I have read (here) and heard (on astronomy podcast) that radio waves decay or are indistinguishable the more distance they travel.
Do any of man made satellites communicate with Earth solely by laser?
Lasers have two advantages over radio waves for communication
There are also a few disadvantages:
No spacecraft has used exclusively Laser Communications, but there have been a number of tests. There is at least one satellite that uses lasers for a relay communication, using lasers on a LEO satellite to communicate with a satellite in GEO orbit, although the communication with the ground still occurs over RF. See European Laser Communication Satellite.
The main reason for reduced received signal with radio communication in space is the spreading loss, that is intensity declines with the square of the distance from source to receiver. This is true even with beamed radio signals.
Laser communications beams suffer from exactly the same loss once the cross-sectional area of the beam exceeds size of the receiving sensor. Which for practical purposes will always be the case for space communications.
The comms. system you choose is more related to bandwidth, absorption losses, immunity to interference, the practicality of the technology, ... but not spreading losses.
For SETI laser communications signals will be more difficult to detect unless they are deliberated attempts to contact others by an alien civilisation own SETI program, as lasers usually have much narrower beam widths than radio transmitters.
It's not the case that radio waves decay. Radio waves are a very good choice for most long distance communication, owing to their penetration of the atmosphere and the relative ease with which even distant, low-power sources can be received. In these ways, radio waves are superior to visible laser light. Visible light is blocked by clouds, and low intensity sources are swamped by the brightness of reflected sunlight.
However for high-bandwidth communication lasers do have a place. No spacecraft has been entirely dependent on lasers for communication though.