Abstract :
A binary array is a (d1,k1,d2,k 2) runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 , and the runs of ones in every row and column have length at least d2 and at most k2. Such arrays arise in the context of digital storage devices. Writing N(m,n|d1,k1 ,d2,k2) for the number of (d1,k 1,d2,k2) runlength constrained arrays of size mtimesn, the capacity C(d1,k1,d2 ,k2) is defined to be limm,nrarrinfin(1/mn)log2N(m,n|d1,k 1,d2,k2). Let d2 be an integer such that d2 ges 1. The paper shows that C(1,d2+delta,d2,d2) is positive when delta ges 2, but is zero when delta les 1