TY - GEN
T1 - Mutual information and conditional mean estimation in poisson channels
AU - Guo, Dongning
AU - Verdú, Sergio
AU - Shamai, Shlomo
PY - 2004
Y1 - 2004
N2 - Following the recent discovery of new connections between information and estimation in Gaussian channels, this paper reports parallel results in the Poisson regime. Both scalar and continuous-time Poisson channels are considered. It is found that, regardless of the statistics of the input, the derivative of the input-output mutual information with respect to the dark current can be expressed in the expected difference between the logarithm of the input and the logarithm of its conditional mean estimate (noncausal in case of continuous-time). The same is true for the derivative with respect to input scaling, but with the logarithmic function replaced by x log x.
AB - Following the recent discovery of new connections between information and estimation in Gaussian channels, this paper reports parallel results in the Poisson regime. Both scalar and continuous-time Poisson channels are considered. It is found that, regardless of the statistics of the input, the derivative of the input-output mutual information with respect to the dark current can be expressed in the expected difference between the logarithm of the input and the logarithm of its conditional mean estimate (noncausal in case of continuous-time). The same is true for the derivative with respect to input scaling, but with the logarithmic function replaced by x log x.
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M3 - Conference contribution
AN - SCOPUS:17644382199
SN - 0780387201
T3 - 2004 IEEE Information Theory Workshop - Proceedings, ITW
SP - 265
EP - 270
BT - 2004 IEEE Information Theory Workshop - Proceedings, ITW
T2 - 2004 IEEE Information Theory Workshop - Proceedings, ITW
Y2 - 24 October 2004 through 29 October 2004
ER -