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

Volume

47

Issue

6

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

2505

Lastpage

2515

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;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.945261

Filename

945261