PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 1, Number 3, July–September, 1965

Back to contents page

** Some Questions of Method and the
Recognition Problem
**

A. A. Kharkevich^{†}

pp. 1–6

This article comprises a report given to the Methodological Seminar of the Institute of Problems of Information Transmission of the Academy of Sciences USSR, which took place on 24 March 1965. A.A. Kharkevich died on 30 March 1965.

** Correction of Errors and Erasures with
Bose–Chaudhuri Codes
**

E. L. Blokh

pp. 7–13

**Abstract**—The method proposed by Zierler and Gorenstein for decoding
Bose–Chaudhuri codes with an arbitrary base $q=p^s$ in the presence of errors
is generalized to include the case in which, together with errors, code symbols are
erased.

** Error-Correcting Codes for Arithmetic
Operations
**

V. D. Kolesnik and E. T. Mironchikov

pp. 14–20

**Abstract**—The problem of finding arithmetic error-correcting
codes for nonuniformly distributed errors (so-called error bursts) is of
practical importance. Below we present several theorems that make it possible
to find, either directly or by some sort of inspection, numbers that generate
arithmetic error-correcting codes. The results are tabulated. The article
presents the results of further work of the authors on the theory of
arithmetic error-correcting codes and is a direct continuation of
[E.T. Mironchikov and V.D. Kolesnik, *Radiotekhn.
Elektronika*, 1963, vol. 8, no. 1, pp. 8–15]. The
codes obtained are analogs of the corresponding Fire and Elspas–Short
codes.

** Comparison of Arbitrary Additive Noise
Relative to the Effectiveness of Detection or Correction
**

M. E. Deza

pp. 21–28

**Abstract**—The author considers the problem of comparing noise
in the finite Abelian group of all additive noise of a given volume with
respect to the size of maximal codes that can detect or correct such noise.
Maximal codes for detection or correction of worst and best noise of a given
volume are found correct to the order of the volume; certain properties of
such noise are stated. The problem of comparing noise with respect to
effectiveness of detection is solved definitively for the binary case.

** Matching a Vector Source with a Vector
Channel by Linear Coding and Spectral Transposition
**

I. A. Ovseevich

pp. 29–35

**Abstract**—The author describes a method for matching a vector
source and channel with a frequency-weighted mean-square criterion of
reproduction accuracy. This method, which includes optimal linear coding
(predistortion and correction) and optimal transposition of the frequency
bands of the components of the vector messages, is the best in the class of
possible linear transformations; it yields a frequency-weighted mean-square
deviation no greater than that provided by any other linear methods of coding
and transposition. A procedure is presented for finding optimal
characteristics for coders and decoders with correlated vector-message
components and noise in the presence of linear distortion in the channel.

** $\varepsilon$-Entropy of
Discrete Information Sources
**

L. M. Libkind

pp. 36–42

**Abstract**—This article is concerned with the problem of obtaining
explicit expressions for the $\varepsilon$-entropy of segments of random processes
with a finite number of states and discrete time. The corresponding calculations
show that these expressions are awkward and obscure and take on a sufficiently
simple form only for “small” values of $\varepsilon$. Because of this,
attention is chiefly concentrated on obtaining simple and convenient bounds.

** Synthesis of a Heterodyne Light Signal
Receiver
**

G. P. Tartakovskii

pp. 43–54

**Abstract**—A study is made of the statistical characteristics of
the voltage at the output of a photomixer when fluctuating light signals are
heterodyned. The optimal treatment of this voltage in the receiver, giving
the best characteristics for detecting weak light signals and measuring the
parameters coded in them, is found. The long-term possibilities of light
signal receivers for detection and measurement are estimated.

** Information Transmission in an Ideal
Photon Channel
**

L. B. Levitin

pp. 55–62

**Abstract**—An ideal photon channel with spatial diversity of the
wave vectors is investigated using the concept of an ideal physical
information channel. Expressions are obtained for the transmission capacity
of broadband and narrowband channels in the presence of thermal noise. A
space-time interpretation of a photon channel is given.

** A Method of Information Sorting in
Computer Memories
**

A. A. Papernov and G. V. Stasevich

pp. 63–75

**Abstract**—Relationships are derived for the maximum value and
the mean of the number of operations required in various forms of a sorting
method which utilizes only a minimum of extra memory space. Experimental
results are quoted.

** The Asymptotic Properties of One Form
of Goore Game
**

B. G. Pittel

pp. 76–88

**Abstract**—The author considers one variant of the model of
collective automaton behavior proposed by V.A. Borovikov and
V.I. Bryzgalov. In this model the players have two moves, and in each
multiply repeated play they are simultaneously rewarded with a probability
depending on the number of automata that make the first move. The asymptotic
properties of the final distribution as the number of players increases
without bound are investigated as a function of memory capacity.

** Application of Random Noise to
Optimization and Recognition Problems
**

R. Z. Khas'minskii

pp. 89–93

**Abstract**—It is generally known that by combining gradient
methods of optimization with random search procedures it is possible to find
the absolute extremum of a function. In this paper, we examine such an
optimization model and give some estimates which prove the convergence to the
absolute maximum within the framework of this model. The proposed method may
be suitable for recognition problems.

** A Nonparametric Criterion for
Comparison of Samples
**

K. Sh. Zigangirov

pp. 94–96

**Abstract**—The problem of distinguishing two hypotheses with
population sample data is considered. A rank criterion for solution of this
problem is proposed, as well as a solution for the statistical problem of
comparing two samples.

** Algorithms for Changing Stochastic
Automata Transition Probabilities
**

I. P. Vorontsova

pp. 97–101

**Abstract**—The behavior of stochastic automata with a variable
structure in stationary random media is examined. An algorithm for changing
the transition probabilities, permitting optimal operation of the automaton
in given media, is described.