Coded Modulation

  • Ivan Djordjevic
  • William Ryan
  • Bane Vasic


In this chapter, we describe how to optimally combine modulation with channel coding, and describe several coded-modulation schemes: (a) multilevel coding (MLC) [1, 2, 3, 4], (b) multidimensional coded modulation [5, 6], and (c) coded orthogonal frequency division multiplexing (OFDM) [7, 8, 9, 10, 11, 12]. Using this approach, modulation, coding, and multiplexing are performed in a unified fashion so that, effectively, the transmission, signal processing, detection, and decoding are done at much lower symbol rates. At these lower rates, dealing with the nonlinear effects and polarization mode dispersion (PMD) is more manageable, while the aggregate data rate per wavelength is maintained above 100 Gb/s. The chapter is organized as follows. In Sect. 6.1 we describe M-ary quadrature amplitude multiplexing (QAM) [13, 14], M-ary phase shift keying (PSK), and an optimum signal constellation in minimum mean-square error (MMSE) sense [15]. In Sect. 6.2 we describe MLC, in which the component block codes have different code rates, and bit-interleaved coded modulation (BICM), in which all component codes have the same code rate. In Sect. 6.3 we describe multidimensional coded modulation as an efficient way to increase the spectral efficiency. In Sect. 6.4 we describe coded OFDM as an efficient way to compensate simultaneously for chromatic dispersion (CD) and PMD, and to increase the spectral efficiency.


Orthogonal Frequency Division Multiplex Orthogonal Frequency Division Multiplex System LDPC Code Amplify Spontaneous Emission Orthogonal Frequency Division Multiplex Symbol 
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.


  1. 1.
    Imai H, Hirakawa S (1977) A new multilevel coding method using error correcting codes. IEEE Trans Inform Theory IT-23(3):371–377CrossRefGoogle Scholar
  2. 2.
    Caire G, Taricco G, Biglieri E (1998) Bit-interleaved coded modulation. IEEE Trans Inform Theory 44:927–946MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Djordjevic IB, Vasic B (2006) Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection IEEE/OSA J Lightwave Technol 24:420–428CrossRefGoogle Scholar
  4. 4.
    Djordjevic IB, Cvijetic M, Xu L, Wang T (2007) Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission. IEEE/OSA J Lightwave Technol 25: 3619–3625CrossRefGoogle Scholar
  5. 5.
    Batshon HG, Djordjevic IB, Xu L, Wang T, Cvijetic M (2008) Proposal to achieve 1 Tb/s per wavelength transmission using 3-dimensional LDPC-coded modulation. IEEE Photon Technol Lett 20(9):721–723CrossRefGoogle Scholar
  6. 6.
    Batshon HG, Djordjevic IB, Minkov LL, Xu L, Wang T (2009) Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength optical transmission. IEEE Photon Technol Lett 21:1139–1141CrossRefGoogle Scholar
  7. 7.
    Djordjevic IB, Vasic B (2006) Orthogonal frequency-division multiplexing for high-speed optical transmission. Opt Express 14:3767–3775CrossRefGoogle Scholar
  8. 8.
    Djordjevic IB, Vasic B (2006) 100 Gb/s transmission using orthogonal frequency-division multiplexing. IEEE Photon Technol Lett 18(15):1576–1578CrossRefGoogle Scholar
  9. 9.
    Djordjevic IB (2007) PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM. Opt Express 15:3692–3701CrossRefGoogle Scholar
  10. 10.
    Djordjevic IB, Xu L, Wang T (2008) PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation. Opt Express 16(19):14845–14852CrossRefGoogle Scholar
  11. 11.
    Djordjevic IB, Xu L, Wang T (2008) PMD compensation in coded-modulation schemes with coherent detection using Alamouti-type polarization-time coding. Opt Express 16(18): 14163–14172CrossRefGoogle Scholar
  12. 12.
