Improved bit-stuffing bounds on two-dimensional constraints - Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on

We consider the two-dimensional (2-D) (d, IC) runlengthlimited constraint and the 2-D ‘no isolated bits’ constraint (in short, the n.i.b. constraint). A binary array on the square lattice satisfies the two-dimensional (d, IC) constraint if it satisfies the one-dimensional (d, IC) constraint in both vertical and horizontal directions. Similarly, an array on the hexagonal lattice satisfies the two-dimensional (d, IC) constraint if the onedimensional (d, IC) constraint is met in all three directions. The 2-D n.i.b. constraint requires that each bit is equal to at least one of its four closest neighbors on the square lattice. We denote the (d, IC) constraints on the square and hexagonal lattices by S:;k and S,$!, respectively, while the n.i.b. constraint is denoted by Snib. The capacity of a 2-D constraint S is defined by cap(S) = lim,,,,, ( l /(mn)) . log, IS[m,n]I, where S[m,n] is the set of m x n arrays that satisfy the constraint S. The capacity of 2-D constraints has been investigated by several authors (e.g. [1]-[6]). By examining the behavior of the bit-stuffing encoder presented in [5], we derive improved lower bounds on cap(S$-), for d 2 2. We adapt the encoder and analysis to the hexagonal lattice to derive lower bounds on cap(S,d;r), for d 2 2. For Si ; : , we use results in [4] to compute the exact coding ratio of an efficient bit-stuffing encoder. Finally, we present and analyze a bit-stuffing coding scheme to derive a lower bound on cap(S,d;r).