Low-Signal-Energy Asymptotics of Capacity and Mutual Information for the Discrete-Time Poisson Channel

Details Low-Signal-Energy Asymptotics of Capacity and Mutual Information for the Discrete-Time Poisson Channel Low-Signal-Energy Asymptotics of Capacity and Mutual Information for the Discrete-Time Poisson Channel

2008-08-20

arxiv.org/abs/0808.2703v1

Computer Science

Information Theory

Submitted to IEEE Trans. Inf. Theory

Scientific paper

The first terms of the low-signal-energy asymptotics for the mutual information in the discrete-time Poisson channel are derived and compared to an asymptotic expression of the capacity. In the presence of non-zero additive noise (either Poisson or geometric), the mutual information is concave at zero signal-energy and the minimum energy per bit is not attained at zero capacity. Fixed signal constellations which scale with the signal energy do not attain the minimum energy per bit. The minimum energy per bit is zero when additive Poisson noise is present and $\ew\log 2$ when additive geometric noise of mean $\ew$ is present.

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