Constrained Coding for Optical Communication

  • Anantha Raman Krishnan
  • Shiva K. Planjery


The increase in speed of optical communication systems has brought new technical challenges to the fore. For example, combatting intrachannel cross-phase modulation (IXPM) and intrachannel four-wave mixing (IFWM) in high-speed time division multiplexing (TDM) systems has been a focus of considerable research [1, 2, 3]. IXPM and IFWM are interactions among neighboring bits (pulses) that are a result of fiber nonlinearities. They can limit system performance by causing energy transfer between interacting pulses, thereby resulting in the formation of ghost pulses or shadow pulses. Moreover, these interactions can also lead to timing and amplitude jitters in the system. Though ghost pulses occur due to interactions between pulses in varied positions, it has been observed that certain “resonance” positions lead to more energy transfers than others [2]. In particular, pulses at positions k, l, and m lead to ghost pulse at position \((k + l - m)\). Also, it has been observed that this interaction is the most for pulses that are close to each other. Figure 8.1 illustrates this phenomenon. The figure depicts the creation of a ghost pulse at position 0 as a result of pulses at positions − 1, 2, and 3.


Adjacency Matrix Code Rate Forward Error Correction Error Correction Code LDPC Code 


  1. 1.
    Essiambre R-J, Mikkelsen B, Raybon G (2004) Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems. IEEE Electron Lett 35:1576–1578CrossRefGoogle Scholar
  2. 2.
    Forzati M et al (2002) Reduction of intrachannel four-wave mixing using the alternate-phase RZ modulation format. IEEE Photon Technol Lett 14:1285–1287CrossRefGoogle Scholar
  3. 3.
    Liu X et al (2002) Suppression of interchannel four-wave-mixing-induced ghost pulses in high-speed transmissions by phase inversion between adjacent marker blocks. Opt Lett 27: 1177–1179CrossRefGoogle Scholar
  4. 4.
    Djordjevic IB, Vasic B (2006) Constrained coding techniques for the suppression of intrachannel nonlinear effects in high-speed optical transmission. IEEE/OSA J Lightwave Technol 24:411–419CrossRefGoogle Scholar
  5. 5.
    Vasic B et al (2004) Ghost-pulse reduction in 40-Gb/s systems using line coding. IEEE Photon Lett 16:1784–1786CrossRefGoogle Scholar
  6. 6.
    Immink KAS (1999) Codes for mass data storage systems. Shannon Foundation, Rotterdam, The NetherlandsGoogle Scholar
  7. 7.
    Marcus BH, Siegel PH, Wolf JK (1992) Finite-state modulation codes for data storage. IEEE J Sel Areas Commun 10:5–37CrossRefGoogle Scholar
  8. 8.
    Shannon C (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423, 623–656MathSciNetGoogle Scholar
  9. 9.
    Marcus B, Siegel P (1984) Constrained codes for PRML. IBM Res Rep RJ 4371Google Scholar
  10. 10.
    Marcus B, Siegel P (1988) Constrained codes for partial response channels. In: Proceedings of Beijing International Workshop on Information Theory, pp DI1.1–DI1.4Google Scholar
  11. 11.
    Khayrallah A, Neuhoff D (1989) Subshift models and finite-state codes for input-constrained noiseless channels: a tutorial. Based upon PhD dissertation by A Khayrallah, University of MichGoogle Scholar
  12. 12.
    Djordjevic IB, Chilappagari SK, Vasic B (2006) Suppression of intrachannel nonlinear effects using pseudo-ternary constrained codes. IEEE/OSA J Lightwave Technol 24(2):769–774CrossRefGoogle Scholar
  13. 13.
    Bliss WG (1981) Circuitry for performing error correction calculations on baseband encoded data to eliminate error propagation. IBM Tech Discl Bull 23:4633–4634Google Scholar
  14. 14.
    Mansuripur M (1991) Enumerative modulation coding with arbitrary constraints and post-modulation error correcting coding and data storage systems. Proc SPIE 1499:72–86CrossRefGoogle Scholar
  15. 15.
    Bahl LR, Cocke J, Jelinek F, Raviv J (1991) Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans Inform Theory IT-20(2):284–287Google Scholar
  16. 16.
    Sankaranarayanan S, Vasic B (2005) Message-passing algorithm. In: Vasic B, Kurtas EM (eds.) Coding and signal processing for magnetic recording systems. CRC, Boca Raton, FL, pp 10–1–10–18Google Scholar
  17. 17.
    Vasic B, Pedagani K (2004) Run-length-limited low-density parity-check codes based on deliberate error insertion. IEEE Trans Magn 40:1738–1743CrossRefGoogle Scholar
  18. 18.
    Karabed R, Marcus B (1988) Sliding-block coding for input-restricted channels. IEEE Trans Inform Theory 34(1):2–26CrossRefMathSciNetGoogle Scholar
  19. 19.
    Marcus B (1985) Sofic systems and encoding data. IEEE Trans Inform Theory It-31(3): 366–377Google Scholar
  20. 20.
    Adler R, Friedman J, Kitchens B, Marcus B (1986) State splitting for variable length graphs. IEEE Trans Inform Theory IT-32(1):108–113Google Scholar
  21. 21.
    Heegard C, Marcus B, Siegel P (1991) Sliding-block coding for input-restricted channels. IEEE Trans Inform Theory 37(3):759–777CrossRefMathSciNetGoogle Scholar
  22. 22.
    Marcus B, Roth R (1991) Bounds on number of states in ecnoder graphs for input-constrained channels. IEEE Trans Inform Theory 37(3):742–758CrossRefMathSciNetGoogle Scholar
  23. 23.
    Ashley J (1988) A linear bound for sliding-block decoder with window size. IEEE Trans Inform Theory 34(3):389–399MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Kamabe H (1989) Minimum scope for sliding-block decoder mappings. IEEE Trans Inform Theory 35(6):389–399CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Anantha Raman Krishnan
    • 1
  • Shiva K. Planjery
    • 1
  1. 1.Department of Electrical & Computer EngineeringUniversity of ArizonaTucsonUSA

Personalised recommendations