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Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels

  • Siddhartha MallikEmail author
  • Ralf Koetter
Open Access
Research Article
Part of the following topical collections:
  1. Reliable Communications over Rapidly Time-Varying Channels

Abstract

We study the problem of modulation and coding for doubly dispersive, that is, time and frequency selective, fading channels. Using the recent result that underspread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum-likelihood decoding, we derive the code design criteria as a function of the channel's scattering function. We use ideas from generalized concatenation to design multilevel codes for this canonical channel model. These codes are based on partitioning a constellation carved out from the integer lattice. Utilizing the block fading interpretation of the doubly dispersive channel, we adapt these partitioning techniques to the richness of the channel. We derive an algebraic framework which enables us to partition in arbitrarily large dimensions.

Keywords

Information Technology Linear System Quantum Information Fading Channel Canonical Formulation 

References

  1. 1.
    Kozek W: Matched Weyl-Heisenberg expansions of nonstationary environments, M.S. thesis. Vienna University of Technology, Vienna, Austria; March 1997.Google Scholar
  2. 2.
    Kozek W: Adaptation of Weyl-Heisenberg frames to underspread environments. In Gabor Analysis and Algorithms: Theory and Applications. Edited by: Feichtinger HG, Strohmer T. Birkhäuser, Boston, Mass, USA; 1998:323–352.CrossRefGoogle Scholar
  3. 3.
    Liu K, Kadous T, Sayeed AM: Orthogonal time-frequency signaling over doubly dispersive channels. IEEE Transactions on Information Theory 2004, 50(11):2583–2603. 10.1109/TIT.2004.836931MathSciNetCrossRefGoogle Scholar
  4. 4.
    Giraud X, Boutillon E, Belfiore JC: Algebraic tools to build modulation schemes for fading channels. IEEE Transactions on Information Theory 1997, 43(3):938–952. 10.1109/18.568703MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boutros J, Viterbo E: Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel. IEEE Transactions on Information Theory 1998, 44(4):1453–1467. 10.1109/18.681321MathSciNetCrossRefGoogle Scholar
  6. 6.
    Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982, 28(1):55–66. 10.1109/TIT.1982.1056454MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zadeh L: Time-varying networks, I. Proceedings of IRE 1961, 49: 1488–1503.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York, NY, USA; 2001. chapter 14zbMATHGoogle Scholar
  10. 10.
    Matz G, Hlawatsch F: Time-frequency transfer function calculus of linear time-varying systems. In Time-Frequency Signal Analysis and Processing. Edited by: Boashash B. Prentice-Hall, Englewood Cliffs, NJ, USA; 2003.zbMATHGoogle Scholar
  11. 11.
    Kozek W, Molisch AF: Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels. IEEE Journal on Selected Areas in Communications 1998, 16(8):1579–1589. 10.1109/49.730463CrossRefGoogle Scholar
  12. 12.
    Leeuwin-Boulle K, Belfiore JC: The cutoff rate of time correlated fading channels. IEEE Transactions on Information Theory 1993, 39(2):612–617. 10.1109/18.212291CrossRefGoogle Scholar
  13. 13.
    Wang Z, Giannakis GB: A simple and general parameterization quantifying performance in fading channels. IEEE Transactions on Communications 2003, 51(8):1389–1398. 10.1109/TCOMM.2003.815053CrossRefGoogle Scholar
  14. 14.
    Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transactions on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551MathSciNetCrossRefGoogle Scholar
  15. 15.
    Siwamogsatham S, Fitz MP: Robust space-time codes for correlated Rayleigh fading channels. IEEE Transactions on Signal Processing 2002, 50(10):2408–2416. 10.1109/TSP.2002.803349CrossRefGoogle Scholar
  16. 16.
    Imai H, Hirakawa S: A new multilevel coding method using error-correcting codes. IEEE Transactions on Information Theory 1977, 23(3):371–377. 10.1109/TIT.1977.1055718CrossRefGoogle Scholar
  17. 17.
    Forney GD Jr., Gallager RG, Lang GR, Longstaff FM, Qureshi SU: Efficient modulation for band-limited channels. IEEE Journal on Selected Areas in Communications 1984, 2(5):632–647. 10.1109/JSAC.1984.1146101CrossRefGoogle Scholar
  18. 18.
    Wachsmann U, Fischer RFH, Huber JB: Multilevel codes: theoretical concepts and practical design rules. IEEE Transactions on Information Theory 1999, 45(5):1361–1391. 10.1109/18.771140MathSciNetCrossRefGoogle Scholar
  19. 19.
    Modestino JW, Mui SY: Convolutional code performance in the rician fading channel. IEEE Transactions on Communications 1976, 24(6):592–606. 10.1109/TCOM.1976.1093351CrossRefGoogle Scholar
  20. 20.
    Royden HL: Real Analysis. 3rd edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 1988. chapter 4zbMATHGoogle Scholar

Copyright information

© S. Mallik and R. Koetter. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.The Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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