Two-dimensional interleaving schemes with repetitions: Constructions and bounds

Abstract--Two-dimensional interleaving schemes with repetitions are considered. These schemes are required for the correction of two-dimensional bursts (or clusters) of errors in applications such as optical recording and holographic storage. We assume that a cluster of errors may have an arbitrary shape, and is characterized solely by its area . Thus, an interleaving scheme ( ) of strength with repetitions is an (infinite) array of integers defined by the property that every integer appears no more than times in any connected component of area . The problem is to minimize, for a given and , the interleaving degree deg ( ), which is the total number of distinct integers contained in the array. Optimal interleaving schemes for = 1 (no repetitions) have been devised in earlier work. Here, we consider interleaving schemes for 2. Such schemes reduce the overall redundancy, yet are considerably more difficult to construct and analyze. To this end, we generalize the concept of 1-distance and...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Tuvi Etzion, Alexander Vardy
• Keywords: Interleaving, Interleaving Scheme, TIT 2002, Two-dimensional Interleaving Schemes