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Mean field theory of communication

Statistical-physics approach to wireless communications

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Abstract

We discuss a Gaussian vector channel with random channel matrix, as a mathematical model for various wireless communication systems including multiple-input multiple-output (MIMO) and codedivision multiple-access (CDMA) channels, and how statistical-physics approaches can be applied to analyze the Gaussian vector channel. We then present a mean-field description of the Gaussian vector channel in terms of a joint distribution of any single element of originally sent channel input and its estimate via posterior probability, which is a refinement of the “decoupling” result reported by Guo and Verdú for a set of statistically equivalent elements of channel input, the number of which is extensive.

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References

  1. M. Mézard, G. Parisi, M.A. Virasoro, Spin glass theory and beyond (World Scientific, 1987)

  2. K.H. Fischer, J.A. Hertz, Spin glasses (Cambridge University Press, 1991)

  3. T. Tanaka, IEEE Trans. Info. Theory 48, 2888 (2002)

    Article  MATH  Google Scholar 

  4. D. Guo, S. Verdú, IEEE Trans. Info. Theory 51, 1982 (2005)

    Google Scholar 

  5. D. Tse, P. Viswanath, Fundamentals of wireless communication (Cambridge University Press, 2005)

  6. A. Goldsmith, Wireless communication (Cambridge University Press, 2005)

  7. S. Verdú, Multiuser detection (Cambridge University Press, 1998)

  8. D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)

    Article  ADS  Google Scholar 

  9. K. Nakamura, T. Tanaka (2008), in press arXiv:0801.4198 [cs:IT]

  10. D.N.C. Tse, S.V. Hanly, IEEE Trans. Info. Theory 45, 641 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Tanaka, Europhys. Lett. 54, 540 (2001)

    Article  ADS  Google Scholar 

  12. T. Yano, T. Tanaka, J. Phys. A: Math. Theor. (2007), submitted

  13. K. Takeuchi, T. Tanaka, Hierarchical decoupling principle of a MIMO-CDMA channel in asymptotic limits, in Proc. 2007 IEEE Int. Symp. Info. Theory (Nice, France, 2007), pp. 1271–1275

    Chapter  Google Scholar 

  14. K. Takeuchi, T. Tanaka, T. Yano, IEEE J. Select. A. Commun. 26 (2008), in press arXiv:0706.3170 [cs.IT]

  15. M. Yoshida, T. Tanaka, Analysis of sparsely-spread CDMA via statistical mechanics, in Proc. 2006 IEEE Int. Symp. Info. Theory (Seattle, USA, 2006), pp. 2378–2382

    Chapter  Google Scholar 

  16. J. Raymond, D. Saad, J. Phys. A: Math. Theor. 40, 12315 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. A. Montanari, D. Tse, Analysis fo belief propagation for non-linear problems: the example of CDMA (or: How to prove Tanaka’s formula), in Proc. IEEE Info. Theory Workshop (Punta del Este, Uruguay, 2006), pp. 122–126

    Google Scholar 

  18. D. Guo, C.C. Wang, Random sparse linear systems ovserved via arbitrary channels: a decoupling principle, in Proc. 2007 IEEE Int. Symp. Info. Theory (Nice, France, 2007), pp. 946–950

    Chapter  Google Scholar 

  19. J. Pearl, Probabilistic reasoning in intelligent systems: networks of plausible inference, revised 2nd edn. (Morgan Kaufmann, 1988)

  20. M. Yoshida, T. Uezu, T. Tanaka, M. Okada, J. Phys. Soc. Jpn 76, 054003 (2007)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto-shi, Kyoto, Japan

    T. Tanaka & K. Nakamura

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  1. T. Tanaka
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  2. K. Nakamura
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Correspondence to T. Tanaka.

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Tanaka, T., Nakamura, K. Mean field theory of communication. Eur. Phys. J. B 64, 625–631 (2008). https://doi.org/10.1140/epjb/e2008-00096-x

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  • DOI: https://doi.org/10.1140/epjb/e2008-00096-x

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