PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 49, Number 1, January–March, 2013

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** On Computation of Entropy of an Ellipsoid in a
Hamming Space
**

V. V. Prelov

pp. 1–14

**Abstract**—Asymptotics of the entropy of an ellipsoid in a Hamming space
of a growing dimension is investigated in the case where coefficients of the
ellipsoid are monotone sequences of real numbers.

** On Classical Capacities of Infinite-Dimensional
Quantum Channels
**

A. S. Holevo and M. E. Shirokov

pp. 15–31

**Abstract**—A coding theorem for entanglement-assisted communication via
an infinite-dimensional quantum channel with linear constraints is extended to a
natural degree of generality. Relations between the entanglement-assisted classical
capacity and $\chi$-capacity of constrained channels are obtained, and conditions for
their coincidence are given. Sufficient conditions for continuity of the
entanglement-assisted classical capacity as a function of a channel are obtained.
Some applications of the obtained results to analysis of Gaussian channels are
considered. A general (continuous) version of the fundamental relation between
coherent information and the measure of privacy of classical information transmission
via an infinite-dimensional quantum channel is proved.

** Local Distributions and Reconstruction of
Hypercube Eigenfunctions
**

A. Yu. Vasil'eva

pp. 32–39

**Abstract**—We study eigenfunctions of a binary $n$-dimensional
hypercube. We obtain a formula relating local distributions of such a function in a
pair of orthogonal faces. Based on this, we prove that under certain conditions an
eigenfunction can be reconstructed partially or completely given its values on a
sphere.

** Rank Subcodes in Multicomponent Network Coding
**

E. M. Gabidulin and N. I. Pilipchuk

pp. 40–53

**Abstract**—A new class of subcodes in rank metric is proposed; based on
it, multicomponent network codes are constructed. Basic properties of subspace
subcodes are considered for the family of rank codes with maximum rank distance (MRD
codes). It is shown that nonuniformly restricted rank subcodes reach the Singleton
bound in a number of cases. For the construction of multicomponent codes, balanced
incomplete block designs and matrices in row-reduced echelon form are used. A
decoding algorithm for these network codes is proposed. Examples of codes with seven
and thirteen components are given.

** Non-Crossing Matchings
**

A. A. Vladimirov

pp. 54–57

**Abstract**—We model the secondary structure of an RNA molecule by means
of a maximal non-crossing matching on a random word in a finite alphabet, where ties
are only allowed between certain pairs of letters. We prove that the mean fraction of
unmatched symbols does not vanish as the length of the word tends to infinity.

** Help Desk Center Operating Model as a Two-Phase
Queueing System
**

S. A. Dudin and O. S. Dudina

pp. 58–72

**Abstract**—We consider a two-phase queueing system with a Markovian
arrival flow as an operating model for a help desk center. The first phase is a
multiserver system with a finite buffer and impatient customers. After getting
service in the first phase, a customer either enters the second phase with an
infinite buffer or quits the system. Service times at the first and second stages
have phase-type distributions with different parameters. We obtain an existence
condition for a stationary regime of the system. An algorithm for computing
stationary probabilities and basic performance characteristics of the system is
presented. Laplace–Stieltjes transforms for the distributions of sojourn and
waiting times in the first and second phases are found. Results of numerical
experiments are presented. Optimization problem for the system operation is solved
numerically.

** Secrecy Results for Compound Wiretap Channels
**

I. Bjelaković, H. Boche, and J. Sommerfeld

pp. 73–98

**Abstract**—We derive a lower bound on the secrecy capacity of a compound
wiretap channel with channel state information at the transmitter which matches the
general upper bound on the secrecy capacity of general compound wiretap channels
given by Liang et al. [1],
thus establishing a full coding theorem in this case. We achieve this with a stronger
secrecy criterion and the maximum error probability criterion, and with a decoder
that is robust against the effect of randomization in the encoding. This relieves us
from the need of decoding the randomization parameter, which is in general impossible
within this model. Moreover, we prove a lower bound on the secrecy capacity of a
compound wiretap channel without channel state information and derive a multiletter
expression for the capacity in this communication scenario.