ME (1974) Network analysis, 3rd edn. Prentice-Hall, Englewood CliffsGoogle Scholar
  44. 44.
    Ivkovic M, Djordjevic I, Rajkovic P, Vasic B (2007) Pulse energy probability density functions for long-haul optical fiber transmission systems by using instantons and edgeworth expansion. IEEE Photon Technol Lett 19(20):1604–1606CrossRefGoogle Scholar
  45. 45.
    Divsalar D, Pollara F (1995) Turbo Codes for deep-space communications. TDA progress report 42–120, pp 29–39Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Electrical & Computer EngineeringUniversity of ArizonaTucsonUSA

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