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The Sphere Packing Bound for Memoryless Channels Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-10-19 B. Nakiboğlu
Sphere packing bounds (SPBs)—with prefactors that are polynomial in the block length—are derived for codes on two families of memoryless channels using Augustin’s method: (possibly nonstationary) memoryless channels with (possibly multiple) additive cost constraints and stationary memoryless channels with convex constraints on the composition (i.e., empirical distribution, type) of the input codewords
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Symmetric Block Designs and Optimal Equidistant Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-10-19 L. A. Bassalygo, V. A. Zinoviev, V. S. Lebedev
We prove that any symmetric block design (v, k, λ) generates optimal ternary and quaternary constant-weight equidistant codes, whose parameters n, N, w, d, q are uniquely determined by the parameters of the block design. For one rather special case, we construct symbolwise uniform equidistant codes of the minimum length.
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On Geometric Goppa Codes from Elementary Abelian p -Extensions of $${{\mathbb{F}}}_{{p}^{s}}(x)$$ F p s ( x ) Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-10-19 N. Patanker, S. K. Singh
Let p be a prime number and s > 0 an integer. In this short note, we investigate one-point geometric Goppa codes associated with an elementary abelian p-extension of \({{\mathbb{F}}}_{{p}^{s}}(x)\). We determine their dimension and exact minimum distance in a few cases. These codes are a special case of weak Castle codes. We also list exact values of the second generalized Hamming weight of these codes
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Research on Fractional Critical Covered Graphs Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-10-19 S. Wang, W. Zhang
A graph G is called a fractional (g, f)-covered graph if for any e ∈ E(G), G admits a fractional (g, f)-factor covering e. A graph G is called a fractional (g, f, n)-critical covered graph if for any S ⊆ V(G) with ∣S∣ = n, G − S is a fractional (g, f)-covered graph. A fractional (g, f, n)-critical covered graph is said to be a fractional (a, b, n)-critical covered graph if g(x) = a and f(x) = b for
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Gaussian Two-Armed Bandit: Limiting Description Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-10-19 A. V. Kolnogorov
For a Gaussian two-armed bandit, which arises when batch data processing is analyzed, the minimax risk limiting behavior is investigated as the control horizon N grows infinitely. The minimax risk is searched for as the Bayesian one computed with respect to the worst-case prior distribution. We show that the highest requirements are imposed on the control in the domain of "close” distributions where
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On Adaptive Estimation of Linear Functionals from Observations against White Noise Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-07-14 G. K. Golubev
We consider the problem of adaptive estimation of a linear functional of an unknown multivariate vector from its observations against white Gaussian noise. As a family of estimators for the functional, we use those generated by projection estimators of the unknown vector, and the main problem is to select the best estimator in this family. The goal of the paper is to explain and mathematically justify
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Comparison of Contraction Coefficients for f -Divergences Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-07-14 A. Makur; L. Zheng
Contraction coefficients are distribution dependent constants that are used to sharpen standard data processing inequalities for f-divergences (or relative f-entropies) and produce so-called “strong” data processing inequalities. For any bivariate joint distribution, i.e., any probability vector and stochastic matrix pair, it is known that contraction coefficients for f-divergences are upper bounded
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New Upper Bounds in the Hypothesis Testing Problem with Information Constraints Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-07-14 M. V. Burnashev
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make the best statistical inference? In particular, what is the minimum information sufficient to obtain the same results as if we directly observed all the data? We derive
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Detecting Cycles of Length 8 in the Tanner Graph of a QC-LDPC Code Based on Protograph Analysis Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-07-14 A. V. Kharin; K. N. Zavertkin; A. A. Ovinnikov
For cycles of length 8 in a Tanner graph, we propose an identification procedure based on the analysis of paths in a protograph. We formulate and prove a number of theorems that introduce identification rules for cycles and restrict the number of subgraphs to be analyzed. To distinguish between them, we propose a number of parameters that uniquely determine the group of analyzed paths in the protograph
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Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3, 6) Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 Y. Guan; M. J. Shi; D. S. Krotov
A Steiner triple system (STS) contains a transversal subdesign TD(3, w) if its point set has three pairwise disjoint subsets A, B, C of size w and w2 blocks of the STS intersect with each of A, B, C (those w2 blocks form a TD(3,w)). We prove several structural properties of Steiner triple systems of order 3w + 3 that contain one or more transversal subdesigns TD(3, w). Using exhaustive search, we find
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Piecewise Polynomial Sequences over the Galois Ring Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 A. R. Vasin
We describe the construction of a piecewise polynomial generator over a Galois ring and prove a transitivity criterion for it. We give an estimate for the discrepancy of the output sequences of such a generator. We show that the obtained estimate is asymptotically equivalent to known estimates for special cases of a piecewise polynomial generator, and in some cases it is asymptotically sharper.
