Representation of 2-D RLL Constraints

Weakly constrained codes were introduced for constructing efficient encoding algorithms with low complexities, that is, encoding algorithm which can be implemented with smaller circuits and less memories. In this paper we introduce 2 dimensional (2D) weak constraint codes for 2D storage media and propose some coding rules for 2D weak run-length-limited constraints. Simulation results show that these rules almost strictly obey given constraints. We can show these results theoretically for some constraints. The encoding algorithm also can be considered as a representation or a model of a 2D Run-Length-Limited(RLL) constraint. We show that the model of 2D constraints is complete for 2D (d, k) RLL constraint for positive integers d and with 2d ≤ k and that the model is incomplete for a 2D (2, 4) RLL constraints. Keyword: Bit-stuffing, RLL constraint, 2 dimensional constraints.