I made the mistake once of putting them straight in the garden without composting first. Hell, that's how the pictures of the indians doing it were in my 5th grade history book. Anyhow, it takes a long time for them to decompose that way.
Long enough that the next time you run the tiller, they might pop back up on top and stink to high heaven. Then, they don't want to go back under ground for some reason and then they're too chopped up and spread out by that point to re-bury with a shovel unless you want to spend 2 days messing with it.
I'd think that buried deep on the inside of a good hot working compost pile they should decompose fairly quick - at least quicker than just buried in a dirt garden. Maybe when you turn your pile, just leave that bottom layer with the fish in it to sit unturned, - not sure about that though.
In the south, pretty much any fish that doesn't get bigger than a pound or so is called a perch. For some reason, this drives some people crazy.