Optimal Interleaving Schemes for Two-Dimensional Arrays

Given an mtimesn array of k single random error correction (or erasure) codewords, each having length l such that mn=kl, we construct optimal interleaving schemes that provide the maximum burst error correction power such that an arbitrarily shaped error burst of size t can be corrected for the largest possible value of t. We show that for all such mtimesn arrays, the maximum possible interleaving distance, or equivalently, the largest value of t such that an arbitrary error burst of size up to t can be corrected, is bounded by lfloorradic2krfloor if kleslceil(min{m,n})²/2rceil, and by min{m,n}+lfloor(k-lceil(min{m,n})² /2rceil)/min{m,n}rfloor if kgeslceil(min{m,n})²/2rceil. We generalize the cyclic shifting algorithm developed by the authors in a previous paper and construct, in several special cases, optimal interleaving arrays achieving these upper bounds. Additionally, for codewords of variable lengths, we solve a related array coloring problem for which the same upper bounds hold and can be achieved