A new two-dimensional interleaving technique using successive packing

Yun Q. Shi, Xi Min Zhang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Correction of two-dimensional (2-D) and three-dimensional (3-D) error bursts finds wide applications in secure data handling such as 2-D and 3-D magnetic and optical data storage, charged-coupled devices (CCDs), 2-D barcodes, and information hiding in digital images and video sequences, to name a few. In this paper, we present a new 2-D interleaving technique, called successive packing, to combat 2-D spot burst errors, which is potential to extend to multidimensional (M-D) interleaving. Square arrays of 2 n × 2 n are considered. It is shown that the proposed successive packing technique can spread any error burst of 2 k × 2 k (with 1≤k≤n-1), 2 k×2 k+1 (with 0≤k≤n-1), and 2 k+1×2 k (with 0≤k≤n-1) effectively so that the error burst can be corrected with some simple random-error-correction code (provided the error-correction code is available). It is further shown that the technique is optimal for combating all the above-mentioned error bursts in the sense that the interleaving degree reaches its lower bound. This implies that the algorithm needs to be implemented only once for a given 2-D array and is thereafter optimal for the set of error bursts having different sizes. A performance comparison between the proposed method and some existing techniques is given and the future research is discussed.

Original languageEnglish (US)
Pages (from-to)779-789
Number of pages11
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume49
Issue number6
DOIs
StatePublished - Jun 2002

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Keywords

  • Error burst
  • Multidimensional (2-D and 3-D) interleaving
  • Random-error-correction codes

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