On minimal /spl alpha/-mean error parameter transmission over a Poisson channel

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/spl rarr//spl infin/ and we find the best possible exponent. For more general loss functions of the type |x|/spl alpha/ we find the best possible exponent if /spl alpha//spl ges//spl alpha//sub 0/=(1+/spl radic/5)/2/spl ap/1.618. If 0