I wouldn't bother. Honestly I put mine there in part because I thought not much else would grow so I thought of it as dead space.
Actually weeds and berries seem to thrive in that general area under the walnuts.
Definitely not worth the bother in my book (but I should warn you I am quite lazy!).
Black Walnuts secrete Juglone which inhibits growth of many (not all) other plants. My guess is if you have enough of it in your compost heap then it might inhibit growth.
However, I looked at State University Extension services and they all said it was fine. The Juglone breaks down in compost...