A new two-dimensional interleaving technique using successive packing

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, with potential for extending to multidimensional (M-D) interleaving. Square arrays of 2/sup n/ /spl times/ 2/sup n/ are considered. It is shown that the proposed successive packing technique can spread any error burst of 2/sup k/ /spl times/ 2/sup k/ (with 1 /spl les/ k /spl les/ n-1), 2/sup k/ /spl times/ 2/sup k+1/ (with 0 /spl les/ k /spl les/ n-1), and 2/sup k+1/ /spl times/ 2/sup k/ (with 0 /spl les/ k /spl les/ 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.

[1]  Yun Q. Shi,et al.  2-D Interleaving for Enhancing the Robustness of Watermark Signals Embedded in Still Images , 2000, IEEE International Conference on Multimedia and Expo.

[2]  HIDEKI IMAI,et al.  Two-dimensional Fire codes , 1973, IEEE Trans. Inf. Theory.

[3]  K.A.S. Abdel-Ghaffar,et al.  Achieving the Reiger bound for burst errors using two-dimensional interleaving schemes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[4]  Ronald L. Rivest,et al.  An application of number theory to the organization of raster-graphics memory , 1982, FOCS 1982.

[5]  C. de Almeida,et al.  Two-dimensional interleaving using the set partitioning technique , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[6]  S. Golomb,et al.  Perfect Codes in the Lee Metric and the Packing of Polyominoes , 1970 .

[7]  Ronald L. Rivest,et al.  An application of number theory to the organization of raster-graphics memory , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[8]  M. Blaum,et al.  Two-dimensional interleaving schemes with repetitions , 1997, Proceedings of IEEE International Symposium on Information Theory.

[9]  Khaled A. S. Abdel-Ghaffar,et al.  Two-dimensional burst identification codes and their use in burst correction , 1988, IEEE Trans. Inf. Theory.

[10]  Yun Q. Shi,et al.  3D interleaving for enhancing the robustness of watermark signals embedded in video sequences , 2000, 2000 IEEE International Conference on Multimedia and Expo. ICME2000. Proceedings. Latest Advances in the Fast Changing World of Multimedia (Cat. No.00TH8532).

[11]  Yun-Qing Shi,et al.  Detection and robustness of digital image watermarking signals: a communication theory approach , 1999 .

[12]  S. Wicker.  Error Control Systems for Digital Communication and Storage , 1994 .

[13]  Alexander Vardy,et al.  Interleaving Schemes for Multidimensional Cluster Errors , 1998, IEEE Trans. Inf. Theory.