Can you use old carpet rather than burlap to cover the piles
Burlap is a natural fiber. Old carpet is usually a combination of synthetic fibers often coated with various chemicals. I'd go with burlap.
It should be something porous so air & water can pass through it.
Composting advice needed for novice, thanks.
New Garden Bed preparation question
What Kind of Composting is Best for Me?
Jon Rowley would be able to answer that better than anyone, but he has not been here for a number of years although he is still actively gardening in Seattle. Simply because the carpet is made of synthetic fibers, unless it is an antique Persian carpet, it should not even be considered for use in your garden.