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EURASIP Journal on Advances in Signal Processing
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  • Research Article
  • Open Access

Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels

EURASIP Journal on Advances in Signal Processing20062006:097210

https://doi.org/10.1155/ASP/2006/97210

©  S. Mallik and R. Koetter. 2006

  • Received: 7 June 2005
  • Accepted: 12 May 2006
  • Published:

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

Authors’ Affiliations

(1)
The Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

References

  1. Kozek W: Matched Weyl-Heisenberg expansions of nonstationary environments, M.S. thesis. Vienna University of Technology, Vienna, Austria; March 1997.Google Scholar
  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.View ArticleGoogle Scholar
  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.2004.836931MathSciNetView ArticleGoogle Scholar
  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. 10.1109/18.568703MathSciNetView ArticleGoogle Scholar
  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. 10.1109/18.681321MathSciNetView ArticleGoogle Scholar
  6. Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123MathSciNetView ArticleGoogle Scholar
  7. Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982, 28(1):55–66. 10.1109/TIT.1982.1056454MathSciNetView ArticleGoogle Scholar
  8. Zadeh L: Time-varying networks, I. Proceedings of IRE 1961, 49: 1488–1503.MathSciNetView ArticleGoogle Scholar
  9. Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York, NY, USA; 2001. chapter 14MATHGoogle Scholar
  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.MATHGoogle Scholar
  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. 10.1109/49.730463View ArticleGoogle Scholar
  12. Leeuwin-Boulle K, Belfiore JC: The cutoff rate of time correlated fading channels. IEEE Transactions on Information Theory 1993, 39(2):612–617. 10.1109/18.212291View ArticleGoogle Scholar
  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.2003.815053View ArticleGoogle Scholar
  14. Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transactions on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551MathSciNetView ArticleGoogle Scholar
  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.2002.803349View ArticleGoogle Scholar
  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.1977.1055718View ArticleGoogle Scholar
  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.1984.1146101View ArticleGoogle Scholar
  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. 10.1109/18.771140MathSciNetView ArticleGoogle Scholar
  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.1976.1093351View ArticleGoogle Scholar
  20. Royden HL: Real Analysis. 3rd edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 1988. chapter 4MATHGoogle Scholar

Copyright

© 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.

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