Statute of limitations?

Hey, I was wondering. Is there a statute of limitations on viewing child porn?

Like say if someone in their thirties publicly admits that twenty years ago he watched a video of kids interacting sexually, but the video is destroyed, and law enforcement can't find it anywhere in his house or evidence of anything. But he does admit that "oh yes, it did exist, and I looked at it twenty years ago!"

What would happen if a person just admitted it, but there's actually no proof other than his own "confession"?

How could they lay a specific charge on said person if he won't even elaborate on what he saw???

I'm guessing that these days someone like that would still somehow get in serious trouble, and that there probably isn't a statute of limitations but I wonder how such a thing would play out......