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On q -ary Codes with Two Distances d and d + 1 Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 P. Boyvalenkov; K. Delchev; D. V. Zinoviev; V. A. Zinoviev
We consider q-ary block codes with exactly two distances: d and d + 1. Several constructions of such codes are given. In the linear case, we show that all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes are derived. Tables of lower and upper bounds for small q and n are presented.
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On Distance Distributions of Orthogonal Arrays Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 N. L. Manev
Orthogonal arrays play an important role in statistics and experimental design. Like other combinatorial constructions, the most important and studied problems are questions about their existence and classification. An essential step to solving such problems is determination of Hamming distance distributions of an orthogonal array with given parameters. In this paper we propose an algorithm for computing
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On the Maximum Values of f -Divergence and Rényi Divergence under a Given Variational Distance Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 V. V. Prelov
We consider the problem of finding maximum values of f-divergences Df(P ∥ Q) of discrete probability distributions P and Q with values on a finite set under the condition that the variation distance V(P, Q) between them and one of the distributions P or Q are given. We obtain exact expressions for such maxima of f-divergences, which in a number of cases allow to obtain both explicit formulas and upper
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Bivariate Distributions of Maximum Remaining Service Times in Fork-Join Infinite-Server Queues Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 A. V. Gorbunova; A. V. Lebedev
We study the maximum remaining service time in M(2)∣G2∣∞ fork -join queueing systems where an incoming task forks on arrival for service into two subtasks, each of them being served in one of two infinite-sever subsystems. The following cases for the arrival rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a stochastic process. As examples of service time distributions
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Extended Large Deviation Principle for Trajectories of Processes with Independent and Stationary Increments on the Half-line Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 F. C. Klebaner; A. V. Logachov; A. A. Mogulskii
We establish an extended large deviation principle for processes with independent and stationary increments on the half-line under the Cramer moment condition in the space of functions of bounded variation without discontinuities of the second kind equipped with the Borovkov metric.
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Entropy and Compression: A Simple Proof of an Inequality of Khinchin-Ornstein-Shields Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-04-16 R. Aragona; F. Marzi; F. Mignosi; M. Spezialetti
This paper concerns the folklore statement that “entropy is a lower bound for compression.” More precisely, we derive from the entropy theorem a simple proof of a pointwise inequality first stated by Ornstein and Shields and which is the almost-sure version of an average inequality first stated by Khinchin in 1953. We further give an elementary proof of the original Khinchin inequality, which can be
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Search for a Moving Element with the Minimum Total Cardinality of Tests Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-01-24 A. V. Lebedev; V. S. Lebedev
We consider the moving element search problem with the minimum total cardinality of tests. As a search space, we consider the set of integer points of a segment of length n. We prove that the total test cardinality of an asymptotically optimal adaptive strategy is \(n + 2\sqrt n \).
