Publications (232)155.28 Total impact

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. 
Conference Paper: Estimating with Randomized Encoding the Joint Empirical Distribution in a Correlated Source.
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ABSTRACT: In order to put the present model and our results into the right perspectives we describe first key steps in multiuser source coding theory. 
Conference Paper: Correlation Inequalities in Function Spaces
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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. 
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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. 
Conference Paper: Identification Entropy
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ABSTRACT: Shannon (1948) has shown that a source (U, P, U) with output U satisfying Prob (U = u) = Pu; can be encoded in a prefix code C = {cu : u ε U} ⊂ {0, 1}*such that for the entropy H(P) = Σ Pulog pu < Σ pucu < H(P) + 1,uεu where cu is the length of Cu. We use a prefix code C for another purpose, namely noiseless identification, that is every user who wants to know whether a u (u ε U) of his interest is the actual source output or not can consider the RV Cwith C = Cu = (Cu1.....Cucu) and check whether C = (C1, C2,... ) coincides with Cu in the first, second etc. letter and stop when the first different letter occurs or when C = Cu. Let Lc(P,u) be the expected number of checkings, if code C is used. Our discovery is an identification entropy, namely the function H I(P) =2(1Σ;P2u). uεu We prove that Lc(P, P) = Σ pu Lc(P, u) > HI(P) and thus also uεu that L(P) = min max Lc(P,u) > HI(P) C uεu and related upper bounds, which demonstrate the operational significance of identification entropy in noiseless source coding similar as Shannon entropy does in noiseless data compression. Also other averages such as L̄c (P) = 1u Σ Lc (P, u) are discussed in uεu particular for Huffman codes where classically equivalent Huffman codes may now be different. We also show that prefix codes, where the codewords correspond to the leaves in a regular binary tree, are universally good for this average.  [Show abstract] [Hide abstract]
ABSTRACT: From 15.05.06 to 20.05.06, the Dagstuhl Seminar 06201 ``Combinatorial and Algorithmic Foundations of Pattern and Association Discovery'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available. @InProceedings{ahlswede_et_al:DSP:2006:787, author = {Rudolf Ahlswede and Alberto Apostolico and Vladimir I. Levenshtein}, title = {06201 Abstracts Collection  Combinatorial and Algorithmic Foundations of Pattern and Association Discovery}, 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/2006/787}, annote = {Keywords: Data compression, pattern matching, pattern discovery, search, sorting, molecular biology, reconstruction, genome rearrangements} } 
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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 these data decisions must be made concerning probability distributions of the objects. For N→∞ 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 problem. The optimal subsets of reliabilities which values may be given beforehand and conditions guaranteeing positiveness of all the reliabilities are investigated.  [Show abstract] [Hide abstract]
ABSTRACT: In a series of papers Mauduit and Sarkozy (partly with further coauthors) studied finite pseudorandom binary sequences. In particular, one of the most important applications of pseudorandomness is cryptography. If, e.g., we want to use a binary sequence E"N@?{1,+1}^N (after transforming it into a bit sequence) as a key stream in the standard Vernam cipher [A. Menezes, P. van Oorschot, R. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997], then E"N must possess certain pseudorandom properties. Does E"N need to possess both small welldistribution measure and, for any fixed small k, small correlation measure of order k? In other words, if W(E"N) is large, resp. C"k(E"N) is large for some fixed small k, then can the enemy utilize this fact to break the code? The most natural line of attack is the exhaustive search: the attacker may try all the binary sequences E"N@?{1,+1}^N with large W(E"N), resp. large C"k(E"N), as a potential key stream. Clearly, this attack is really threatening only if the number of sequences E"N@?{1,+1}^N with(i)large W(E"N), resp. (ii)large C"k(E"N) is ''much less'' than the total number 2^N of sequences in {1,+1}^N, besides one needs a fast algorithm to generate the sequences of type (i), resp. (ii). The case (i) is easy, thus, for the sake of completeness, here we just present an estimate for the number of sequences E"N with large W(E"N). The case (ii), i.e., the case of large correlation is much more interesting: this case will be studied in Section 2. In Section 3 we will sharpen the results of Section 2 in the special case when the order of the correlation is 2. Finally, in Section 4 we will study a lemma, which plays a crucial role in the estimation of the correlation in some of the most important constructions of pseudorandom binary sequences.  [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 insentive 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 scenarious of interplay we refer also to [R. Ahlswede, Advances on extremal problems in number theory and combinatorics, European Congress of Mathematics, Barcelona 2000, Vol. I, 147–175, Carles Casacuberta, Rosa Maria Miró–Roig, Joan Verdera, Sebastiá Xambó–Descamps, edit., Progress in Mathematics, Vol. 201, Birkhäuser Verlag, Basel–Boston–Berlin, 2001].  [Show abstract] [Hide abstract]
ABSTRACT: We report on ideas, problems and results, which occupied us during the past two decades and which seem to extend the frontiers of information theory in several directions. The main contributions concern information transfer by channels. There are also new questions and some answers in new models of source coding. While many of our investigations are in an explorative state, there are also hard cores of mathematical theories. In particular we present a unified theory of information transfer, which naturally incorporates Shannon's theory of information transmission and the theory of identification in the presence of noise as extremal cases. It provides several novel coding theorems. On the source coding side we introduce the concept of identification entropy. Finally we are led beyond information theory to new concepts of solutions for probabilistic algorithms. 
Article: Secrecy Systems for Identification Via Channels with AdditiveLike Instantaneous Block Encipherers
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ABSTRACT: In this paper, we propose a model of secrecy systems for identification via channels with ALIB encipherers and find out the smallest asymptotic key rate of the ALIB encipherers needed for the requirement of security.  [Show abstract] [Hide abstract]
ABSTRACT: We consider problems of fault diagnosis in multiprocessor systems. Preparata, Metze and Chien (1967) introduced a graph theoretical model for systemlevel diagnosis, in which processors perform tests on one another via links in the system. Faultfree processors correctly identify the status of tested processors, while the faulty processors can give arbitrary test results. The goal is to identify correctly all faulty processors based on the test results. A system is said to be tdiagnosable if all faulty units can be identified provided the number of faulty units present does not exceed t. Here we explore the diagnosis problems for ncube systems. We give new upper and lower bounds for the diagnosability of ncube under sequential diagnosis strategy. We also describe a sequential diagnosis algorithm, which can be applied for arbitrary topology based systems. 
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ABSTRACT: We study a model for language evolution which was introduced by Nowak and Krakauer ([M.A. Nowak and D.C. Krakauer, The evolution of language, PNAS 96 (14) (1999) 80288033]). We analyze discrete distance spaces and prove a conjecture of Nowak for all metrics with a positive semidefinite 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.  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate the exact solution of the asymptotics of the multiple packing problem in a finite space with a sumtype metric. 
Article: Estimating with Randomized Encoding the Joint Empirical Distribution in a Correlated Source
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ABSTRACT: In order to put the present model and our results into the right perspectives we describe first key steps in multiuser source coding theory. 
Article: Identification Entropy

Article: Tshift synchronization codes
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ABSTRACT: In this paper we give a construction of T shift synchronization codes, i.e. block codes capable of correcting synchronization shifts of length at most T in either direction (left or right). We prove lower and upper bounds on the maximal cardinality of such codes. An infinite number of the constructed codes turn to be asymptotically optimal.
Publication Stats
9k  Citations  
155.28  Total Impact Points  
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Institutions

2013

The Institute for Information Transmission Problems
Moskva, Moscow, Russia


19762011

Bielefeld University
 Faculty of Mathematics
Bielefeld, North RhineWestphalia, Germany


19681976

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


1969

Cornell University
Ithaca, New York, United States
