PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 26, Number 1, January–March, 1990
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Detection of a Radiation Source Moving relative to the Receiver, with Estimation of Its Velocity and Minimum-Distance Time
G. P. Tartakovskii
pp. 1–8

Abstract—The detection problem with parameter estimation is solved for passive location of a radiation source.

 

Estimation of Trispectral Density of a Stationary Stochastic Process
V. G. Alekseev
pp. 9–14

Abstract—We investigate the statistical properties of nonparametric estimates of trispectral density of a stationary stochastic process. We show that the mean square of the absolute value of the estimation error of trispectral density essentially depends on the degree of smoothness of its real and imaginary parts. A method of trispectral density estimation is suggested for the case with systematically missing observations.

 

Quasilinear Estimates of Signals in $L_2$
G. K. Golubev
pp. 15–20

Abstract—Nonlinear estimates are constructed in the problem of nonparametric estimation of a signal observed in the presence of white noise. With a mean square accuracy criterion, these estimates are asymptotically minimax on any parametric set from a sufficiently broad class of ellipsoids in $L_2$.

 

Estimation of a Linearly Filtered Signal
R. D. Dodunekova
pp. 20–30

Abstract—We consider the estimation of a signal $s$ observed after passing through a channel with Gaussian white noise of intensity $\varepsilon^2$, an $n$th order filter, and another channel with white noise of intensity $\delta^2$. The estimation accuracy is compared to that in estimation from direct observations.

 

Recursive Estimation of the Mode of a Multivariate Distribution
A. B. Tsybakov
pp. 31–37

Abstract—A simple recursive estimator of the mode of a multivariate distribution is proposed. Conditions for the convergence of the estimator with probability $1$ are given. The rate of mean-square convergence of the estimator is calculated. It is shown that no mode estimators exist with a higher order of rate of convergence.

 

Minimax Estimation of Linear Functionals in the Presence of Two-Dimensional Noise
V. S. Lebedev
pp. 38–48

Abstract—Problems of linear minimax estimation of linear functions from observations in a Gaussian random field are considered. The results of [I.A. Ibragimov and R.Z. Khas'minskii, Teor. Veroyatn. Primen., 29, No. 1, 19–32 (1984); 32, No. 1, 35–44 (1987)] are extended to this case. As an example, we examine minimax estimation of the value of the function $f(t,s)$ and its derivatives $\partial^{\alpha}f(t,s)/\partial t^{\alpha_1}\partial s^{\alpha_2}$. It is shown that the problems of estimation of a certain class of unbounded (in $L_2$) linear functions from observations in random fields with correlation operators $I$ and $R$ are equivalent in a certain sense if $R=I+K$, where $I$ is the identity operator and $K$ is a completely continuous operator.

 

Bounds on the Capacity of FCFS Multiple-Access Algorithms
N. D. Vvedenskaya and M. S. Pinsker
pp. 49–56

Abstract—A class of FCFS (first-come-first-served) multiple-access algorithms is considered. Several subclasses are identified and the capacity of the corresponding algorithms is estimated. A conjecture concerning the capacity of the entire class of FCFS algorithms is advanced.

 

Comparison of Some Multiple-Access Systems
B. S. Tsybakov
pp. 57–62

Abstract—Multiple-access systems use two types of protocols—station control and packet control. Typical representatives of these protocols are compared: time sharing is compared with the stack algorithm, token-passing access is compared with the stack algorithm in a local-area network. Poisson arrivals are assumed for all $M$ stations with equal intensities $\lambda/M$. The comparison criterion is the mean packet delay. The set of possible $(\lambda,M)$ is partitioned into regions, such that station-control systems are preferred in one region and packet-control systems are preferred in the other.

 

Instability of Slotted ALOHA
G. I. Falin
pp. 63–67

Abstract—The slotted ALOHA system is unstable in the sense that eventually, after a time which is finite with probability $1$ and which moreover satisfies the Cramer condition, the channel will contain only conflicts. This result was obtained by exploiting the concept of comparability of stochastic models as a corollary of some general assertion on transience of a special type of Markov chains.

 

Rates for Multiple Description of a Source with Given Error Exponents and Distortion Levels
R. Sh. Marutyan
pp. 68–74

Abstract—The achievable rate region is determined for a two-decoder memoryless discrete source with given exponents $E=(E_1,E_2)$ of the probability of exceeding the specified distortion levels $\Delta=(\Delta_1,\Delta_2)$.

 

Bounds on Probability of Connectedness of a Random Graph
B. P. Polesskii
pp. 75–82

Abstract—Let $(M,q)$ be a random matroid, i.e., a matroid $M$ on the set $E$ whose elements are deleted independently of one another with probability $q$, and let $P(M,q)$ be the probability that the rank of a random subset of the set $E$ is equal to the rank $r$ of the matroid $M$. The following effective and exact lower bound on the probability $P(M,q)$ is proved: $$ \prod\limits_1^r(1-q^{\delta_i})\le P(M,q), $$ where $(\delta_1,\dots,\delta_r)$ is the so-called base spectrum of the matroid $M$, $\sum\limits_1^r\delta_i=|E|$.

 

Asymptotically Exact Uniform Bounds for Spectra of Cosets of Linear Codes
V. M. Blinovsky
pp. 83–86

Abstract—Asymptotically exact lower bounds are obtained for the spectrum of cosets of linear codes and a lower bound for the proportion of linear codes satisfying Goblick's bound to the covering radius.

 

Fast Group-Theoretical Transform
A. L. Vishnevetskii
pp. 87–89

Abstract—For an arbitrary integer $n=q2^m$, where $q\mid 2^m-1$, we find a group $G$ of order $n$ for which the $G$-spectrum of a complex signal of length $n$ can be computed in approximately $n\log_2(n/q)$ operations. In particular, for $q=2^m-1$, the number of operations is half the number of operations for FFT computation of a signal of the same length.

 

Optimality of Sequential Estimation Plans for the Parameters of Recursive Processes
V. Z. Borisov and V. V. Konev
pp. 90–92

Abstract—We investigate the properties of sequential estimation plans of the parameters of stochastic processes described by stochastic difference equations. For a fixed average signal energy, sequential estimation is minimax optimal.