Title :
On minimal α-mean error parameter transmission over a Poisson channel
Author :
Burnashev, Marat V. ; Kutoyants, Yury A.
Author_Institution :
Inst. of Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia
fDate :
9/1/2001 12:00:00 AM
Abstract :
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
Keywords :
mean square error methods; optical signal detection; parameter estimation; stochastic processes; telecommunication channels; 1D parameter transmission; MSE; Poisson channel; direct-detection photon channel; estimator; exponent; input signal; intensity; loss functions; lower bound; mean-square error; minimal α-mean error parameter transmission; one-dimensional parameter transmission; peak energy constraint; transmission time; upper bound; Block codes; Gaussian noise; Random processes; Rate-distortion; Signal processing; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
