Two dimensional RC/Subarray Constrained Codes: Bounded Weight and Almost Balanced Weight
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In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given p,ϵ>0, we study (i) The p-bounded constraint: a binary vector of size m is said to be p-bounded if its weight is at most pm, and (ii) The ϵ-balanced constraint: a binary vector of size m is said to be ϵ-balanced if its weight is within [(0.5-ϵ)*m,(0.5+ϵ)*m]. 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 ϵ-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 ϵ = 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 ϵ. Furthermore, for certain values of p and ϵ, we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit.
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