Asymptotic capacity of the two-dimensional square constraint

Two-dimensional run length limited codes satisfying the square constraint are considered. Let S denote a square of area A(S) and let /spl alpha//sub n/ be a positive sequence satisfying lim/sub n/spl rarr//spl infin///spl alpha//sub n/=/spl infin/. It is shown that the capacity C/sub n/ corresponding to the set S/sub n/=/spl alpha//sub n/S/spl cap/Z/sup 2/ asymptotically satisfies lim/sub n/spl rarr//spl infin//C/sub n/[/spl alpha//sub n//sup 2//log/sub 2//spl alpha//sub n//sup 2/]=4/A(S).