Not 100% sure what the LDP is, but it sounds like you may have a similar problem to one that I had. The fuel vent valve, or roll over valve, that is located behind the fuel tank may be bad. It is part of the EVAP system. IIRC it has two big hoses going to either side of it, then a small vaccum hose going to a nipple on the top, and then one more large hose connected to the bottom of it. The inner rubber diaphragm is made of thin rubber, and can tear after some time, espeically if you are boosted. I had a pesky CEL for a while too relating to the EVAP system, and after removing the valve from the car and taking it apart it was obvious. Although it looked unscathed from the outside, once I took it apart it was obvious the inner diaphragm was in fact torn.

Check it out, its worth a shot..