PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance $3$
D. S. Krotov
pp. 1–9

Abstract—We propose inductive constructions of perfect $(n,3;n-1)_3$ codes (ternary constant-weight codes of length $n$ and weight $n-1$ with distance $3$), which are modifications of constructions of perfect binary codes. The construction yields at least $2^{2^{n/2-2}}$ different perfect $(n,3;n-1)_3$ codes. To perfect $(n,3;n-1)_3$ codes, perfect matchings in a binary hypercube without close (at distance $1$ or $2$ from each other) parallel edges are equivalent.

Joint Source-Channel Coding Using Variable-Length Codes
V. B. Balakirsky
pp. 10–23

Abstract—We address the problem of joint source-channel coding when variable-length codes are used for information transmission over a discrete memoryless channel. Data transmitted over the channel are interpreted as pairs $(m_k,t_k)$, where $m_k$ is a message generated by the source and $t_k$ is a time instant when the transmission of the $k$th codeword begins. The decoder constructs an estimate of the transmitted sequence of pairs, and the $k$th decoding error is introduced as the event that the pair $(m_k,t_k)$ does not belong to this sequence. We describe the maximum likelihood decoding algorithm and prove a lower bound on the exponent of the decoding error probability. For a subclass of discrete memoryless sources and discrete memoryless channels, this bound is asymptotically tight.

Asymptotically Efficient Smoothing in the Wicksell Problem under Squared Losses
G. K. Golubev and F. N. Enikeeva
pp. 24–45

Abstract—In the Wicksell problem, it is required to reconstruct a distribution function of radii of balls located in an opaque medium from measurements of radii of circles obtained by intersecting the medium with a certain plane. This problem is intimately bound up with estimating a fractional derivative of order $1/2$ for a distribution function concentrated on the positive semi-axis. In this paper, the locally asymptotically minimax risk in the Wicksell problem is evaluated up to a constant. Estimators on which this risk is attained are also constructed.

Optimal Detection of a Signal with Unknown Appearance and Disappearance Times
A. P. Trifonov and Yu. E. Korchagin
pp. 46–64

Abstract—We obtain maximum likelihood and optimal (Bayesian) algorithms for detection and measurement of moments of appearance and disappearance of a signal having arbitrary shape and observed in additive white Gaussian noise. Asymptotic expressions for characteristics of the maximum likelihood algorithms are obtained. By means of computer modeling, characteristics of the Bayesian algorithms are found.

Large Deviation Principle for Poisson Random Variables and Young Diagrams
V. M. Blinovsky
pp. 65–69

Abstract—We prove the local large deviation principle (LLDP) for the shape of a random Young diagram with a specific distribution using the large deviation principle for a sequence of Poisson random variables.

Analysis of Queuing Systems for Random-Length Arrivals with Limited Cumulative Volume
O. M. Tikhonenko and K. G. Klimovich
pp. 70–79

Abstract—Two queuing systems for variable-length customers, namely, a processor-sharing system and a multiline system without waiting places, are considered, for which arrivals are completely random, the joint arrival-length and service-time distribution is arbitrary, and the cumulative arrival volume is limited. For these systems, the stationary state probabilities and the arrival loss probability are determined.

Key Secrecy in a Quantum Cryptography System Based on Error-Correcting Codes
I. M. Arbekov
pp. 80–85

Abstract—In [Probl. Peredachi Inf., 1999, vol. 35, no. 1, pp. 100–109], an algorithm based on error-correcting codes was proposed for generating a common key in information transmission through a quantum communication channel. In the present paper, we study the application of this algorithm in a quantum cryptography system where bits of key information are encoded by two nonorthogonal photon polarizations. An estimate for the key secrecy with respect to the “translucent” eavesdropping method is given in the form of a lower bound on the cardinality of the set of admissible key values.