Convex Programming Upper Bounds on the Capacity of 2-D Constraints

—The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear equalities and inequalities. In this paper, certain aspects of this characterization are extended to 2-D constraints. The result is a method for calculating an upper bound on the capacity of 2-D constraints. The key steps are: The maxentropic stationary probability distribution on square configurations is considered. A set of linear equalities and inequalities is derived from this stationarity. The result is a convex program, which can be easily solved numerically. Our method improves upon previous upper bounds for the capacity of the 2-D “no independent bits” constraint, as well as certain 2-D RLL constraints.

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Ido Tal, Ron M. Roth
• Keywords: 2-D Constraints, Linear Equalities, Probability Distribution, TIT 2011