Calculation of the Asymptotically Optimal Capacity of a T-User M-Frequency Noiseless Multiple-Access Channel

  • Leonid Bassalygo
  • Mark Pinsker
Chapter

Abstract

The statement of the problem is taken from [1]. Let T(T ≥ 2) be the number of users every of which transmits one symbol from the alphabet {1, 2, ..., M}, M ≥ 2, at each time instant (the time is discrete); and the output is a binary sequence of length M where the symbol 0 is in the m-th position if and only if none user transmitted the symbol m. Such channel is referred to as an A-channel in [1]. Denote by X = (X 1, ..., X T ) an M-ary sequence at the input of the channel and by Y = (Y 1, ..., Y M ) a binary sequence at the output. Then (see [1]) the sum capacity of an A-channel is
$${C_{sum}}(T,M) = \max H(Y),$$
where the maximum is taken over all product distributions on input random variables X 1, ..., X T :
$$P\left( X \right) = {P_1}\left( {{X_1}} \right)...{P_T}\left( {{X_T}} \right).$$
(1)

Keywords

Uniform Distribution Time Instant Product Distribution Binary Sequence Binomial Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    S. C. Chang and J. K. Wolf, “On the T-user M-frequency noiseless multiple-access channels with and without intensity information”, IEEE Trans. Inform. Theory., 27, No. 1, 1981, 41–48.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    L. Wilhelmsson and K. Sh. Zigangirov, “On the asymptotical capacity of a multiple-access channel”, Probl. Inf. Trans. 33, No. 1, 1997, 12–20.Google Scholar
  3. [3]
    A. J. Grant and C. Schlegel, “Collision-type multiple-user communications”, IEEE Trans. Inform. Theory. 43, No. 5, 1997, 1725–1736.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    P. Gober and A. J. Han Vinck “ Note on ”On the asymptotical capacity of a multiple-access channel“ by L. Wilhelmsson and K. Sh. Zigangirov (Probl. Inf. Trans. 1997. Vol. 33, n.1, 9–16)” sunmitted Probl. Inf. Trans..Google Scholar
  5. [5]
    A. J. Han Vinck and J. Keuning, “On the capacity of the asynchronous T-user M-frequency noiseless multiple-access channel without intensity information”, IEEE Trans. Inform. Theory. 42, No. 6., 1996, 2235–2238.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Leonid Bassalygo
    • 1
  • Mark Pinsker
    • 1
  1. 1.Institute for Problems of Information Transmission, RASMoscowRussia

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