2,837 research outputs found
Interleaving schemes for multidimensional cluster errors
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
PHORMA: Perfectly Hashable Order Restricted Multidimensional Arrays
In this paper we propose a simple and efficient data structure yielding a
perfect hashing of quite general arrays. The data structure is named phorma,
which is an acronym for perfectly hashable order restricted multidimensional
array.
Keywords: Perfect hash function, Digraph, Implicit enumeration,
Nijenhuis-Wilf combinatorial family.Comment: 12 pages, 4 figures, 2 tables. Revised version. Submitted to Discrete
Applied Mathematic
On the symbol error probability of regular polytopes
An exact expression for the symbol error probability of the four-dimensional
24-cell in Gaussian noise is derived. Corresponding expressions for other
regular convex polytopes are summarized. Numerically stable versions of these
error probabilities are also obtained
Fast Color Space Transformations Using Minimax Approximations
Color space transformations are frequently used in image processing,
graphics, and visualization applications. In many cases, these transformations
are complex nonlinear functions, which prohibits their use in time-critical
applications. In this paper, we present a new approach called Minimax
Approximations for Color-space Transformations (MACT).We demonstrate MACT on
three commonly used color space transformations. Extensive experiments on a
large and diverse image set and comparisons with well-known multidimensional
lookup table interpolation methods show that MACT achieves an excellent balance
among four criteria: ease of implementation, memory usage, accuracy, and
computational speed
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