Two-dimensional runlength constrained arrays with equal horizontal and vertical constraints
Simon R. Blackburn⋆ · IEEE Transactions on Information Theory · 2006
A binary array is a (d1,k1,d2,k2) runlength constrained array if the runs of zeros in every row and column have length at least d1and at most k1, and the runs of ones in every row and column have length at least d2and 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,k1,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,k1,d2,k2). Let d2be an integer such that d2ges 1. The paper shows that C(1,d2+delta,d2,d2) is positive when delta ges 2, but is zero when delta les 1