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×n rectangle is said to be (d₁ , k₁, d₂, k₂) constrained if it satisfies a one-dimensional (d₁, k₁)-constraint horizontally and a one-dimensional (d₂,k₂)-constraint vertically. The two-dimensional (d₁, k₁, d₂, k₂)-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 (d₁, k₁, d₂, k₂), and the main results are summarized