Electromagnetic channel capacity for practical purposes

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.