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On minimal α-mean error parameter transmission over a Poisson channel

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2 Author(s)
Burnashev, M.V. ; Inst. of Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia ; Kutoyants, Y.A.

We consider the problem of one-dimensional parameter transmission over a Poisson channel when the input signal (intensity) obeys a peak energy constraint. We show that it is possible to choose input signals and an estimator in such a way that the mean-square error of parameter transmission will decrease exponentially with transmission time T→∞ and we find the best possible exponent. For more general loss functions of the type |x|α we find the best possible exponent if α⩾α0=(1+√5)/2≈1.618. If 0<α<α0 then some lower and upper bounds for the best possible exponent are established

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 6 )