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On the Cardinality Spectrum and the Number of Latin Bitrades of Order 3 Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-01-24 D. S. Krotov; V. N. Potapov
By a (Latin) unitrade of order k, we call a subset of vertices of the Hamming graph H(n, k) that intersects any maximal clique at either 0 or 2 vertices. A bitrade is a bipartite unitrade, i.e., a unitrade that can be split into two independent subsets. We study the cardinality spectrum of bitrades in the Hamming graph H(n, k) with k = 3 (ternary hypercube) and the growth of the number of such bitrades
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On Lower Bounds on the Spectrum of a Binary Code Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-01-24 M. V. Burnashev
We refine a lower bound on the spectrum of a binary code. We give a simple derivation of the known bound on the undetected error probability of a binary code.
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The Augustin Capacity and Center Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-01-24 B. Nakiboğlu
For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and convex constraint set with
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On a Frankl-Wilson Theorem Probl. Inf. Transm. (IF 0.593) Pub Date : 2020-01-24 A. A. Sagdeev
We derive an analog of the Frankl-Wilson theorem on independence numbers of some distance graphs. The obtained results are applied to the problem of the chromatic number of a space ℝn with a forbidden equilateral triangle and to the problem of chromatic numbers of distance graphs with large girth.
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Divisible Arcs, Divisible Codes, and the Extension Problem for Arcs and Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 I. Landjev; A. Rousseva
In an earlier paper we developed a unified approach to the extendability problem for arcs in PG(k - 1, q) and, equivalently, for linear codes over finite fields. We defined a special class of arcs called (t mod q)-arcs and proved that the extendabilty of a given arc depends on the structure of a special dual arc, which turns out to be a (t mod q)-arc. In this paper, we investigate the general structure
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Upper Bounds for the Holevo Information Quantity and Their Use Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 M. E. Shirokov
We present a family of easily computable upper bounds for the Holevo (information) quantity of an ensemble of quantum states depending on a reference state (as a free parameter). These upper bounds are obtained by combining probabilistic and metric characteristics of the ensemble. We show that an appropriate choice of the reference state gives tight upper bounds for the Holevo quantity which in many
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Optimal Upper Bounds for the Divergence of Finite-Dimensional Distributions under a Given Variational Distance Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 V. V. Prelov
We consider the problem of finding the maximum values of divergences D(P‖Q) and D(Q‖P) for probability distributions P and Q ranging in the finite set \(\mathcal{N}=\left\{1,\;2,...,n\right\}\) provided that both the variation distance V (P,Q) between them and either the probability distribution Q or (in the case of D(P‖Q)) only the value of the minimal component qmin of the probability distribution
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Note on “Smaller Explicit Superconcentrators” by N. Alon and M. Capalbo Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 L. A. Bassalygo
We slightly improve the superconcentrator construction by Alon and Capalbo.
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On Alphabetic Coding for Superwords Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 S. S. Marchenkov
We consider alphabetic coding of superwords. We establish an unambiguity coding criterion for the cases of finite and infinite codes. We prove that in the case of an infinite code the ambiguity detection problem is m-complete in the ∃1∀0 class of Kleene’s analytical hierarchy.
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Generalization of IPP Codes and IPP Set Systems Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 E. E. Egorova
A quarter century ago Chor, Fiat, and Naor proposed mathematical models for revealing a source of illegal redistribution of digital content (tracing traitors) in the broadcast encryption framework, including the following two combinatorial models: nonbinary IPP codes, based on an (n, n)-threshold secret sharing scheme, and IPP set systems, based on the general (w, n)-threshold secret sharing scheme
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Traceability Codes and Their Generalizations Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 G. A. Kabatiansky
Codes with the identifiable “parent” property appeared as one of solutions for the broadcast encryption problem. We propose a new, more general model of such codes, give an overview of known results, and formulate some unsolved problems.
