PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 11, Number 4, October–December, 1975
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Shannon's Theorems for a Complete Class of Discrete Memoryless Channels Whose State is Known at the Output
S. Z. Stambler
pp. 263–270

Abstract—Coding theorems and their weak converse are proved for a complete class of discrete memoryless channels for ordinary and randomized codes with mean error, and also for randomized codes with maximum error under the assumption that the channel state is known at the output.

 

Upper Bounds on the Error Probability for Discrete Memoryless Channels with Feedback
A. G. Dyachkov
pp. 271–283

Abstract—The upper bound on the error probability from [K. Sh. Zigangirov, Probl. Inf. Trans., 1970, vol. 6, no. 2, pp. 159–163; A. G. Dyachkov, Probl. Inf. Trans., 1972, vol. 8, no. 4] for block transmission of discrete messages over a symmetrical discrete memoryless channel with a binary input and with complete feedback are generalized to the case of a $K$-ary symmetrical memoryless channel and an arbitrary discrete memoryless channel with a binary input.

 

On Linear Cyclic Codes with $\lambda$-Connected and Certain Other Checks
V. S. Kugurakov
pp. 283–291

Abstract—The article considers linear cyclic codes that correct additive errors by $\lambda$-connected checks and certain other more general checks. A necessary condition which these codes must satisfy is obtained. In particular, this condition yields certain lower bounds for the minimum number of redundant symbols in codes that correct one error by $\lambda$-connected checks. The possibility of using certain specific codes (in particular, BCH codes) for correcting errors by $\lambda$-connected checks is also considered.

 

Conditional Estimation of Linear Functionals
B. Ya. Levit
pp. 291–302

Abstract—The article considers the problem of statistical estimation of linear functionals, this incorporating the isolation of a constant signal in additive noise for the case in which noise parameters such as the variance, asymmetry, etc., are known. $U$-statistics are used to construct a class of estimates $T_n$ with adaptation; it is established that they are asymptotically optimal (locally minimax) relative to a broad class of loss functions under certain general sufficient conditions. As is shown, the latter are close to being necessary in a certain sense.

 

On Maximum-Likelihood Estimate for Signal Parameter in White Gaussian Noise
M. V. Burnashev
pp. 302–313

Abstract—Nonasymptotic upper bounds are obtained for the standard deviation of the maximum-likelihood estimate for a one-parameter signal for the case in which a continuous signal is transmitted over a channel with white noise. The bounds go over into exact equations for the asymptotically effective estimates. Using the example of frequency modulation, the author studies the reliability function of a channel with white noise for the case of a continuous parametric set.

 

Use of the Method of Lyapunov Functionals to Investigate the Stability of Stochastic Systems with Delay
L. E. Shaikhet
pp. 313–318

Abstract—The article investigates a system with delayed feedback whose parameters are subject to random perturbations, these being an arbitrary process with independent increments. Sufficient conditions are obtained for the system in question to be asymptotically $p$-stable, and specific examples are examined.

 

Structural Simplification of the Logic Unit of a Finite Automaton Whose States Are Assigned by the Columns of the Transition Table
V. V. Sapozhnikov and Vl. V. Sapozhnikov
pp. 319–326

Abstract—The authors propose state assignment algorithms for an asynchronous finite automaton (AFA) that represent an extension of the Liu-Sagalovich method [C. N. Liu, J. Assoc. Comp. Mach., 1963, vol. 10, no. 2, pp. 209–216; Yu. L. Sagalovich, Probl. Inf. Trans., 1967, vol. 3, no. 2, pp. 56–64], the purpose being to simplify the structure of the logic unit. A necessary and sufficient existence condition for complete parallel decomposition of AFA is obtained.

 

Gibbsian Distribution of Random Fields Whose Conditional Probabilities May Vanish
M. B. Averintsev
pp. 326–334

Abstract—The article considers Markov random fields with an arbitrary set of values on a finite or infinite graph. It is shown that such random fields admit a Gibbsian description when their conditional probabilities can vanish with certain constraints. The concept of a random field with vacuum state is introduced to describe these constraints. Moreover, for potentials of fairly general form the article investigates a class of transformations that do not alter the Gibbsian conditional distribution.

 

The Problem of Self-Assembly of Segments
A. M. Leontovich
pp. 335–341

Abstract—This paper deals with self-assembly of segments (this problem having arisen in attempts to model the self-assembly of viruses). In this problem, a segment $[1,n]$ is formed from individual particles $1,\ldots,n$ (the particles are assumed to be different). This occurs as follows: adjacent particles collide and form two-particle units; adjacent units collide and form larger units, until the segment $[1,n]$ is generated. The appropriate system of differential equations is written; it turns out that its solutions have an extremely simple form. The paper determines how the number of segments $[1,n]$ increases and considers some generalizations of the problem.

 

On One Numerical Experiment Involving Calculation of the Spectra of Random Processes
V. G. Alekseev
pp. 342–344

Abstract—For two models of a stationary random process $\xi_k$, $k=0,\pm 1,\ldots$, with a spectral density $f(\lambda)$ that is known in advance the author constructs, using a sample of fixed size, estimates for $f(\lambda)$ that are based on the use of nonnegative and sign-changing weighting functions. Comparison of the estimates thus constructed indicates that, for a specified sample size, estimates based on the use of sign-changing weighting functions result in smaller estimation error in both cases.

 

Description of Stationary Probabilities of Some Markov Interaction Systems
A. V. Vasil'ev
pp. 344–346

Abstract—Each point of an infinite $n$-dimensional lattice can be in one of $N$ states. The state of a point at instant $t$ depends randomly on the status of points in some neighborhood of it at a preceding point of time. Conditions are given under which the Markov chain describing the behavior of the system has an invariant Bernoulli measure.

 

Dispersion of the Estimate for the State Probability in a Queuing System with an Infinite Number of Lines
D. G. Polyak
pp. 347–351

Abstract—A queuing system with an infinite number of lines is considered for the case in which there is a nonstationary Poisson incoming flow and an arbitrarily distributed servicing time. A formula is obtained for the correlation function of the random process that indicates the event “at instant $t$ there were $n$ busy lines in the system.” This result is used to compute the dispersion of the estimate for the stationary state probabilities. Certain approximate formulas are obtained for the dispersion under small traffic.

 

INDEX
pp. 353–358