PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS

Computation of the Fundamental Limits of Data Compression for Certain Nonstationary ARMA Vector Sources
J. Gutiérrez-Gutiérrez, Í. Barasoain-Echepare, M. Zárraga-Rodríguez, and X. Insausti
pp. 1–11

Abstract—In the present article, the differential entropy rate and the rate distortion function (RDF) are computed for certain nonstationary real Gaussian autoregressive moving average (ARMA) vector sources.

Constructions of Nonbinary Codes Meeting the Johnson Bound
L. A. Bassalygo, V. A. Zinoviev, and V. S. Lebedev
pp. 12–20

Abstract—We propose several constructions of nonbinary constant-weight codes meeting the Johnson bound.

Correcting a Single Error in an Asymmetric Feedback Channel
I. V. Vorobyev, A. V. Lebedev, and V. S. Lebedev
pp. 21–27

Abstract—We prove a new lower bound on the size of a code with complete feedback correcting a single error in a binary asymmetric channel. We also present an upper bound on the size of the code, which is close to the new lower bound.

On Measuring the Topological Charge of Anyons
A. A. Morozov
pp. 28–34

Abstract—We discuss principles of measuring a topological charge or representation that travels in a set of anyons. We describe the procedure and analyze how it works for different values of theory parameters. We also show how it can be modified to be more efficient.

Prediction of Locally Stationary Data Using Expert Advice
V. V. V'yugin, V. G. Trunov, and R. D. Zukhba
pp. 35–52

Abstract—We address the lifelong machine learning problem. Within the game-theoretic approach, in the calculation of the next prediction we use no assumptions on the stochastic nature of a source that generates the data flow: the source can be either analog, or algorithmic, or probabilistic; its parameters can change at random times; when constructing a prediction model, only structural assumptions are used about the nature of data generation. We present an online forecasting algorithm for a locally stationary time series. We also obtain an estimate for the efficiency of the proposed algorithm. The obtained estimates for the regret of the algorithm are illustrated by results of numerical experiments.

Elementary Solution to the Fair Division Problem
M. L. Blank and M. O. Polyakov
pp. 53–70

Abstract—A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges (signed measures). The setting of the problem with charges is considered for the first time. The problem comes down to analyzing properties of trajectories of a specially constructed dynamical system acting in the space of finite measurable partitions. Exponentially fast convergence to a limit solution is proved for both the case of true measures and the case of charges.