Zero/Positive Capacities of Two-Dimensional Runlength Constrained Arrays

A binary sequence satisfies a one-dimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint if every run of zeroes has length at least d 1 and at most k 2 and every run of ones has length at least d 2 and at most k 2 . A two-dimensional binary array is (d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 ) constrained if it satisfies the one-dimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint horizontally and the one-dimensional (d 3 , k 3 , d 4 , k 4 ) runlength constraint vertically. For given d 1 , k 1 , d 2 , k 2 , d 3 , k 3 , d 4 , k 4 , the two-dimensional capacity is defined as d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 ) denotes the number of (d 1 , k 1 , d 2 , k 2 ; d 3 , k 3 , d 4 , k 4 )- constrained m n binary arrays. Such constrained systems can find application in twodimensional digital storage applications