Capacity achieving code constructions for two classes of (d,k) constraints

This correspondence presents two variable-rate encoding algorithms that achieve capacity for the (d,k) constraint when k=2d+1, or when k-d+1 is not prime. The first algorithm, symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran In addition to achieving capacity for (d,2d+1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf. This method uses fewer than k-d biased bit streams to achieve capacity for (d,k) constraints with k-d+1 not prime. In particular, the encoder for (d,d+2^m-1) constraints 2 ≤ m < ∞ requires only m biased bit streams.