A Wringing Method: An Elementary Proof of the Strong Converse Theorem for Multiple-Access Channels

  • Rudolf AhlswedeEmail author
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 15)


The methods of the analysis of the multiple description problem described in this chapter essentially use the methods developed for multiple-access channels (MACs). One of these methods concern the strong converse theorem which was proved by Dueck [1] in the sense of Wolfowitz [2] using the Ahlswede-Gács-Körner [3] method of “blowing up decoding sets” in conjunction with a new “wringing technique”. We will present the results of [4] where this theorem was proved without using the method of “blowing up decoding sets”, and considerations are based on non-elementary combinatorial work of Margulis [5].


  1. 1.
    G. Dueck, The strong converse to the coding theorem for the multiple-access channel. J. Comb. Inf. Syst. Sci. 6(3), 187–196 (1981)MathSciNetzbMATHGoogle Scholar
  2. 2.
    J. Wolfowitz, The coding of messages subject to chance errors. Illinois J. Math. 4, 591–606 (1957)MathSciNetzbMATHGoogle Scholar
  3. 3.
    R. Ahlswede, P. Gács, J. Körner, Bounds on conditional probabilities with applications in multi-user communication. Z. Wahrscheinlichkeitstheorie u. verw. Gebiete 34, 157–177 (1976)MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Ahlswede, An elementary proof of the strong converse theorem for the multiple-access channel. J. Comb. Inf. Syst. Sci. 7(3), 216–230 (1982)MathSciNetzbMATHGoogle Scholar
  5. 5.
    G.A. Margulis, Probabilistic characteristics of graphs with large connectivity. Problemy Perdachi Informatsii 10, 101–108 (1974)MathSciNetzbMATHGoogle Scholar
  6. 6.
    R. Ahlswede, On two-way communication channels and a problem by Zarankiewics. in Transactions 6-th Prague Conference on Information Theory, Sept. 1971 (Publishing House of the Czechoslovakian Academy of Sciences, 1974), pp. 23–37Google Scholar
  7. 7.
    R. Ahlswede, The capacity region of a channel with two senders and two receivers. Ann. Prob. 2(5), 805–814 (1974)MathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Ahlswede, Multi–way communication channels. in 2nd International Symposium on Information Theory, Thakadsor, 1971 (Publishing House of the Hungarian Academy of Sciences, 1973), p. 23–52Google Scholar
  9. 9.
    U. Augustin, Gedächtnisfreie Kanäle für diskrete Zeit. Z. Wahrscheinlichkeitstheorie u. verw. Gebiete 6, 10–61 (1966)Google Scholar
  10. 10.
    J. Wolfowitz, Note on a general strong converse. 12, 1–4 (1968)MathSciNetCrossRefGoogle Scholar
  11. 11.
    J.H.B. Kemperman, Studies in Coding Theory I, Mimeo graphed lecture notes (1961)Google Scholar
  12. 12.
    K. Zarankiewicz, Problem P 101. Golloq. Math. 2, 301 (1951)Google Scholar
  13. 13.
    G. Dueck, Maximal error capacity regions are smaller than average error capacity regions for multi-user channels. Probl. Control Inf. Theory 7(1), 11–19 (1978)MathSciNetzbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.BielefeldGermany

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