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Problemy Peredachi Informatsii, 1979, Volume 15, Issue 1, Pages 27–37 (Mi ppi1472)  

Information Theory

Channel Capacity with a Constraint on the Smoothness of the Transmitted Signal

I. A. Ibragimov, R. Z. Khas'minskii
Abstract: The authors determine the asymptotic behavior of the capacity of a channel with white Gaussian noise under constraints on the mean power and the smoothness of the periodic transmitted signal $S(t)$. It is shown that the capacity depends very strongly on the degree of smoothness of $S(t)$. In particular, for a periodic function $S(t)$ whose derivative of order $\gamma$ is bounded in the mean square by some constant, the capacity $C$ is asymptotically proportional to $T^{1/(2\gamma+1)}$ if the transmission time $T$ is large.
Received: 03.02.1977
Bibliographic databases:
Document Type: Article
UDC: 621.391.1:519.27
Language: Russian
Citation: I. A. Ibragimov, R. Z. Khas'minskii, “Channel Capacity with a Constraint on the Smoothness of the Transmitted Signal”, Probl. Peredachi Inf., 15:1 (1979), 27–37; Problems Inform. Transmission, 15:1 (1979), 18–26
Citation in format AMSBIB
\Bibitem{IbrKha79}
\by I.~A.~Ibragimov, R.~Z.~Khas'minskii
\paper Channel Capacity with a~Constraint on the Smoothness of the Transmitted Signal
\jour Probl. Peredachi Inf.
\yr 1979
\vol 15
\issue 1
\pages 27--37
\mathnet{http://mi.mathnet.ru/ppi1472}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=549170}
\zmath{https://zbmath.org/?q=an:0434.94009|0423.94011}
\transl
\jour Problems Inform. Transmission
\yr 1979
\vol 15
\issue 1
\pages 18--26
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