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

TL;DR

This paper introduces two low-complexity algorithms, symbol sliding and interleaving, that achieve capacity for specific noiseless (d,k) constrained channels, expanding the range of constraints where capacity can be efficiently attained.

Contribution

The paper proposes novel generalized algorithms for capacity achievement in (d,k) constraints, extending existing methods to broader cases with reduced complexity.

Findings

Symbol sliding achieves capacity for (d,2d+1) constraints.

Interleaving method achieves capacity with fewer biased streams.

Algorithms perform well even when k-d+1 is not prime.

Abstract

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.