Abstract

Within this work, the basic ideas of a recently presented
technique to calculate very tight upper bounds on channel capacity
are introduced. The focus is set on fiber optical channels,
therefore principles of a direct detection photon channel, also
referred to as “Poisson channel”, are illustrated and the channel
law is deduced. Already published results on the capacity of
Poisson channels are summarized in order to draw comparisons. The
core of this work is an improved lower bound on the conditional
Poisson entropy. With that, various upper bounds on the channel
capacity are calculated, considering either an average power
constraint, a peak power constraint or both. New bounds are
presented and known bounds are improved. Assuming infinite
bandwidth, some of the proposed upper bounds meet the exact
capacity of the Poisson channel. Moreover, an upper bound on the
capacity for a given input spectrum is calculated.

Keywords

Channel capacity, dual expression, upper bounds, Poisson channel,
direct detection photon channel, Poisson entropy.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Fri Feb 12 16:28:39 CET 2021