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Some q -ary Cyclic Codes from Explicit Monomials over $$\mathbb{F}_{q}m$$ F q m Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 L. Li; S. Zhu; L. Liu; X. Kai
Cyclic codes as a subclass of linear codes have practical applications in communication systems, consumer electronics, and data storage systems due to their efficient encoding and decoding algorithms. The objective of this paper is to construct some cyclic codes by the sequence approach. More precisely, we determine the dimension and the generator polynomials of three classes of q-ary cyclic codes
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Erratum to: On Completely Regular Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-10-16 J. Borges, J. Rifà, V. A. Zinoviev
Abstract—We correct mistakes in the formulations of Theorem 19 and Proposition 17 of the original article, published in vol. 55, no. 1, 1–45.
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Reliable Communication under the Influence of a State-Constrained Jammer: An Information-Theoretic Perspective on Receive Diversity Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-07-12 C. Arendt; J. Nötzel; H. Boche
The impact of diversity on reliable communication over arbitrarily varying channels (AVC) is investigated as follows. First, the concept of an identical state-constrained jammer is motivated. Second, it is proved that symmetrizability of binary symmetric AVCs (AVBSC) caused by identical state-constrained jamming is circumvented when communication takes place over at least three orthogonal channels
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Non-split Toric Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-07-12 D. I. Koshelev
We introduce a new wide class of error-correcting codes, called non-split toric codes. These codes are a natural generalization of toric codes where non-split algebraic tori are taken instead of usual (i.e., split) ones. The main advantage of the new codes is their cyclicity; hence, they can possibly be decoded quite fast. Many classical codes, such as (doubly-extended) Reed-Solomon and (projective)
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Geometry of Translations on a Boolean Cube Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-07-12 M. N. Vyalyi; V. K. Leontiev
The operation of Minkowski addition of geometric figures has a discrete analog, addition of subsets of a Boolean cube viewed as a vector space over the two-element field. Subsets of the Boolean cube (or multivariable Boolean functions) form a monoid with respect to this operation. This monoid is of interest in classical discrete analysis as well as in a number of problems related to information theory
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The Geometry of Big Queues Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-07-12 A. A. Puhalskii
We use Hamilton equations to identify most likely scenarios of long queues being formed in ergodic Jackson networks. Since the associated Hamiltonians are discontinuous and piecewise Lipschitz, one has to invoke methods of nonsmooth analysis. Time reversal of the Hamilton equations yields fluid equations for the dual network. Accordingly, the optimal trajectories are time reversals of the fluid trajectories
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On Application of the Modulus Metric to Solving the Minimum Euclidean Distance Decoding Problem Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-07-12 V. A. Davydov
We prove equivalence of using the modulus metric and Euclidean metric in solving the soft decoding problem for a memoryless discrete channel with binary input and Q-ary output. For such a channel, we give an example of a construction of binary codes correcting t binary errors in the Hamming metric. The constructed codes correct errors at the output of a demodulator with Q quantization errors as (t
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Strong Converse Theorems for Multimessage Networks with Tight Cut-Set Bound Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-04-24 S. L. Fong; V. Y. F. Tan
This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network whose cut-set bound is tight, i.e., achievable. Our result implies that for any fixed rate vector that resides outside the capacity region, the average error probability of any sequence of length-n
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Probability of Inversion of a Large Spin in the Form of an Asymptotic Expansion in a Series of Bessel Functions Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-04-24 E. A. Karatsuba; P. Morettib
An exact expression for the probability of inversion of a large spin is established in the form of an asymptotic expansion in the series of Bessel functions with orders belonging to an arithmetic progression. Based on the new asymptotic expansion, a formula for the inversion time of the spin is derived.
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On Extreme Values of the Rényi Entropy under Coupling of Probability Distributions Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-04-24 V. V. Prelov
We consider the problem of determining extreme values of the Rényi entropy for a discrete random variable provided that the value of the α-coupling for this random variable and another one with a given probability distribution is fixed.
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On Completely Regular Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-04-24 J. Borges; J. Rifà; V. A. Zinoviev
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures, and construction methods are considered. The existence problem is also discussed, and known results for some particular cases are established. In addition, we present several new results on completely regular codes with covering radius ρ = 2 and on extended completely regular codes.
