Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints
<|reference_start|>Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints: In this paper, we present two low complexity algorithms that achieve capacity for the noiseless (d,k) constrained channel when k=2d+1, or when k-d+1 is not prime. The first algorithm, called symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. [1]. 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 [2]. 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, 1\le m<\infty, requires only m biased bit streams.<|reference_end|>
@article{sankarasubramaniam2004capacity,
    title={Capacity Achieving Code Constructions for Two Classes of (d,k)
  Constraints},
    author={Yogesh Sankarasubramaniam, Steven W. McLaughlin},
    journal={arXiv preprint arXiv:cs/0411006},
    year={2004},
    doi={10.1109/TIT.2006.876224},
    archivePrefix={arXiv},
    eprint={cs/0411006},
    primaryClass={cs.IT math.IT}
}