Two dimensional RC/Subarray Constrained Codes: Bounded Weight and Almost Balanced Weight

In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given p, ǫ > 0 , we study • The p -bounded constraint: a binary vector of size m is said to be p -bounded if its weight is at most pm , • The ǫ -balanced constraint: a binary vector of size m is said to be ǫ -balanced if its weight is within . 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 ǫ -balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every subarray, regarded as 2D subarray constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where p = 1 / 2 and ǫ = 0 , this work provides efficient coding methods that work for both 2D RC constrained codes and 2D subarray constrained codes, and more importantly, the methods are applicable for arbitrary values of p and ǫ . Furthermore, for certain values of p and ǫ , we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit. we show that for sufficiently large n , there exist efficient encoders/decoders for B RC ( n ; p ) , Bal RC ( n ; ǫ ) , B S ( n, m ; p ) and Bal S ( n, m ; ǫ ) , that incur at most one redundant bit.