Existence of a folding in multidimensional coding

Abstract Folding a sequence into a multidimensional box is an important technique in multidimensional coding. In this paper, the definition of folding defined by T. Etzion is explained from an algebraic point of view, and furthermore, a necessary and sufficient condition is derived for the existence of a folding for any given shape in Z m .

[1]  Tuvi Etzion,et al.  Constructions for perfect maps and pseudorandom arrays , 1988, IEEE Trans. Inf. Theory.

[2]  John P. Robinson Golomb rectangles as folded rulers , 1997, IEEE Trans. Inf. Theory.

[3]  N. Jacobson,et al.  Basic Algebra I , 1976 .

[4]  Alexander Vardy,et al.  Two-dimensional interleaving schemes with repetitions: Constructions and bounds , 2002, IEEE Trans. Inf. Theory.

[5]  M A Neifeld,et al.  Error correction for increasing the usable capacity of photorefractive memories. , 1994, Optics letters.

[6]  Martin Bossert,et al.  Array Codes Correcting a Two-Dimensional Cluster of Errors , 1998, IEEE Trans. Inf. Theory.

[7]  I. M. Boyarinov Two-dimensional array codes correcting rectangular burst errors , 2006, Probl. Inf. Transm..

[8]  Claire Gu,et al.  Crosstalk limited storage capacity of volume holographic memory , 1992, Optical Society of America Annual Meeting.

[9]  公庄 庸三 Basic Algebra = 代数学入門 , 2002 .

[10]  L Hesselink,et al.  Volume Holographic Storage and Retrieval of Digital Data , 1994, Science.

[11]  F. MacWilliams,et al.  Pseudo-random sequences and arrays , 1976, Proceedings of the IEEE.

[12]  M. Blaum,et al.  Array codes for cluster-error correction , 1994 .

[13]  Moshe Schwartz,et al.  Two-dimensional cluster-correcting codes , 2005, IEEE Transactions on Information Theory.

[14]  T. Etzion,et al.  Two-dimensional interleaving schemes with repetitions: constructions and bounds , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[15]  Eitan Yaakobi,et al.  Error-Correction of Multidimensional Bursts , 2007, ISIT.

[16]  Tuvi Etzion Sequence Folding, Lattice Tiling, and Multidimensional Coding , 2011, IEEE Transactions on Information Theory.