Publications (283)143.59 Total impact
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ABSTRACT: We give a condition for a Borel measure on R [0,1] which is sufficient for the validity of an ADtype correlation inequality in the function space.08/2006: pages 572577;  [Show abstract] [Hide abstract]
ABSTRACT: Consider (X,E)(X,{\mathcal E}), where X is a finite set and E{\mathcal E} is a system of subsets whose union equals X. For every natural number n ∈ℕ define the cartesian products X n =∏1 n X and En=Õ1nE{\mathcal E}_n=\prod_1^n{\mathcal E}. The following problem is investigated: how many sets of En{\mathcal E}_n are needed to cover X n ? Let this number be denoted by c(n). It is proved that for all n ∈ℕ exp{Cn} £ c(n) £ exp{Cn+logn+loglogX}+1.\exp\{C\cdot n\}\leq c(n)\leq\exp\{Cn+\log n+\log\logX\}+1. A formula for C is given. The result generalizes to the case where X and E{\mathcal E} are not necessarily finite and also to the case of non–identical factors in the product. As applications one obtains estimates on the minimal size of an externally stable set in cartesian product graphs and also estimates on the minimal number of cliques needed to cover such graphs.08/2006: pages 926937;  [Show abstract] [Hide abstract]
ABSTRACT: We analyze wiretape channels with secure feedback from the legitimate receiver. We present a lower bound on the transmission capacity (Theorem 1), which we conjecture to be tight and which is proved to be tight (Corollary 1) for Wyner’s original (degraded) wiretape channel and also for the reversely degraded wiretape channel for which the legitimate receiver gets a degraded version from the enemy (Corollary 2). Somewhat surprisingly we completely determine the capacities of secure common randomness (Theorem 2) and secure identification (Theorem 3 and Corollary 3). Unlike for the DMC, these quantities are different here, because identification is linked to nonsecure common randomness.08/2006: pages 258275;  [Show abstract] [Hide abstract]
ABSTRACT: Let F be a finite family of sets and G(F) be the intersection graph of F (the vertices of G(F) are the sets of family F and the edges of G(F) correspond to intersecting pairs of sets). The transversal number τ(F) is the minimum number of points meeting all sets of F. The independent (stability) number α(F) is the maximum number of pairwise disjoint sets in F. The clique number ω(F) is the maximum number of pairwise intersecting sets in F. The coloring number q(F) is the minimum number of classes in a partition of F into pairwise disjoint sets.08/2006: pages 10641065;  [Show abstract] [Hide abstract]
ABSTRACT: To a large extent the present work is far from being conclusive, instead, new directions of research in combinatorial extremal theory are started. Also questions concerning generalizations are immediately noticeable. The incentive came from problems in several fields such as Algebra, Geometry, Probability, Information and Complexity Theory. Like several basic combinatorial problems they may play a role in other fields. For scenarios of interplay we refer also to [9].08/2006: pages 955970;  [Show abstract] [Hide abstract]
ABSTRACT: We continue the investigation of Part I, keep its terminology, and also continue the numbering of sections, equations, theorems etc. Consequently we start here with Section 6. As mentioned in Section 4 we present now criteria for a triple (r,t,p) to be k–admissible. Then we consider the f–complexity (extended now to k–ary alphabets) Gk(F)\Gamma_k(\mathcal{F}) of a family F\mathcal{F}. It serves again as a performance parameter of key spaces in cryptography. We give a lower bound for the f–complexity for a family of the type constructed in Part I. In the last sections we explain what can be said about the theoretically best families F\mathcal{F} with respect to their f–complexity Gk(F)\Gamma_k(\mathcal{F}). We begin with straightforward extensions of the results of [4] for k=2 to general k by using the same Covering Lemma as in [1].08/2006: pages 308325;  [Show abstract] [Hide abstract]
ABSTRACT: Denote by Ω={1,...,n} an n–element set. For all A,B Î \binomWkA,B\in\binom{\Omega}k, the k–element subsets of Ω, define the relation ~ as follows: A~B iff A and B have a common shadow, i.e. there is a C Î \binomWk1C\in\binom{\Omega}{k1} with C ⊂A and C ⊂B. For fixed integer α, our goal is to find a family A{\mathcal A} of k–subsets with size α, having as many as possible ~–relations for all pairs of its elements. For k=2 this was achieved by Ahlswede and Katona [2] many years ago.08/2006: pages 9791005; 
Conference Paper: Another diametric theorem in Hamming spaces: optimal group anticodes
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ABSTRACT: In the last century together with Levon Khachatrian we established a diametric theorem in Hamming space H<sup>n</sup>=(X<sup>n</sup>,d H ). Now we contribute a diametric theorem for such spaces, if they are endowed with the group structure G<sup>n</sup>=<sup>n</sup>Σ 1 G, the direct sum of a group G on X={0,1,...,q1}, and as candidates are considered subgroups of G<sup>n</sup>. For all finite groups G, every permitted distance d, and all n≥d subgroups of G<sup>n</sup>with diameter d have maximal cardinality q<sup>d</sup>. Other extremal problems can also be studied in this setting.Information Theory Workshop, 2006. ITW '06 Punta del Este. IEEE; 04/2006  [Show abstract] [Hide abstract]
ABSTRACT: We investigate nonbinary error correcting codes with noiseless feedback, localized errors, or both. It turns out that the Hamming bound is a central concept. For block codes with feedback we present here a coding scheme based on an idea of erasions, which we call the {bf rubber method}. It gives an optimal rate for big error correcting fraction $tau$ ($>{1over q}$) and infinitely many points on the Hamming bound for small $tau$. We also consider variable length codes with all lengths bounded from above by $n$ and the end of a word carries the symbol $Box$ and is thus recognizable by the decoder. For both, the $Box$model with feedback and the $Box$model with localized errors, the Hamming bound is the exact capacity curve for $tau <1/2.$ Somewhat surprisingly, whereas with feedback the capacity curve coincides with the Hamming bound also for $1/2leq tau leq 1$, in this range for localized errors the capacity curve equals 0. Also we give constructions for the models with both, feedback and localized errors. @InProceedings{ahlswede_et_al:DSP:2006:784, author = {Rudolf Ahlswede and Christian Deppe and Vladimir Lebedev}, title = {Nonbinary error correcting codes with noiseless feedback, localized errors, or both}, booktitle = {Combinatorial and Algorithmic Foundations of Pattern and Association Discovery}, year = {2006}, editor = {Rudolf Ahlswede and Alberto Apostolico and Vladimir I. Levenshtein}, number = {06201}, series = {Dagstuhl Seminar Proceedings}, ISSN = {18624405}, publisher = {Internationales Begegnungs und Forschungszentrum f{"u}r Informatik (IBFI), Schloss Dagstuhl, Germany}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2006/784}, annote = {Keywords: Errorcorrecting codes, localized errors, feedback, variable length codes} }01/2006; 
Conference Paper: Transmission, Identification and Common Randomness Capacities for WireTape Channels with Secure Feedback from the Decoder.
General Theory of Information Transfer and Combinatorics; 01/2006 
Conference Paper: Appendix: On Common Information and Related Characteristics of Correlated Information Sources.
General Theory of Information Transfer and Combinatorics; 01/2006 
Conference Paper: Correlation Inequalities in Function Spaces.
General Theory of Information Transfer and Combinatorics; 01/2006 
Conference Paper: A Fast SuffixSorting Algorithm.
General Theory of Information Transfer and Combinatorics; 01/2006 
Conference Paper: On Logarithmically Asymptotically Optimal Testing of Hypotheses and Identification.
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ABSTRACT: We introduce a new aspect of the influence of the informationtheoretical methods on the statistical theory. The procedures of the probability distributions identification for K(≥1) random objects each having one from the known set of M(≥2) distributions are studied. Nsequences of discrete independent random variables represent results of N observations for each of K objects. On the base of such samples decisions must be made concerning probability distributions of the objects. For N ® ¥N \longrightarrow \infty the exponential decrease of the test’s error probabilities is considered. The reliability matrices of logarithmically asymptotically optimal procedures are investigated for some models and formulations of the identification problems. The optimal subsets of reliabilities which values may be given beforehand and conditions guaranteeing positiveness of all the reliabilities are investigated.General Theory of Information Transfer and Combinatorics; 01/2006  01/2006;

