Numbers, Information and Complexity pp 177-180 | Cite as

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

Chapter

## Abstract

The statement of the problem is taken from [1]. Let
where the maximum is taken over all product distributions on input random variables

*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$${C_{sum}}(T,M) = \max H(Y),$$

*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
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## References

- [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]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]A. J. Grant and C. Schlegel, “Collision-type multiple-user communications”,
*IEEE Trans. Inform. Theory.*43, No. 5, 1997, 1725–1736.MathSciNetMATHCrossRefGoogle Scholar - [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]A. J. Han Vinck and J. Keuning, “On the capacity of the asynchronous T-user M-frequency noiseless multiple-access channel without intensity information”,
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© Springer Science+Business Media New York 2000