PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Stochastic Equations of Nonlinear Filtering of Markovian Jump Processes
A. N. Shiryaev
pp. 1–18

Abstract—Let $(\theta_t,\eta_t)$ be a Markov process where $\theta_t$ is a non-observable component which is a Markovian jump process, and $\eta_t$ is the observable component satisfying the equation $$ d\eta_t=A(\theta_t,\eta_t,t)\,dt+B(\eta_t,t)\,dW_t,\quad \eta_0=0. $$ This paper derives stochastic equations which the a posteriori probabilities $\pi_t(\mathfrak{A})=\mathbf{P}\{\theta_t\in\mathfrak{A}\,|\,\eta(\tau),\:\tau\le t\}$ satisfy [see Eq. (4)] and which are sufficient statistics in various problems in nonlinear filtering, extrapolation, in optimal control problems, pattern recognition, etc.

Asymptotic Behavior of the Error Probabilities of the First and Second Kind in Hypothesis Testing of the Spectrum of a Stationary Gaussian Process
D. S. Apokorin
pp. 19–31

Abstract—This paper derives expressions for the rate of convergence to zero of errors of the first and second kind, $\alpha_n$ and $\beta_n$ respectively, according to the Neyman–Pearson criterion for different hypotheses $H_i$, $i=1,2,$, and for known sampling $x_k=x(Tk/n)$, $k=0,1,\ldots,n$, for $n\to\infty$. Hypothesis $H_i$ states that the spectral density of the process $x(t)$ is equal to $f_i(\lambda)\asymp|\lambda|^{(-1+\lambda_i)}$ for $\lambda\to\infty$. In order to derive the asymptotic behavior of $\lambda_n$ and $\beta_n$ the distribution of eigenvalues of the matrix $B_1B_2^{-1}$ is determined, where $B_1B_2^{-1}$ is the correlation matrix of the random variables $x_k$, $k=0,1,\ldots,n$, under the condition that hypothesis $H_i$ holds. Afterwards the theorem on large deviations for independent random variables is applied.

The Correction of Errors of Multiplicity $t\ge\frac{d}{2}$ in Majority Decoding
Yu. M. Shtar'kov
pp. 32–38

Abstract—The efficiency of the correction of symbols in the shift register is demonstrated for majority decoding. Sufficient conditions are found for the correction of several errors of multiplicity $t\ge\dfrac{d}{2}$. Two different methods are considered for passing from the detection to the correction of errors in the case of an even code distance.

Quantum Theory of Message Transmission
V. V. Mityugov
pp. 39–46

Abstract—The question of the quantity of information transferable by a given ensemble of pure quantal states for a known reception characteristic is considered. The cases are discussed where the sets of states which can be sent by the transmitter and fixed by the receiver are nonorthogonal. The formulas derived are applied for the calculation of the quantity of information transferable by an ensemble of pure radiation states with given values of the field intensity, and receivable by a linear receiver. The density matrices of these states (quantal time functions) are found by the principle of maximum disinformation. In conclusion a comparison is made between a linear and a square law receiver, and a simple calculation is carried out for estimating their efficiencies.

On an Algorithm for the Recognition of Binary Codes
M. N. Vaintsvaig
pp. 47–53

Abstract—An algorithm is proposed for learning to classify objects described by a set of binary variables. The training is reduced to the selection of attributes of each class sufficient for the collection of examples. These attributes are sought among conjunctive variables describing the objects. In the selection each attribute is estimated by the number of examples possessing it. In recognition, the number of attributes of each class which the given object possesses is counted. The object is referred to the class for which this number is greatest. The algorithm has been successfully applied to the classification of oil bearing and water bearing strata.

Behavior of Continuous Automata in Stochastic Media
V. I. Varshavskii and A. M. Gersht
pp. 54–60

Abstract—In this paper the behavior of continuous automata in stationary and non-stationary stochastic media is studied. Formulas are obtained for the mathematical expectation of a reward (or a penalty) in these media. These formulas allow us to speak of the functional equivalence of the construction of the continuous automaton proposed in the note with an automaton with a linear tactic.

Stability of Stochastic Systems
M. B. Nevel'son and R. Z. Khas'minskii
pp. 61–74

Abstract—This paper studies the properties of signals at the output of a system whose parameters are subjected to random fluctuations of the white noise type. A basis is laid for the possibility of linearizing such systems in order to facilitate stability studies. It is proven that the process at the output of the system is dissipative if the input signal has a finite mathematical expectation and the system itself is stable in a sufficiently strong sense.

Method of Simplifying the Logical Schemes of Algorithms Allowing for Unused Sets of Values of the Variables
V. F. D'yachenko and V. G. Lazarev
pp. 75–79

Abstract—A method of simplifying the logical schemes of algorithms is considered which is based on taking into account the sets of values of the variables not encountered in satisfying the algorithm. The method of simplifying the logical schemes of algorithms (LSA) consists of the transformation of transition formulas with unsupplemented definitions and the deduction of a general solution from which a particular solution is selected as a transition formula. Then the transition formulas are transformed into a logical scheme of algorithms. Allowing for the unused sets enables the total number of logical conditions to be reduced, and the order in which they are tested to be changed, and in some cases this may lead to an additional combination of identical expressions in the LSA. An example of the simplification of an LSA is given.

Uniform Convolutional Codes
L. A. Bassalygo
pp. 80–82

Abstract—A class of uniform convolutional codes is described.

On the Optimal Losses on the Arrival of an Unusual Flow
G. L. Ionin
pp. 82–83

Abstract—The losses in a complete access group are compared in the case of the arrival of an unusual Poisson flow (with total intensity $\Lambda$) and of the simplest flow (with intensity $\lambda$). It is proved that in the case of the arrival of the simplest flow the losses are minimal. The conditions for which the losses are maximal are discussed in an example.