Abstract
In this work, we study two types of constraints on two-dimensional binary arrays. Given p ? [0, 1], ? ? [0, 1/2], we study 1) the p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn, and 2) the ?-balanced constraint: a binary vector of size n is said to be ?-balanced if its weight is within [(1/2 - ?)n, (1/2 + ?)n]. Such constraints are crucial in several data storage systems, those regard the information data as two-dimensional (2D) instead of one-dimensional (1D), such as the crossbar resistive memory arrays and the holographic data storage. In this work, efficient encoding/decoding algorithms are presented for binary arrays so that the weight constraint (either p -bounded constraint or ?-balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every window (where each window refers to as a sub array consisting of consecutive rows and consecutive columns), regarded as 2D sliding-window (SW) constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where p = 1/2 and ? = 0, this work provides efficient coding methods that work for both 2D RC constrained codes and 2D SW constrained codes, and more importantly, the methods are applicable for arbitrary values of p and ?. Furthermore, for certain values of p and ?, we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit.