Cascading methods for runlength-limited arrays

Runlength-limited sequences and arrays have found applications in magnetic and optical recording. While the constrained sequences are well studied, little is known about constrained arrays. In this correspondence we consider the question of how to cascade two arrays with the same runlength constraints horizontally and vertically, in such a way that the runlength constraints will not be violated. We consider binary arrays in which the shortest run of a symbol in a row (column) is d(1)(d(2)) and the longest run of a symbol in a row (column) is k(1)(k(2)). We present three methods to cascade such arrays. If k(1) > 4d(1) - 2 our method is optimal, and if k(1) greater than or equal to d(1) + 1 we give a method which has a certain optimal structure. Finally, we show how cascading can be applied to obtain runlength-limited error-correcting array codes.