8,290 research outputs found
Reduced Dimensional Optimal Vector Linear Index Codes for Index Coding Problems with Symmetric Neighboring and Consecutive Side-information
A single unicast index coding problem (SUICP) with symmetric neighboring and
consecutive side-information (SNCS) has messages and receivers, the
th receiver wanting the th message and having the
side-information . The single unicast index coding problem with
symmetric neighboring and consecutive side-information, SUICP(SNCS), is
motivated by topological interference management problems in wireless
communication networks. Maleki, Cadambe and Jafar obtained the symmetric
capacity of this SUICP(SNCS) and proposed optimal length codes by using
Vandermonde matrices. In our earlier work, we gave optimal length
-dimensional vector linear index codes for SUICP(SNCS) satisfying some
conditions on and \cite{VaR1}. In this paper, for SUICP(SNCS) with
arbitrary and , we construct optimal length
-dimensional vector linear index codes. We
prove that the constructed vector linear index code is of minimal dimension if
is equal to . The proposed
construction gives optimal length scalar linear index codes for the SUICP(SNCS)
if divides both and . The proposed construction is independent
of field size and works over every field. We give a low-complexity decoding for
the SUICP(SNCS). By using the proposed decoding method, every receiver is able
to decode its wanted message symbol by simply adding some index code symbols
(broadcast symbols).Comment: 13 pages, 1 figure and 5 table
Graphing of E-Science Data with varying user requirements
Based on our experience in the Swiss Experiment, exploring experimental, scientific data is often done in a visual way. Starting from a global overview the users are zooming in on interesting events. In case of huge data volumes special data structures have to be introduced to provide fast and easy access to the data. Since it is hard to predict on how users will work with the data a generic approach requires self-adaptation of the required special data structures. In this paper we describe the underlying NP-hard problem and present several approaches to address the problem with varying properties. The approaches are illustrated with a small example and are evaluated with a synthetic data set and user queries
The Euclidean Algorithm for Generalized Minimum Distance Decoding of Reed-Solomon Codes
This paper presents a method to merge Generalized Minimum Distance decoding
of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean
that the steps taken to perform the Generalized Minimum Distance decoding are
similar to those performed by the extended Euclidean algorithm. The resulting
algorithm has a complexity of O(n^2)
Generalized companion matrix for approximate GCD
We study a variant of the univariate approximate GCD problem, where the
coefficients of one polynomial f(x)are known exactly, whereas the coefficients
of the second polynomial g(x)may be perturbed. Our approach relies on the
properties of the matrix which describes the operator of multiplication by gin
the quotient ring C[x]=(f). In particular, the structure of the null space of
the multiplication matrix contains all the essential information about GCD(f;
g). Moreover, the multiplication matrix exhibits a displacement structure that
allows us to design a fast algorithm for approximate GCD computation with
quadratic complexity w.r.t. polynomial degrees.Comment: Submitted to MEGA 201
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