TY - JOUR
T1 - A new two-dimensional interleaving technique using successive packing
AU - Shi, Yun Q.
AU - Zhang, Xi Min
N1 - Funding Information:
Manuscript received May 1, 2001; revised January 3, 2002. This work is supported in part by New Jersey Commission of Science and Technology under project New Jersey Center for Wireless Telecommunication, in part by the New Jersey Commission of High Education Project NJ-I-TOWER, and in part by the National Science Foundation Project IUCRC for Next Generation Video. This paper was recommended by Co-Guest Editor M. N. S. Swamy.
PY - 2002/6
Y1 - 2002/6
N2 - 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.
AB - 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.
KW - Error burst
KW - Multidimensional (2-D and 3-D) interleaving
KW - Random-error-correction codes
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U2 - 10.1109/TCSI.2002.1010033
DO - 10.1109/TCSI.2002.1010033
M3 - Article
AN - SCOPUS:0036601386
SN - 1057-7122
VL - 49
SP - 779
EP - 789
JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
IS - 6
ER -