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In this paper, we propose a column by column encoding scheme suitable fortwo-dimensional (2D) constraint codes and derive a lower bound of its maximumachievable rate. It is shown that the maximum achievable rate is equal to thelargest minimum degree of a subgraph of the maximal valid pair graph. A graphtheoretical analysis to provide a lower bound of the maximum achievable rate ispresented. For several 2D-constraints such as the asymmetric and symmetricnon-isolated bit constraints, the values of the lower bound are evaluated.

Asymptotic Achievable Rate of Two-Dimensional Constraint Codes based on Column by Column Encoding