PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel
A. S. Holevo
pp. 177–183

Abstract—Certain bounds are derived for the quantity of information transmitted by a quantum channel. It is proved that if at least two of the set of density operators $\rho_0,\ldots,\rho_n$ do not commute, then $J(\pi)<\mathcal H\bigl(\sum\limits_\alpha\pi_\alpha\rho_\alpha\bigr) -\sum\limits_\alpha\pi_\alpha\mathcal H(\rho_\alpha)$, where $J(\pi)$ is the upper bound of the quantity of information with respect to all generalized measurements at the channel output for a fixed distribution $\pi=(\pi_0,\ldots,\pi_n)$ at the input. A sharper upper bound for $J(\pi)$ is explicitly stated.

Nonanticipatory and Prognostic Epsilon Entropies and Message Generation Rates
A. K. Gorbunov and M. S. Pinsker
pp. 184–191

Abstract—The concepts of the nonanticipatory and prognostic epsilon entropies of a message and message generation rates of a source are defined, and their properties are investigated.

Discrimination of Random Fields against Background Noise
A. G. Ramm
pp. 192–202

Abstract—Statistical inference theory is applied to the discrimination problem for random fields. The integral equation to which the problem is reduced is subjected to an analytical investigation.

Discrete Representation of Signals with an Unbounded Generalized Spectrum
V. A. Medvedev, B. I. Oleinikov, B. M. Stepanov, and V. N. Filinov
pp. 203–208

Abstract—A theorem is formulated and proved, making possible the discrete representation of signals with an unbounded generalized spectrum and the same spectral properties as real signals. This general result is used to derive an exact expression and error estimates for the model of a signal with a bounded generalized spectrum.

Optimum Estimation in Quantum Channels by the Generalized Heisenberg Inequality Method
V. P. Belavkin and B. A. Grishanin
pp. 209–215

Abstract—The optimization of indirect quantum measurement at the output of a quantum channel is investigated for a quadratic figure of merit. A lower bound compatible with the Heisenberg uncertainty principle is found for the estimation risk. This lower bound is used in the Gaussian case to establish the linearity of optimum estimation and to give a specific description of an appropriate optimum indirect measurement procedure.

Information-Theoretic Inequalities and Superefficient Estimates
I. A. Ibragimov and R. Z. Khas'minskii
pp. 216–227

Abstract—It is proved that superefficient estimates for a matrix loss function do not exist in the class of estimates uniformly at least asymptotically efficient. An analogous result is established for sequential estimates. Integral asymptotic bounds for the estimation risks are also obtained for a large class of loss functions and a priori distribution functions.

Optimum Linear Estimates for the Regression Coefficients of Isotropic Random Fields
M. I. Yadrenko
pp. 228–237

Abstract—Isotropic random fields (fields whose correlation functions are invariant under rotations about a fixed point) are discussed. Linear unbiased estimates optimum in the sense of minimizing the mean-square error are given for the regression coefficients when the random field is observed on a sphere. It turns out, in particular, that the optimum unbiased estimate of an unknown expectation coincides with the average over the sphere. Optimum nonlinear estimates for random regression coefficients are investigated.

Application of a Generalized Poisson Flow to the Investigation of Reliability-Improvement Methods
B. E. Aksenov, A. M. Aleksandrov, and A. N. Bakanov
pp. 238–242

Abstract—The feasibility of using a generalized Poisson flow to investigate reliability-improvement methods is discussed.

Synchronization of a Rectangular Array of Automata
E. I. Petrov
pp. 243–249

Abstract—Variants of the synchronization problem are discussed for a rectangular array of homogeneous automata. It is shown that the synchronization problem for an $n\times m$ array reduces to the synchronization problem for a line of $n+m-1$ automata [E.F. Moore, Sequential Machines, Addison-Wesley, Reading, Mass., 1964, pp. 212–214; V.I. Levenshtein, Probl. Peredachi Inf., 1965, vol. 1, no. 4, pp. 20–32]. An expression is derived for the minimum synchronization time after the delivery of a starting signal to an arbitrary automaton in the array. It is remarked that with respect to the synchronization time the result of [V.I. Varshavskii, V.B. Marakhovskii, and V.A. Peschanskii, Probl. Peredachi Inf., 1968, vol. 4, no. 3, pp. 73–83] is a special case of the problem treated here. Each automaton of the array except the corner members has 19 states; the corner automata have 23 states each.

Symmetric Games for Large Aggregates of Probabilistic Automata
B. G. Sushkov
pp. 250–253

Abstract—Equations are proposed for the approximate description of a system of interacting automata in which the transition probability of an automaton from one state to another is a symmetric function of the states of all the automata. It is proved that the solution of the approximate equations converges to the exact solution as the number of automata is increased without bound.

Information Storage in a Memory Assembled from Unreliable Components
A. V. Kuznetsov
pp. 254–264

Abstract—Storage devices with a correcting block of adders modulo 2 and threshold elements for the correction of random errors in the memory cells are discussed. It is assumed that all the logic elements of the correcting block, as well as the memory cells, are liable to random errors. The existence of storage devices in which a finite number of 1-bit information storage elements is used and for which the storage error probability tends exponentially to zero as the length of the code words is increased for a fixed relative storage capacity is proved.

Universal Sequential Search Problems
L. A. Levin
pp. 265–266

Abstract—Several well-known large-scale problems of the “sequential search” type are discussed, and it is proved that those problems can be solved only in the time that it takes to solve any problems of the indicated type, in general.

A New Class of Pseudorandom Sequences of Binary Signals
K. A. Meshkovskii
pp. 267–269

Abstract—A particular pseudorandom sequence of Hall binary signals is used as the basis for the formation of a class of such sequences.