The principle that there is a presumption of innocence in favor of the accused is the undoubted law, axiomatic and elementary, and its enforcement lies at the foundation of the administration of our criminal law.
Scalia's misguided notion about innocence:
This Court has never held that the Constitution forbids the execution of a convicted defendant who has had a full and fair trial but is later able to convince a habeas court that he is "actually" innocent. Quite to the contrary, we have repeatedly left that question unresolved, while expressing considerable doubt that any claim based on alleged "actual innocence" is constitutionally cognizable.
Scalia aside, one problem is we don't really know who's innocent. As I wrote then:
There's no way to know if someone is innocent when they didn't have competent counsel at trial, were identified as a result of an overly suggestive eyewitness procedure, had a confession beaten out of them, no DNA testing, were ratted out by a lying jailhouse snitch, may have an IQ below the level establishing mental retardation, or may be incompetent, delusional or otherwise severely mentally incapacitated. The question is not "did they do it?" but were they convicted following a a fair trial at which their constitutional rights were protected? Everyone is presumed innocent until a jury returns a verdict of guilty at the conclusion of a fair and impartial trial at which they are afforded their full panapoly of rights. If we can't trust in the credibility of the verdict, we can't trust in the integrity of the system that delivered it.
There is simply no excuse for executing someone who has a reasonable claim of innocence before providing him or her with a full and fair hearing on their claim. It's not what a civilized nation does, it's contrary to almost every constitutional right we have, from due process of law to the Sixth Amendment guarantee of a fair trial and effective assistance of counsel, to the 8th Amendment ban on cruel and unusual punishment. And it's certainly not justice.