PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 49, Number 1, January–March, 2013
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CONTENTS

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
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.