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Refinements of Levenshtein Bounds in q -ary Hamming Spaces Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-01-28 P. Boyvalenkov; D. Danev; M. Stoyanova
We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. We investigate the first relevant cases and present new bounds. In particular, we derive generalizations and q-ary analogs of the MacEliece bound. Furthermore, we provide evidence that our approach
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Exponentially Ramsey Sets Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-01-28 A. A. Sagdeev
We study chromatic numbers of spaces \(\mathbb{R}_p^n=(\mathbb{R}^n, \ell_p)\) with forbidden monochromatic sets. For some sets, we for the first time obtain explicit exponentially growing lower bounds for the corresponding chromatic numbers; for some others, we substantially improve previously known bounds.
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On the Complexity of Fibonacci Coding Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-01-28 I. S. Sergeev
We show that converting an n-digit number from a binary to Fibonacci representation and backward can be realized by Boolean circuits of complexity O(M(n) log n), where M(n) is the complexity of integer multiplication. For a more general case of r-Fibonacci representations, the obtained complexity estimates are of the form \({2^O}{(\sqrt {\log n} )_n}\).
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Noise Level Estimation in High-Dimensional Linear Models Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-01-28 G. K. Golubev; E. A. Krymova
We consider the problem of estimating the noise level σ2 in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ℝn is a standard discrete white Gaussian noise and β ∈ ℝp an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood
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Polar Codes with Higher-Order Memory Probl. Inf. Transm. (IF 0.593) Pub Date : 2019-01-28 H. Afşer; H. Deliç
We introduce a construction of a set of code sequences {Cn(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {Cn(m)} is a generalization of polar codes presented by Arıkan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n − 1) and N(n − m), and {Cn(m)} coincides with the original polar codes when m = 1. We show that {Cn(m)}
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On m -Near-Resolvable Block Designs and q -ary Constant-Weight Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 L. A. Bassalygo; V. A. Zinoviev; V. S. Lebedev
We introduce m-near-resolvable block designs. We establish a correspondence between such block designs and a subclass of (optimal equidistant) q-ary constant-weight codes meeting the Johnson bound. We present constructions of m-near-resolvable block designs, in particular based on Steiner systems and super-simple t-designs.
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Propagation of Chaos and Poisson Hypothesis Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 A. A. Vladimirov; S. A. Pirogov; A. N. Rybko; S. B. Shlosman
We establish the strong Poisson hypothesis for symmetric closed networks. In particular, we prove asymptotic independence of nodes as the size of the system tends to infinity.
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New Good’s Type Kronecker Power Expansions Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 M. S. Bespalov
We propose a new version of the proof of Good’s theorem stating that the Kronecker power of an arbitrary square matrix can be represented as a matrix power of a sparse matrix Z. We propose new variants of sparse matrices Z. We observe that for another version of the tensor power of a matrix, the b-power, there exists an analog of another Good’s expansion but no analog of this theorem.
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A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 N. D. Vvedenskaya; A. V. Logachov; Yu. M. Suhov; A. A. Yambartsev
The paper considers a continuous-time birth–death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotic for the probability of trajectories of a re-scaled process contained within a neighborhood of a given continuous nonnegative function.
