This article is cited in 6 papers

Methods of Signal Processing

Limits of Attainable Accuracy for Transmission of a Parameter over a White Gaussian Channel

M. V. Burnashev


Abstract: Assume that an unknown parameter $\theta\in[0,1]$, while a modulating signal $S_t(\theta)$ is transmitted over a channel with white Gaussian noise
$$ dX_t=S_t(\theta)dt+dW_t,\quad t\in T,\quad \theta\in\Theta=[0,1], $$
where $S_t(\theta)$ satisfies only the energy constraint
$$ \int^1_0\|S_t(\theta)\|^2d\theta\leqslant A. $$
New upper and lower bounds are obtained for the minimum possible mean $\alpha$-power risk
$$ e_\alpha(A)=\inf_{S,\hat{\theta}}e_\alpha(S,\hat{\theta}) $$
In particular, for $\alpha\geqslant3$ the exponents of the upper and lower bounds coincide.

UDC: 621.391.1, 519.27

Received: 28.11.1975
Revised: 06.12.1976

 English version: Problems of Information Transmission, 1977, 13:4, 251–260

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