Improved Bit-Stuffing Bounds on Two-Dimensional Constraints

Abstract

We derive lower bounds on the capacity of certain two-dimensional (2-D) constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders. A more detailed analysis of a previously proposed bit-stuffing encoder for (d,/spl infin/)-runlength-limited (RLL) constraints on the square lattice yields improved lower bounds on the capacity for all d /spl ges/ 2. This encoding approach is extended to (d,/spl infin/)-RLL constraints on the hexagonal lattice, and a similar analysis yields lower bounds on the capacity for d /spl ges/ 2. For the hexagonal (1,/spl infin/)-RLL constraint, the exact coding ratio of the bit-stuffing encoder is calculated and is shown to be within 0.5% of the (known) capacity. Finally, a lower bound is presented on the coding ratio of a bit-stuffing encoder for the constraint on the square lattice where each bit is equal to at least one of its four closest neighbors, thereby providing a lower bound on the capacity of this constraint.