Erm, not really, tamago. I think you might have gotten it mixed
up with a supercharger.
In a supercharger (SC), it is dependent on the engine's rpm. This
however, as tailslide has explained, does nothing to increase
compression. I think you might have confused it with the resultant
increased pressure in the combustion chamber.
The Compression Ratio is that of volume of cylinder at bottom dead
centre : volume of cylinder at top dead centre. This can't be
increased/decreased just because a turbocharger or supercharger has
been added.
The turbocharger makes use of the pressure of hot exhaust gases to
spin the turbine. This turbine sucks in the air, which is
compressed during the suction process, resulting in its temperature
rising rapidly. The air then goes through an intercooler, where it
is allowed to cool before being sent to the engine.
Pros, please correct me if I'm wrong.