By decreasing the compression ratio you are reducing the engine efficiency, and the transient response as well as performance when the turbo is out of its opperating range.
The benifits of decreasing the compression rato are that by decreasing it, you are reducing the pressure and temperature to which the intake charge is being compressed in the cylinder. This allows for more 'boost', and ignition advance (both of which improve performance in the turbo opperating range generally speaking) before the compressed charge gets to autoignition temperature.
This is when the fuel air mixture will self ignite at hotspots in the cylinder (usually around the wall, or on sharp intrusions in the pistons or combustion chamber) this is called Knock. This causes unsteady burning of the charge, rather than a nice steady flame front across the cylinder ignited by the spark plug like we want. Knock is a bad thing, also called detonation, and it leads to molten pistons!

So if you were planning on running a high boost engine, with a limited effective opperating range to when the turbo is spooled up (ie rallying where antilag is adopted to keep the turbo spinning) then you want low compression ratio to enable high boost, and therefore high on boost power.
For most road applications its a balance between keeping the off boost response of the engine relatively good, whilst maintaining good on boost performance.
Depends wether your able to put up with worse lag for more on boost performance.