A convolution interpretation of (M,d,k) run-length-limited capacity

This paper considers the problem of capacity equivalence for a general class of (M,d,k) run-length-limited constraints, namely we look for pairs (M,d,k) and (M´,d´,k´) that have the same capacity. Our approach is based on a time domain interpretation where the characteristic (M,d,k) polynomial is viewed as an impulse train and factorization is related to convolution in discrete time. Using this interpretation, we first derive the known binary equivalence relations and then generalize to the M-ary case.