    Djordjevic IB, Xu L, Wang T (2009) Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection. IEEE/OSA J Opt Commun Netw 1(1):50–56CrossRefGoogle Scholar
  13. 13.
    Proakis JG (2001) Digital communications. McGaw-Hill, Boston, MAGoogle Scholar
  14. 14.
    Webb WT, Steele R (1995) Variable rate QAM for mobile radio. IEEE Trans Comm 43: 2223–2230CrossRefGoogle Scholar
  15. 15.
    Peric ZH, Djordjevic IB, Bogosavljevic SM, Stefanovic MC (1998) Design of signal constellations for Gaussian channel by iterative polar quantization. In: Proceedings of the 9th mediterranean electrotechnical conference, vol 2, pp 866–869, Tel-Aviv, Israel, 18–20 May 1998Google Scholar
  16. 16.
    Hou J, Siegel PH, Milstein LB, Pfitser HD (2003) Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes. IEEE Trans Inform Theory 49(9):2141–2155CrossRefMathSciNetGoogle Scholar
  17. 17.
    Wachsmann U, Fischer RFH, Huber JB (1999) Multilevel codes: theoretical concepts and practical design rules. IEEE Trans Inform Theory 45:1361–1391MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hou J, Lee MH (2004) Multilevel LDPC codes design for semi-BICM. IEEE Comm Lett 8:674–676CrossRefGoogle Scholar
  19. 19.
    Limpaphayom P, Winick KA (2004) Power- and bandwidth-efficient communications using LDPC codes. IEEE Trans Comm 52:350–354CrossRefGoogle Scholar
  20. 20.
    ten Brink S (2000) Designing iterative decoding schemes with the extrinsic information transfer chart. AEÜ Int J Electron Comm 54:389–398Google Scholar
  21. 21.
    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
  22. 22.
    Hou J, Siegel PH, Milstein LB (2005) Design of multi-input multi-output systems based on low-density parity-check codes IEEE Trans Comm 53:601–611Google Scholar
  23. 23.
    Tan J, Stüber GL (2005) Analysis of symbol mappers for iteratively decoded BICM. IEEE Trans Wireless Comm 4:662–672CrossRefGoogle Scholar
  24. 24.
    Benedetto S, Poggiolini P (1992) Theory of polarization shift keying modulation. IEEE Trans Comm 4:708–721CrossRefGoogle Scholar
  25. 25.
    Bahl L, Cocke J, Jelinek F, Raviv J (1974) Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans Inform Theory IT-20(2):284–287CrossRefMathSciNetGoogle Scholar
  26. 26.
  27. 27.
    Jäger M, Rankl T, Speidel J, Bülow H, Buchali F (2006) Performance of turbo equalizers for optical PMD channels. IEEE/OSA J Lightwave Technol 24(3):1226–1236CrossRefGoogle Scholar
  28. 28.
    Prasad R (2004) OFDM for wireless communications systems. Artech House, BostonGoogle Scholar
  29. 29.
    Shieh W, Djordjevic IB (2009) OFDM for optical communications. Academic, Burlington, MAGoogle Scholar
  30. 30.
    Djordjevic IB, Vasic B, Neifeld MA (2006) LDPC coded orthogonal frequency division multiplexing over the atmospheric turbulence channel. In: Proceedings of the CLEO/QELS 2006, paper CMDD5Google Scholar
  31. 31.
    Djordjevic IB, Vasic B, Neifeld MA (2007) LDPC coded OFDM over the atmospheric turbulence channel. Opt Express 15(10):6332–6346CrossRefGoogle Scholar
  32. 32.
    Shieh W, Athaudage C (2006) Coherent optical frequency division multiplexing. Electron Lett 42:587–589CrossRefGoogle Scholar
  33. 33.
    Lowery AJ, Du L, Armstrong J (2006) Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems. In: Proceedings of the OFC postdeadline papers, March 2006, paper no. PDP39Google Scholar
  34. 34.
