PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 14, Number 3, July–September, 1978
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CONTENTS

Information in Words (Initial Approximation: Memoryless Information)
V. D. Goppa
pp. 159–170

Abstract—An algebraic approach to the determination of word information is developed. Nonprobabilistic models of source and channel are introduced, and analogs of Shannon coding theorems are proved for them.

On Error-Burst-Correcting Convolutional Codes
G. L. Tauglikh
pp. 170–173

Abstract—New classes of binary convolutional codes, analogs of error-burst-correcting cyclic codes, are obtained. Many of them attain the Peterson–Weldon bound.

Some New Maximal Codes over $GF(4)$
I. I. Dumer and V. A. Zinov'ev
pp. 174–181

Abstract—For lengths $n\ge 5$ the authors construct linear codes over $GF(4)$ that correct two errors and have maximum possible numbers (from the standpoint of the Hamming bound) of information symbol $k$. The first nontrivial example of these new codes is a $4$-ary $(n=11,\, k=6,\, d=5)$ code. Its extension is a $(12,6,6)$ code and is interesting in that changing over to the binary form of elements of $GF(4)$ yields a $(24,12,8)$ Golay code. Thus this unique code can be represented in cascade form.

Weight Spectra of Some Classes of Cyclic Codes over $GF(q)$
V. I. Tairyan
pp. 181–185

Abstract—Weight spectra and code distances are determined for three classes of cyclic codes over $GF(q)$. The corresponding formulas depend only on the degrees and periods of the irreducible polynomials over $GF(q)$ that appear in the expansion of the check polynomial of the code.

Optimal Construction of Radio Images with Compensation of Phase Distortion
Yu. V. Zhulina
pp. 186–196

Abstract—An algorithm for optimal construction of an image of an object on the basis of signals scattered by it is synthesized. Phase distortion in the signal and additive noise in the receiving aperture are taken into account.

Optimum Filtering for the Case of Indirect Observation of a Diffusion Process with a Delayed Argument
N. K. Kul'man and V. M. Khametov
pp. 197–204

Abstract—The article examines the problem of estimating a continuous Markov process for the case in which the observed process depends both on the process being estimated and on a delayed copy of it. Stochastic equations in the a posteriori probabilities are obtained. The case of Gaussian a posteriori probabilities is considered, and equations are given for the estimates and a posteriori variances.

Asymptotically Efficient Estimation of Nonlinear Functionals
B. Ya. Levit
pp. 204–209

Abstract—It is shown that the Rosenblatt–Bhattacharyya method for setting up estimates of an unknown density and its derivatives leads to asymptotically efficient nonparametric estimates in a class of smooth nonlinear functionals of an unknown distribution.

Local Asymptotic Normality for Dependent Observations
S. Yu. Efroimovich
pp. 210–217

Abstract—Conditions of local asymptotic normality are given for a sequence of dependent observations.

On Local Properties of Estimate of Spectral Function
I. G. Zhurbenko
pp. 218–222

Abstract—Statistical estimates are set up for the spectral density $f(\lambda)$ with respect to a sample from a stationary sequence $X(t)$ at a specified point $\lambda$, which depends as little as possible on the behavior of $X(t)$ at all remaining frequencies. The asymptotic properties of the first two moments of these estimates are investigated and compared with the asymptotic properties of some other known estimates. The possibility of using the mixing properties of stationary sequence $X(t)$ for setting up unbiased consistent spectral density estimates is investigated. The problem of extracting useful signals from noise concentrated at nearby adjacent frequencies is solved in a general fashion.

One-Dimensional Uniform Arrays That Wash Out Finite Islands
P. Gach, G. L. Kurdyumov, and L. A. Levin
pp. 223–226

Abstract—Both deterministic and probabilistic one-dimensional uniform systems of finite automata with local interaction are considered. A state of a deterministic system is called attracting if it is maintained in time and any finite deviation from it disappears over a finite time. Three simple examples are given of systems with a nonunique uniform attracting state. Results of computer simulations of probabilistic systems obtained by superimposing random noise on such systems are given. The simulation results indicate that the systems may be nonergodic in the case of low noise.

On Behavior of Systems of Automata in Small Groups with a Hierarchy
Yu. I. Kryukov
pp. 226–232

Abstract—The author investigates the behavior in random media of automaton models of small groups with and without a leader. The advantages of the behavior dynamics of groups with a leader are ascertained. It is shown that “optimism” in ratings by team members of the results of their actions facilitates an increase in the mean gain of the system.

Solution of the Problem of Extrapolation over Entire Past History of a Process with Quasipolynomial Spectral Density
Abstract—Yaglom’s lemma and methods of the theory of analytic functions are used to find an explicit form of the spectral characteristic of linear extrapolation over the entire past history of processes with $R$-quasipolynomial and inverse $R$-quasipolynomial spectral densities.