Positive capacity region of two-dimensional asymmetric run length constrained channels

Run length constraints derive from digital storage applications. For nonnegative integers d and k, a binary sequence is said to satisfy a one-dimensional (d,k)-constraint if every run of zeros has length at least d and at most k (if two ones are adjacent in the sequence we say that a run of zeros of length zero is between them). A two-dimensional binary pattern arranged in an m/spl times/n rectangle is said to be (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/) constrained if it satisfies a one-dimensional (d/sub 1/, k/sub 1/)-constraint horizontally and a one-dimensional (d/sub 2/,k/sub 2/)-constraint vertically. The two-dimensional (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/)-capacity is defined. In the present paper we determine whether or not the two-dimensional capacity is positive, for a large set of asymmetric constraints (d/sub 1/, k/sub 1/, d/sub 2/, k/sub 2/), and the main results are summarized.