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

  • Leonid Bassalygo
  • Mark Pinsker


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 :
$$P\left( X \right) = {P_1}\left( {{X_1}} \right)...{P_T}\left( {{X_T}} \right).$$


Uniform Distribution Time Instant Product Distribution Binary Sequence Binomial Coefficient 
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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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