Optimal Interleaving Schemes for 2-D Arrays

Abstract

Given an m times 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 times 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 lfloorradic2krfloor if k les lceil(min{m, n})2/2rceil, and by min{m, n} + lfloor(k - lceil(min{m, n})2/2rceil) / min{m, n}rfloor if k ges lceil(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