A translation of Problemy Peredachi Informatsii

Volume 12, Number 3, July–September, 1976
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Class of Correcting Codes for Errors With a Lattice Configuration
V. R. Sidorenko
pp. 165–171

Abstract—The article describes a quasioptimal class of codes for correcting errors of lattice configuration over parallel channels; codes consisting of rectangular matrices, in a special rank metric, are considered. Asymptotically precise limits for code rates are obtained. For square matrices of order $n$, codes with codes distance $2,\,3,\,4,\,n$ are constructed, as well as codes which will detect bursts of lattice errors.


Synthesis of Single-Error-Correcting $AN$-Codes
V. M. Gritsenko
pp. 172–176

Abstract—The theory of power residues is employed for synthesizing arithmetic $AN$-codes to the base $r>2$ that can correct an arbitrary error in one position. A procedure is given for synthesizing simple and composite generators $A$ with specified properties.


Statistical Description of an Adaptive Quantizer
V. S. Molodtsov, N. I. Pilipchuk, and V. P. Yakovlev
pp. 177–183

Abstract—Integral equations are derived for the joint distribution of signal values and quantization range which is the controlled parameter of the quantizer. Solutions are obtained for a Gaussian signal of Markov type for both large and small correlation coefficients of adjacent readings, and also for an arbitrarily distributed signal with limited variations.


Two-Sample Problem of Hypothesis Testing With Large Samples
A. I. Pinskii
pp. 183–188

Abstract—Regularity conditions are given such that, for a two-sample problem of hypothesis testing, it is possible to set up rules that are asymptotically optimal in the class of differentially asymptotically similar rules.


On Approximation of Binary Random Vectors in Discriminant-Analysis Problems
L. G. Malinovskii
pp. 188–192

Abstract—With reference to the construction of a discriminant function, this paper makes a comparison of the approximation quality of the probability distributions of binary random vectors for which the number of independent parameters is $2^l-1$. A comparison is made of the Bahadur function and the probability density function of the normal distribution law, with number of parameters equal to $l(l+1)/2$. It is shown that these approximations are equally effective for setting up a classification rule; this makes it easier to investigate binary random vectors and random vectors containing binary and continuous features.


On Asymptotic Behavior of Certain Estimates of Shift and Scale Parameters
L. B. Klebanov and I. A. Melamed
pp. 193–204

Abstract—Assume that we have $n$ observations of the form $x_i=\theta+\sigma\varepsilon_i$, where the errors $\varepsilon_i$ are independent and identically distributed with distribution function $F(x)$. “Polynomial” Pitman estimates are derived for the parameters $\theta$ and $\varepsilon$, and their asymptotic behavior is investigated. The results are applied to studying the Pitman estimates of $\theta$ and $\varepsilon$.


Homodyne Reception of Quantized Electromagnetic Signals
A. S. Drikker
pp. 205–214

Abstract—The author investigates indirect measurement of coherent electromagnetic signals, a process termed homodyne reception by analogy with the classical process. It is shown that homodyne reception makes it possible to achieve asymptotically, for large filling numbers, the capacity of an ideal channel. Unlike the classical case, maximum capacity is achieved at a homodyne power that is roughly equal to the signal power.


Asymmetry Principle of Measurement Logic
A. P. Stakhov
pp. 214–220

Abstract—A property of measurement asymmetry is found which leads to the elaboration of a nontrivial theorem of optimum measurement algorithms that is of applied interest for the theory of enumerative coding and the arithmetic of digital machines (“Fibonacci reckoning systems”).


Unstable Multicomponent Systems
A. L. Toom
pp. 220–225

Abstract—Systems are considered that consist of an infinite number of interconnected finite probabilistic automata operating in discrete time. Systems are called ergodic if they “forget” their initial state in the limit with respect to time. A sufficient condition for ergodicity is given. Two examples are cited of families of systems that are ergodic for positive parameter values and possess the opposite property of zero values.


Slow-Down in Universal Simulation
A. V. Koganov
pp. 225–231

Abstract—The article considers computing media (iterative structures) on lattices, and derives estimates for the slow-down that occurs in simulating a large class of media by one such medium. It is shown that the requirement of a guaranteed slow-down on the entire class of media with fixed input and output alphabets is not compatible with the requirement of element-by-element recoding of the initial state of the simulated medium to the initial state of the model (regular simulation). Examples of universal models with minimum possible guaranteed slow-down and examples of regular universal models are given.


On Minimal Matroid Coverings
A. K. Kel'mans, M. V. Lomonosov, and V. P. Polesskii
pp. 231–241

Abstract—Matroid $M$ on finite set $E$ is considered; packings and coverings of $E$ and of its subsets by sets from $M$ are examined.


Minimax Bound on the Risk of Nonparametric Density Estimates
A. M. Samarov
pp. 242–244

Abstract—The author obtains a minimax lower bound, exact in order of magnitude as $n\to\infty$, for moments $\|\gamma_n-f\|$, where $f(\cdot)$ is an unknown density from some class of sufficiently smooth functions, $\gamma_n(\cdot)$ is the density estimate, and $\|\cdot\|$ is the norm in $L_2(-\infty,\infty)$. The results are allied to those of Chentsov and Farrell [N. N. Chentsov, Statistical Decision Rules and Optimal Conclusions (in Russian), Nauka, Moscow, 1972; R. Farrell, Ann. Math. Statist., 1972, vol. 43, no. 1, pp. 170–180].