Optimal tristance anticodes in certain graphs
Journal of Combinatorial Theory Series A
Optimal interleaving schemes for correcting two-dimensional cluster errors
Discrete Applied Mathematics
IBM Journal of Research and Development
Optimal 2-dimensional 3-dispersion lattices
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Error-correction of multidimensional bursts
IEEE Transactions on Information Theory
Two-dimensional patterns with distinct differences: constructions, bounds, and maximal anticodes
IEEE Transactions on Information Theory
Basis arrays and successive packing for M-D interleaving
Multidimensional Systems and Signal Processing
Autonomic k-interleaving construction scheme for p2p overlay networks
ATC'06 Proceedings of the Third international conference on Autonomic and Trusted Computing
Three-dimensional cyclic Fire codes
Designs, Codes and Cryptography
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We present two-dimensional and three-dimensional interleaving techniques for correcting two- and three-dimensional bursts (or clusters) of errors, where a cluster of errors is characterized by its area or volume. Correction of multidimensional error clusters is required in holographic storage, an emerging application of considerable importance. Our main contribution is the construction of efficient two-dimensional and three-dimensional interleaving schemes. The proposed schemes are based on t-interleaved arrays of integers, defined by the property that every connected component of area or volume t consists of distinct integers. In the two-dimensional case, our constructions are optimal: they have the lowest possible interleaving degree. That is, the resulting t-interleaved arrays contain the smallest possible number of distinct integers, hence minimizing the number of codewords required in an interleaving scheme. In general, we observe that the interleaving problem can be interpreted as a graph-coloring problem, and introduce the useful special class of lattice interleavers. We employ a result of Minkowski, dating back to 1904, to establish both upper and lower bounds on the interleaving degree of lattice interleavers in three dimensions. For the case t≡0 mod 6, the upper and lower bounds coincide, and the Minkowski lattice directly yields an optimal lattice interleaver. For t≠0 mod 6, we construct efficient lattice interleavers using approximations of the Minkowski lattice