Information theory's most celebrated result is Shannon's formula for
capacity C= max_{P_X} I(X;Y). It gives an upper bound on the rate
that can be transmitted reliably over a channel. There is just one
caveat; `reliably' means that the probability of error tends to zero
as the blocklength n approaches infinity. But what if we were to
ask the more practical question: How much information can be
transmitted over a channel if the blocklength is not infinite? In
this case, we set some probability of error that should not be
exceeded. This question has been the focus of many works which
mainly addressed discrete-time channels. In this report, we extend
these results slightly into the arena of continuous-time channels,
where, instead of a finite blocklength, we deal with a waveform of
finite duration. We study the continuous-time Poisson channel under
the assumptions of a pulse amplitude modulated waveform in the limit
of the pulse-width approaching 0.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web: http://moser-isi.ethz.ch/

Last modified: Mon Jul 3 11:19:06 CEST 2017