Article: Combinatorial and Algorithmic Foundations of Pattern and Association Discovery, 14.05.  19.05.2006
01/2006;  J. Comb. Theory, Ser. A. 01/2006; 113:16211628.
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ABSTRACT: We consider codes over the alphabet Q={0,1,..,q1}intended for the control of unidirectional errors of level l. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a component smaller than the transmitted one. Moreover, the absolute value of the difference between a transmitted component and its received version is at most l. We introduce and study qary codes capable of correcting all unidirectional errors of level l. Lower and upper bounds for the maximal size of those codes are presented. We also study codes for this aim that are defined by a single equation on the codeword coordinates(similar to the VarshamovTenengolts codes for correcting binary asymmetric errors). We finally consider the problem of detecting all unidirectional errors of level l.CoRR. 01/2006; abs/cs/0607132. 
Conference Paper: Appendix: On EdgeIsoperimetric Theorems for Uniform Hypergraphs.
General Theory of Information Transfer and Combinatorics; 01/2006 
Conference Paper: Information Theoretic Models in Language Evolution.
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ABSTRACT: We study a model for language evolution which was intro duced by Nowak and Krakauer ((12)). We analyze discrete distance spaces and prove a conjecture of Nowak for all metrics with a positive semidefi nite associated matrix. This natural class of metrics includes all metrics studied by different authors in this connection. In particular it includes all ultrametric spaces. Furthermore, the role of feedback is explored and multiuser scenarios are studied. In all models we give lower and upper bounds for the fitness.General Theory of Information Transfer and Combinatorics; 01/2006
Publication Stats
6k  Citations  
143.59  Total Impact Points  
Top Journals
Institutions

1976–2013

Bielefeld University
 • Faculty of Mathematics
 • Institute of Mathematical Economics
Bielefeld, North RhineWestphalia, Germany


2007

Alfréd Rényi Institute of Mathematics
Budapeŝto, Budapest, Hungary


2003

Eötvös Loránd University
 Department of Algebra and Number Theory
Budapest, Budapest fovaros, Hungary


2002

University of Rostock
Rostock, MecklenburgVorpommern, Germany


1968–1976

The Ohio State University
 Department of Mathematics
Columbus, Ohio, United States


1969

Cornell University
Ithaca, New York, United States
