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

机译：凸规划二维约束能力的上限

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摘要

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 as follows: The maxentropic stationary probability distribution on square configurations is considered; set of linear equalities and inequalities is derived from this stationarity; the result is then a convex program, which can be easily solved numerically. Our method improves upon previous upper bounds for the capacity of the 2-D “no isolated bits” constraint, as well as certain 2-D RLL constraints.
机译：一维约束的容量由相应的静态最大熵马尔可夫链的熵给出。即，熵在一组概率分布上最大化，该概率分布由一些线性等式和不等式定义。在本文中，此表征的某些方面扩展到了二维约束。结果是一种用于计算2-D约束的容量的上限的方法。关键步骤如下：考虑正方形配置的正熵平稳概率分布；线性等式和不等式的集合是从这种平稳性得出的；结果是一个凸程序，可以很容易地在数值上求解。我们的方法针对2-D“无隔离位”约束以及某些2-RLLLL约束的容量改进了先前的上限。

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