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Characterization and Optimization of LDPC Codes for the 2-User Gaussian Multiple Access Channel

EURASIP Journal on Wireless Communications and Networking volume 2007, Article number: 074890 (2007) Cite this article

Abstract

We address the problem of designing good LDPC codes for the Gaussian multiple access channel (MAC). The framework we choose is to design multiuser LDPC codes with joint belief propagation decoding on the joint graph of the 2-user case. Our main result compared to existing work is to express analytically EXIT functions of the multiuser decoder with two different approximations of the density evolution. This allows us to propose a very simple linear programming optimization for the complicated problem of LDPC code design with joint multiuser decoding. The stability condition for our case is derived and used in the optimization constraints. The codes that we obtain for the 2-user case are quite good for various rates, especially if we consider the very simple optimization procedure.

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References

  1. Rimoldi B, Urbanke R: A rate-splitting approach to the Gaussian multiple-access channel. IEEE Transactions on Information Theory 1996,42(2):364-375. 10.1109/18.485709

    Article  MATH  Google Scholar 

  2. Ahlswede R: Multi-way communication channels. Proceedings of the 2nd IEEE International Symposium on Information Theory (ISIT '71), 1971, Aremenian Prague, Czech Republic 23-52.

    Google Scholar 

  3. Liao H: Multiple access channels, Ph.D. thesis. University of Hawaii, Honolulu, Hawaii, USA; 1972.

    Google Scholar 

  4. Palanki R, Khandekar A, McEliece R: Graph based codes for synchronous multiple access channels. Proceedings of the 39th Annual Allerton Conference on Communication, Control, and Computing, October 2001, Monticello, Ill, USA

    Google Scholar 

  5. Amraoui A, Dusad S, Urbanke R: Achieving general points in the 2-user Gaussian MAC without time-sharing or rate-splitting by means of iterative coding. Proceedings of IEEE International Symposium on Information Theory (ISIT '02), June-July 2002, Lausanne, Switzerland 334.

    Chapter  Google Scholar 

  6. De Baynast A, Declercq D: Gallager codes for multiple user applications. Proceedings of IEEE International Symposium on Information Theory (ISIT '02), June-July 2002, Lausanne, Switzerland 335.

    Chapter  Google Scholar 

  7. Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001,47(2):498-519. 10.1109/18.910572

    Article  MathSciNet  MATH  Google Scholar 

  8. Pearl J: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, Calif, USA; 1988.

    MATH  Google Scholar 

  9. Tanner RM: A recursive approach to low complexity codes. IEEE Transactions on Information Theory 1981,27(5):533-547. 10.1109/TIT.1981.1056404

    Article  MathSciNet  MATH  Google Scholar 

  10. Richardson TJ, Urbanke R: The capacity of low-density parity-check codes under message-passing decoding. IEEE Transactions on Information Theory 2001,47(2):599-618. 10.1109/18.910577

    Article  MathSciNet  MATH  Google Scholar 

  11. Ten Brink S: Designing iterative decoding schemes with the extrinsic information transfer chart. International Journal of Electronics and Communications 2000,54(6):389-398.

    Google Scholar 

  12. Roumy A, Guemghar S, Caire G, Verdú S: Design methods for irregular repeat-accumulate codes. IEEE Transactions on Information Theory 2004,50(8):1711-1727. 10.1109/TIT.2004.831778

    Article  MathSciNet  MATH  Google Scholar 

  13. Bennatan A, Burshtein D: On the application of LDPC codes to arbitrary discrete-memoryless channels. IEEE Transactions on Information Theory 2004,50(3):417-438. 10.1109/TIT.2004.824917

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang C-C, Kulkarni SR, Poor HV: Density evolution for asymmetric memoryless channels. IEEE Transactions on Information Theory 2005,51(12):4216-4236. 10.1109/TIT.2005.858931

    Article  MathSciNet  MATH  Google Scholar 

  15. Chung S-Y, Richardson TJ, Urbanke R: Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation. IEEE Transactions on Information Theory 2001,47(2):657-670. 10.1109/18.910580

    Article  MathSciNet  MATH  Google Scholar 

  16. Hu X-Y, Eleftheriou E, Arnold D-M: Progressive edge-growth tanner graphs. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '01), November 2001, San Antonio, Tex, USA 2: 995-1001.

    Article  Google Scholar 

  17. Tian T, Jones C, Villasenor JD, Wesel RD: Construction of irregular LDPC codes with low error floors. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 5: 3125-3129.

    Google Scholar 

  18. Richardson TJ, Shokrollahi MA, Urbanke R: Design of capacity-approaching irregular low-density parity-check codes. IEEE Transactions on Information Theory 2001,47(2):619-637. 10.1109/18.910578

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, Rennes Cedex, 35042, France

    Aline Roumy

  2. ETIS/ENSEA, University of Cergy-Pontoise/CNRS, 6 Avenue du Ponceau, Cergy-Pontoise, 95014, France

    David Declercq

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  1. Aline Roumy
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  2. David Declercq
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Correspondence to Aline Roumy.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Roumy, A., Declercq, D. Characterization and Optimization of LDPC Codes for the 2-User Gaussian Multiple Access Channel. J Wireless Com Network 2007, 074890 (2007). https://doi.org/10.1155/2007/74890

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  • DOI: https://doi.org/10.1155/2007/74890

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