Optimal Interleaving Schemes for 2-D Arrays

Given an m x n 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 m x n 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 [¿2k] if k ¿ [(min{m, n})2/2], and by min{m, n} + [(k -[(min{m, n})2/2])/ min{m, n}] if k ¿ [(min{m, n})2/2]. 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.