Sod it!

[bykimbo]

Maybe I know odd people, but I'd expect a compost heap/bin to be covered so that nothing grows. Typically people use bits of old carpet, black plastic, or left-over corrugated tin.

[PoppyGrove]

If its a home made compost bin any manner of things can be used to cover it - the things bykimbo mentions and thick polythene too.

A quick way to rot the clumps of sod, bundle them into an old potting compost bag or similar thick polythene bag, add plenty of water to soak which helps the rotting process, seal the top (tie it with string, wire, cable-tie) and leave. It should be rotten in anything around the 8 to 10 months period.

For clearing areas that are heavily grassed over, or heavily weeded, without the use of chemicals and without the hard backbreaking work of digging - cover the whole area with black polythene, with stones to weigh down the edges. Over time, about 10 to 12 months if I remember right from when I did it, the weeds / grass deprived of sunlight and rain, rot, put feed back into the ground so it can be turned and used.