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2008

The Poisson Channel at Low Input Powers

Lapidoth, Amos, Shapiro, Jeffrey H., Venkatesan, Vinodh et al.

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The asymptotic capacity at low input powers of an average-power limited or an average- and peak-power limited discrete-time Poisson channel is considered.

For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power $E$, capacity scales like $E\log\frac{1}{E}$ for small $E$.
For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like $E\log\log\frac{1}{E}$ for small $E$.

The Poisson Channel at Low Input Powers · Around

Built on

S. Shamai (Shitz), “Capacity of a pulse amplitude modulated direct detection photon channel,” in Proc. IEE , vol. 137, pt. I (Communications, Speech and Vision), no. 6, Dec. 1990, pp. 424–430
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Earlier work this paper cites.
S. Verdú, “On channel capacity per unit cost,” IEEE Trans. Inform. Theory , vol. 36, pp. 1019–1030, Sept. 1990
1990
Earlier work this paper cites.
A. Lapidoth and S. M. Moser, “Bounds on the capacity of the discrete-time Poisson channel,” in Proc. 41st Allerton Conf. Comm., Contr. and Comp. , Allerton H., Monticello, Il, Oct. 1–3, 2003
2003
Earlier work this paper cites.

Similar

——, “Capacity bounds via duality with applications to multiple-antenna systems on flat fading channels,” IEEE Trans. Inform. Theory , vol. 49, no. 10, pp. 2426–2467, Oct. 2003
2003
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V. Giovanetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, “Classical capacity of the lossy bosonic channel: the exact solution,” Phys. Rev. Lett. , vol. 92, no. 2, p. 027902, 2004
2004
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——, “On the capacity of the discrete-time Poisson channel,” to app. in IEEE Trans. Inform. Theory
Cited in the paper.

Then

V. Venkatesan, “On low power capacity of the Poisson channel,” Master’s thesis, Signal and Inform. Proc. Lab., ETH Zurich, Switzerland, Apr. 2008, supervised by Prof. Dr. Amos Lapidoth, Ligong Wang
2008
Closest in time.
A. Martinez, “Low-signal-energy asymptotics of capacity and mutual information for the discrete-time poisson channel,” Aug. 2008, subm. to IEEE Trans. Inform. Theory
2008
Closest in time.

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