PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii
250th Anniversary of the Academy of
Sciences of the USSR
Prognostic Epsilon Entropy of a
Gaussian Message and a Gaussian Source
A. K. Gorbunov and M. S. Pinsker
AbstractIt is shown that the nonanticipatory and prognostic epsilon entropies and message generation rates for Gaussian messages and sources are realized in input and output messages that together form Gaussian processes. Representations of these processes are found for Markov messages and sources, and analytical expressions are given for the epsilon entropy and message generation rate.
Minimum Redundancy of Binary
V. I. Levenshtein
AbstractNew lower bounds are obtained for the redundancy of arbitrary and equilibrium binary codes correcting a fixed proportion of errors.
Upper Bounds for the Number of Points
of a Binary Code with a Specified Code Distance
V. M. Sidel'nikov
AbstractAn upper bound is obtained for the number of points of a binary code of length $n$ and code distance $d$; the new bound improves the Elias bound by a factor that grows exponentially with $n$; a new upper bound is also obtained for the number of points of a binary equilibrium code.
Coding in a Memory with Defective Cells
A. V. Kuznetsov and B. S. Tsybakov
AbstractInformation storage in a memory containing defective cells gives rise to a coding problem in which the positions and types of error of the defective memory cells are known during encoding, but not in decoding. We describe an information-theoretic approach to the reliable storage of information under the stated conditions by means of special defect-correcting codes. These codes are less redundant than error-correcting codes.
Note on Two Classes of Nonlinear Codes
M. N. Nalbandyan
AbstractCodes correcting multiple asymmetric errors are investigated. New proofs are given for Theorems 1 and 2, which were first proved by Varshamov [Dokl. Akad. Nauk SSSR, 1970, vol. 194, no. 2, pp. 284287].
Estimation of the Mean in a Normal Set
I. A. Ibragimov and R. Z. Khas'minskii
AbstractThe estimation of a signal in Gaussian white noise is discussed. It is well known that the arithmetic mean estimator $\bar x$ can be improved if certain a priori information is known about the possible values of the signal parameter. Corrections to $\bar x$ are formulated [see Eqs. (6) and (8)] such that the risk for a quadratic loss function coincides with the minimum risk up to higher-order terms than the risk of $\bar x$ under various assumptions concerning the a priori signal density function.
Conditionally Gaussian Random Processes
R. Sh. Liptser
AbstractA class of non-Gaussian processes $(\theta_t,\xi_t,\:0\le t\le T)$ is defined by means of nonlinear Ito stochastic differential equations with the property that the conditional finite-dimensional distribution functions of the process $(\theta_s,\: s\le t)$ subject to the condition $(\xi_s,\: s\le t)$ are with probability $1$ Gaussian. This fact yields effective results in statistical problems of random processes, in particular a nonlinear generalization of the KalmanBucy filtering problem.
A Property of Hadamard Matrices
A. A. Nikanorov
AbstractBinary codes obtained from Hadamard matrices of order $m=q+1$, where $q$ is a power of an odd prime, are investigated in connection with the problem of encoding the states of an asynchronous finite automaton to enhance its structural reliability. An estimate is obtained for the corrective power of the matrices in the given class when races are present in the memory elements. It is shown that the lower bound for the corrective power is reached.
Probabilistic Characteristics of Graphs
with Large Connectivity
G. A. Margulis
AbstractIt is possible to associate with every finite graph $G$ a function $f_G(p)$, $0\le p\le 1$, representing the probability that $G$ will cease to be connected under the condition that every edge is severed with probability $p$. It is shown that for graphs $G$ with large connectivity the function $f_G(p)$ almost coincides with the characteristic function of a certain interval (the precise formulation is given in Sec. 1.1). This proposition is proved by means of Theorems 2.2 and 2.4 on subsets in Hamming space.
Statistical Characteristics of the
Photocurrent in a Two-Element Intensity Interferometer
A. A. Manuk'yan
AbstractGenerating functionals are used to derive a system of equations describing the relationship between the statistical characteristics of the photocurrent in a two-element intensity interferometer and the luminous flux for arbitrary temporal and spatial correlations. The bivariate distribution function for the occurrence of $n_1,n_2$ electrons in the interval $(0,T)$ in the case of slow temporal fluctuations coincides with the distribution function obtained in [A.A. Manuk'yan, Probl. Peredachi Inf., 1972, vol. 8, no. 2, pp. 3339] by diagonalization of the corresponding density operator, while in the case of fast temporal fluctuations with a rectangular spectrum $\Delta f$ it is the distribution function for the sum of $l=\Delta fT$ bivariate independent stochastic variables, each of which is distributed according to the function for slow fluctuations.