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 et al. In addition in 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 + 2m - 1) constraints 2 ≤ m < ∞ requires only m biased bit streams. [ABSTRACT FROM AUTHOR]