Efficient Design of Capacity-Approaching Two-Dimensional Weight-Constrained Codes

In this work, given $n, p > 0$, efficient encoding/decoding algorithms are presented for mapping arbitrary data to and from $n\times n$ binary arrays in which the weight of every row and every column is at most $pn$. Such constraint, referred as $p$-bounded-weight-constraint, is crucial for reducing the parasitic currents in the crossbar resistive memory arrays, and has also been proposed for certain applications of the holographic data storage. While low-complexity designs have been proposed in the literature for only the case $p=1/2$, this work provides efficient coding methods that work for arbitrary values of $p$. The coding rate of our proposed encoder approaches the channel capacity for all $p$.