Error-correction of multidimensional bursts

  • Authors:

  • Tuvi Etzion;Eitan Yaakobi

  • Affiliations:

  • Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel;Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA and Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

We present several methods and constructions to generate binary codes for correction of a multidimensional cluster-error, whose shape can be a box-error, a Lee sphere error, or an error with an arbitrary shape. Our codes have very low redundancy, close to optimal, and a large range of parameters of arrays and clusters. Our main results are summarized as follows. 1) A construction of two-dimensional codes capable to correct a rectangular-error with considerably more flexible parameters from previously known constructions. This construction is easily generalized for D dimensions. 2) A novel method based on D colorings of the D-dimensional space for constructing D-dimensional codes correcting a D-dimensional cluster-error of various shapes. 3) A transformation of the D-dimensional space into another D-dimensional space in a way that a D-dimensional Lee sphere is transformed into a shape located in a D-dimensional box of a relatively small size. 4) Applying the coloring method to correct more efficiently a two-dimensional error whose shape is a Lee sphere. 5) A construction of D-dimensional codes capable to correct a D-dimensional cluster-error of size b in which the number of erroneous positions is relatively small compared to b. 6) We present a code which corrects a D-dimensional arbitrary cluster-error with relatively small redundancy.