PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 4, Number 2, April–June, 1968
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Equidistant $q$-ary Codes with Maximal Distance and Resolvable Balanced Incomplete Block Designs
N. V. Semakov and V. A. Zinoviev
pp. 1–7

Abstract—Equidistant $q$-ary codes with the maximal possible distance $d$ (for the given base $q$, number of words $N$, and number of digits $n$), called $ED_m$-codes, are considered. These $ED_m$-codes have parameters $N=qt$, $n=c(qt-1)/(q-1,t-1)$, $d=ct(q-1)/(q-1,t-1)$, where $c$ is an integer. The equivalence of $q$-ary $ED_m$-codes and resolvable balanced incomplete block designs is demonstrated. It is shown that extremal $ED_m$-codes with $n=(N-1)/(t-1)$ are equivalent to resolvable block designs with $\lambda=1$, and $ED_m$-codes with $n=(N-1)/(q-1)$ are equivalent to affine resolvable block designs and to complete orthogonal arrays of strength two.

 

Summation of the Products of Codes
A. S. Marchukov
pp. 8–15

Abstract—A class of codes is constructed by the operations of summation and multiplication. Decoding for codes of this class is described.

 

Systematic Classes of Binary Convolutional Codes with a Majority Decoding Scheme
O. V. Rychnikov
pp. 16–22

Abstract—Systematic classes of binary convolutional codes with a majority decoding scheme are considered. The codes described may be used for data transmission over channels with independent and correlated errors.

 

Piecewise-Cyclic Codes and Their Majority Decoding Schemes
V. V. Zyablov
pp. &23#150;27

Abstract—The subclass of linear codes called piecewise-cyclic is considered. The connection of piecewise-cyclic codes with incidence matrices of difference classes is studied. A method of constructing piecewise-cyclic codes permitting complete orthogonalization is developed, and the simplicity of their decoding is demonstrated. The increase of the code distance of these codes with increase of the code combination length is estimated.

 

Arithmetic Composition Codes with Error Correction
Yu. G. Dadaev
pp. 28–34

Abstract—A new class of arithmetic codes correcting independent errors is presented. In their construction the idea of the representation of arithmetic distance as the sum of the distances between the information symbols and groups of check symbols is used. Examples of two types of composition codes correcting double errors are presented.

 

Method of Control of Multistage Switching Networks
V. G. Lazarev and V. M. Chentsov
pp. 35–39

Abstract—A method of control taking into account the correlation in time of connections from different inputs and the attraction of the latter to groups of outputs of the multistage switching network is considered. The working conditions of the controlling device realizing the proposed method of control are formulated in terms of automaton games. The block diagram of such a control device is described.

 

An Unreliable Unit with Requests of Several Types and Priority Service of a Request Interrupted by a Breakdown
P. P. Bocharov
pp. 40–47

Abstract—A single queue serving system with an unreliable unit at which there arrives a multivariate simple flow of requests is considered. The requests of the different types have exponentially distributed serving times. The time of sojourn of the unit in serviceable and unserviceable states is also exponentially distributed. The case is considered where on interruption of the service by a breakdown, the request returns to the queue. The cases of a finite and an infinite queue are analyzed. Two numerical examples are given.

 

Recognition of Vowel Sounds from a Clipped Speech Signal
V. N. Trunin-Donskoi and G. I. Tsemel
pp. 48–54

Abstract—A method of obtaining features and an algorithm for the recognition of vowel sounds are described. Before clipping the speech signal passes through circuits in one of which mainly the range of the first formant is amplified, in the other the mean audio frequencies. The number of pulses at the outputs of these circuits corresponds approximately to the first two formant frequencies and characterizes the individual vowels well (with the exception of the discrimination of [i] and [y]). The reliability of recognition of the hard variants of the vowels and [i] by two features amounts to 88.2%. The soft variants of the vowels, having an inhomogeneous (diphthongal) structure, are recognized in more than 90% of cases as one of their component sounds.

 

A Controllable Branching Process
L. V. Levina, A. M. Leontovich, and I. I. Pyatetskii-Shapiro
pp. 55–64

Abstract—The following model is considered in this paper. There is a population of cells, each of which lives for a unit of time, after which it either divides into two or dies. The probability of division $p(i)$ depends only on the size of the population $2i$. A study is made of the random variables $\tau_i$, the time at which the population number deviates from given limits. It is proved that $\mathbf{M}\tau_i\lt\infty$ always. An asymptotic function of the distribution of the random variable $\tau_i/\mathbf{M}\tau_i$ is found with wide assumptions. The results of the calculation of $\mathbf{M}\tau_i$ on a computer are given for some particular cases.

 

Sequential Decoding Procedure with Error Probability Exponent Given by Random Coding
K. Sh. Zigangirov
pp. 65–67

Abstract—A sequential decoding procedure is proposed in which the probability of erroneously decoding a symbol decreases exponentially with increase of the code constraint in accordance with the upper bound of the error probability given by random coding, and the mean number of operations is bounded for all transmission rates less than a certain computation rate $R^r_{\rm comp}$.

 

The Averaging Principle for Stochastic Differential Equations
R. Z. Khas'minskii
pp. 68–69

Abstract—The averaging principle established by Krylov and Bogolyubov is a powerful tool for investigating the properties of dynamic systems involving a small parameter. Its extension to Markov processes is described in papers [R.Z. Khas'minskii, Teor. Veroyatn. Primen., 1963, vol. 8, no. 1, pp. 3–25; I.I. Gikhman, in Winter School on the Theory of Probability and Mathematical Statistics, Kiev, 1964; I. Vrkoc, Czech. Math. J., 1966, vol. 16, pp. 518–544]. In this note it is supposed that both the “slow” and “fast” motions are components of a Markov process of diffusion type.