    Lowery AJ, Armstrong J (2005) 10 Gb/s multimode fiber link using power-efficient orthogonal-frequency-division multiplexing. Opt Express 13(25):10 003–10 009CrossRefGoogle Scholar
  35. 35.
    Djordjevic IB (2007) LDPC-coded OFDM transmission over graded-index plastic optical fiber links. IEEE Photon Technol Lett 19(12):871–873CrossRefMathSciNetGoogle Scholar
  36. 36.
    Shieh W (2006) PMD-supported coherent optical OFDM systems. IEEE Photon Technol Lett 19:134–136CrossRefGoogle Scholar
  37. 37.
    Shieh W, Yi X, Ma Y, Tang Y (2007) Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems. Opt Express 15:9936–9947CrossRefGoogle Scholar
  38. 38.
    Jansen SL, Morita I, Takeda N, Tanaka H (2007) 20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-pilot tone phase compensation. In: Proceedings of the OFC/ NFOEC 2007 postdeadline papers, Anaheim, CA, March 25–29, 2007, paper no. PDP15Google Scholar
  39. 39.
    Schmidt BJ, Lawery AJ, Amstrong J (2007) Experimental demonstration of 20 Gbit/s direct-detection optical OFDM and 12 Gbit/s with a colorless transmitter. In: Proceedings of the OFC/ NFOEC 2007 postdeadline papers, Anaheim, CA, March 25–29, 2007, paper no. PDP18Google Scholar
  40. 40.
    Du LB, Lowery AJ (2009) Fiber nonlinearity compensation for CO-OFDM systems with periodic dispersion maps. In: Proceedings of the optical fiber telecommunications (OFC 2009), San Diego, CA, paper no. OTuO1Google Scholar
  41. 41.
    Du LB, Lowery AJ (2008) Improved nonlinearity precompensation for long-haul high-data-rate transmission using coherent optical OFDM. Opt Express 16(24):19920–19925CrossRefGoogle Scholar
  42. 42.
    Du LB, Lowery AJ (2008) Improving nonlinear precompensation in direct-detection optical OFDM communications systems. In: Proceedings of the european conference on optical communications (ECOC), Brussels, September 2008, paper no. P. 4.08Google Scholar
  43. 43.
    Cvijetic M (1996) Coherent and nonlinear lightwave communications. Artech House, BostonGoogle Scholar
  44. 44.
    Penninckx D, Morenás V (1999) Jones matrix of polarization mode dispersion. Opt Lett 24:875–877CrossRefGoogle Scholar
  45. 45.
    Goldsmith A (2005) Wireless communications. Cambridge University Press, CambridgeGoogle Scholar
  46. 46.
    Foschini GJ (1996) Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas. Bell Labs Tech J 1:41–59CrossRefGoogle Scholar
  47. 47.
    Biglieri E, Calderbank R, Constantinides A, Goldsmith A, Paulraj A, Poor HV (2007) MIMO wireless communications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  48. 48.
    Alamouti S (1998) A simple transmit diversity technique for wireless communications. IEEE J Sel Areas Commun 16:1451–1458CrossRefGoogle Scholar
  49. 49.
    Djordjevic IB, Batshon HG, Cvijetic M, Xu L, Wang T (2007) PMD compensation by LDPC-coded turbo equalization. IEEE Photon Technol Lett 19(15):1163–1165CrossRefGoogle Scholar
  50. 50.
    Sun H, Wu K-T, Roberts K (2008) Real-time measurements of a 40 Gb/s coherent system. Opt Express 16:873–879CrossRefGoogle Scholar
  51. 51.
    Djordjevic IB, Arabaci M, Minkov L (2009) Next generation FEC for high-capacity communication in optical transport networks. IEEE/OSA J Lightwave Technol 27(16):3518–3530 (invited paper)CrossRefGoogle 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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