The IHT was established under the US orchestrated Coalition Provision Authority (CPA) and was continued once Iraq was granted full sovereignty. The CPA, under L. Paul Bremer, had originally abolished the death penalty in Iraq, though it was reinstated by the Iraqi interim government in 2004.
The IHT is an example of imposing ex post facto, as Iraqi law lacked explicit provisions for human rights violations under Saddam Hussein. The IHT relies heavily on international laws of war outlined in the Geneva Convention and incorporates some national Iraqi law in regards to general abuse of power and interfering with the judicial process.
This is a novel example of the Tribunal system attempting to seek justice for past atrocities. It is rather unconventional for an atrocities regime to be established while occupying forces are still holding sovereignty. Further, the IHT does not appear to incorporate jurists from the international community, bringing various issues of venue into question. And, the enforcement of penalties prior to full exploration of other atrocities occurring in Saddam's Iraq leaves many questions of justice unresolved.
Iraq's human rights minister is reported as stating intentions to abolish the death penalty there, though Iraqi law requires the carrying out of sentence within 30 days of their delivery.
The Law of the Supreme Iraqi Criminal Tribunal may be found here.
The Center for Defense Information has a detailed exploration into the IHT here.