Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints

Details Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints

2004-11-03

arxiv.org/abs/cs/0411006v1

Computer Science

Information Theory

16 pages, submitted to the IEEE Transactions on Information Theory

Scientific paper

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.

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