The way to fix America's prison problem is simple, it will also help race relations. All you have to do are a few simple things:

Since we are the United States of America, take away state and local laws. All laws should come from the U.S. government and should be executed at the state and local level by officials. Set strict punishments for crimes with no grey area so that they can't be misinterpreted willfully or otherwise. That way if the same crime is committed in one state it garners the same exact punishment in another. This will deter citizens from being reckless and making careless decisions. It creates more accountability from all.

By doing that you can then make punishments for violent crimes even stricter. Start dropping 50 year minimums for armed robberies and just see how fast they drop. Committed a cold blooded murder? "Sir/Ma'am would you like to die by firing squad or rope? Your choice." I know there are finer details to murder like crimes of passion, but you can really break down the fundamental elements to make sure we don't execute innocent people. By doing this though we keep hard core criminals off the streets for longer or even permanently. More citizens would come forward to testify against criminals like these if they knew for certain they'd be going away for a long time.

Lastly, legalize marijuana. It has more benefits for health than most prescription drugs. If it is legalized you will see more shops open up selling it. That will destroy the local weed man's business, thus making the neighborhood that much more safe. He may resorts to violent crimes, but part two has that covered. Percentages of the tax revenue from sales would go right back into law enforcement keeping departments strong financially, allowing them to hire more and train better.

It isn't perfect, but if you get the right economist to map it out correctly it can work for the betterment of society as a whole.