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On the Complexity of Polynomial Recurrence Sequences Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 S. S. Marchenkov
We consider recurrence sequences over the set of integers with generating functions being arbitrary superpositions of polynomial functions and the sg function, called polynomial recurrence sequences. We define polynomial-register (PR) machines, close to random-access machines. We prove that computations on PR machines can be modeled by polynomial recurrence sequences. On the other hand, computation
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Infinite Spectra of First-Order Properties for Random Hypergraphs Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 S. N. Popova
We study the asymptotic behavior of probabilities of first-order properties for random uniform hypergraphs. In 1990, J. Spencer introduced the notion of a spectrum for graph properties and proved the existence of a first-order property with an infinite spectrum. In this paper we give a definition of a spectrum for properties of uniform hypergraphs and establish an almost tight bound for the minimum
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Analytical Properties of Shannon’s Capacity of Arbitrarily Varying Channels under List Decoding: Super-Additivity and Discontinuity Behavior Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 H. Boche; R. F. Schaefer; H. V. Poor
The common wisdom is that the capacity of parallel channels is usually additive. This was also conjectured by Shannon for the zero-error capacity function, which was later disproved by constructing explicit counterexamples demonstrating the zero-error capacity to be super-additive. Despite these explicit examples for the zero-error capacity, there is surprisingly little known for nontrivial channels
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On Some Optimization Problems for the Rényi Divergence Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-10-13 V. V. Prelov
We consider the problem of determining the maximum and minimum of the Rényi divergence Dλ(P||Q) and Dλ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.
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Improved Frankl–Rödl Theorem and Some of Its Geometric Consequences Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 A. A. Sagdeev
We substantially improve a presently known explicit exponentially growing lower bound on the chromatic number of a Euclidean space with forbidden equilateral triangle. Furthermore, we improve an exponentially growing lower bound on the chromatic number of distance graphs with large girth. These refinements are obtained by improving known upper bounds on the product of cardinalities of two families
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On the Smallest Size of an Almost Complete Subset of a Conic in PG(2, q ) and Extendability of Reed–Solomon Codes Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 D. Bartoli; A. A. Davydov; S. Marcugini; F. Pambianco
Abstract—In the projective plane PG(2, q), a subset S of a conic C is said to be almost complete if it can be extended to a larger arc in PG(2, q) only by the points of C \ S and by the nucleus of C when q is even. We obtain new upper bounds on the smallest size t(q) of an almost complete subset of a conic, in particular,$$t(q) < \sqrt {q(3lnq + lnlnq + ln3)} + \sqrt {\frac{q}{{3\ln q}}} + 4 \sim \sqrt
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Clique Numbers of Random Subgraphs of Some Distance Graphs Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 A. S. Gusev
We consider a class of graphs G(n, r, s) = (V (n, r),E(n, r, s)) defined as follows:$$V(n,r) = \{ x = ({x_{1,}},{x_2}...{x_n}):{x_i} \in \{ 0,1\} ,{x_{1,}} + {x_2} + ... + {x_n} = r\} ,E(n,r,s) = \{ \{ x,y\} :(x,y) = s\} $$where (x, y) is the Euclidean scalar product. We study random subgraphs G(G(n, r, s), p) with edges independently chosen from the set E(n, r, s) with probability p each. We find
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Information-Theoretic Approach to Estimating the Capacity of Distributed Memory Systems Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 B. Ya. Ryabko
Systems with cash memory (or more generally, with distributed memory) are very widely used in information technologies. Such are content delivery networks (CDN) of various types, which deliver digital movies, books, and similar content; peer-to-peer (P2P) networks, where millions of members exchange various information; and many other systems and devices of this kind. We introduce the notions of capacity
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Compositional Restricted Multiple Access Channel Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 E. E. Egorova; V. S. Potapova
We introduce the notion of a q-ary s-compositional code and prove that the rate, R, of the best such code satisfies for large s the asymptotic inequalities$$(q - 1)\frac{{{{\log }_q}s}}{{4s}} \lesssim 2(q - 1)\frac{{{{\log }_q}s}}{{4s}}$$.
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Maximum Remaining Service Time in Infinite-Server Queues Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 A. V. Lebedev
We study the maximum remaining service time in infinite-server queues of type M|G|∞ (at a given time and in a stationary regime). The following cases for the arrival flow rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a random process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In
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On Discrimination between Classes of Distribution Tails Probl. Inf. Transm. (IF 0.593) Pub Date : 2018-07-14 I. V. Rodionov
We propose a test to distinguish between two classes of distribution tails using only higher order statistics of a sample and prove its consistency. We do not assume the corresponding distribution functions to belong to any maximum domain of attraction.
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