I think this is one of those questions that can't really be fully answered in a satisfactory way in a vacuum like this, sure you can talk about causes and how communism would mitigate those causes, but that might not amount to much without tying it to a material situation with specific resources and pressures.

In general I'd be more interested in reading an analysis of how you can handle crime as a newly revolutionary state with all the remains and birthmarks of capitalism in your society compared to how a stateless society would handle this.