Two-Dimensional Interleaving Schemes with Repetitions

We present 2-dimensional interleaving schemes, with repetition, for correcting 2- dimensional bursts (or clusters) of errors, where a cluster of errors is characterized by its area. A recent application of correction of 2-dimensional clusters appeared in the context of holographic storage. Known interleaving schemes are based on arrays of integers with the property that every connected component of area t consists of distinct integers. Namely, they are based on the use of 1-error-correcting codes. We extend this concept by allowing repetitions within the arrays, hence, providing a trade-off between the error-correcting capability of the codes and the degree of the interleaving schemes.