  We give analytic upper bounds to the channel capacity C for transmission of
classical information in electromagnetic channels (bosonic channels with
thermal noise). In the practically relevant regimes of high noise and low
transmissivity, by comparison with know lower bounds on C, our inequalities
determine the value of the capacity up to corrections which are irrelevant for
all practical purposes. Examples of such channels are radio communication,
infrared or visible-wavelength free space channels. We also provide bounds to
active channels that include amplification.
