PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Two Comparison Theorems for Distributions of Gaussian Quadratic Forms
M. V. Burnashev
pp. 203–214

Abstract—We present new results on comparison of distributions of Gaussian quadratic forms.

On Coupling of Probability Distributions and Estimating the Divergence through Variation
V. V. Prelov
pp. 215–221

Abstract—Let $X$ be a discrete random variable with a given probability distribution. For any $\alpha$, $0\le\alpha\le 1$, we obtain precise values for both the maximum and minimum variational distance between $X$ and another random variable $Y$ under which an $\alpha$-coupling of these random variables is possible. We also give the maximum and minimum values for couplings of $X$ and $Y$ provided that the variational distance between these random variables is fixed. As a consequence, we obtain a new lower bound on the divergence through variational distance.

A Note on Random Coding Bounds for Classical-Quantum Channels
M. Dalai
pp. 222–228

Abstract—A modified derivation of achievability results in classical-quantum channel coding theory is proposed, which has, in our opinion, two main benefits over previously used methods: it allows to (i) follow in a simple and clear way how binary hypothesis testing relates to channel coding achievability results, and (ii) derive in a unified way all previously known random coding achievability bounds on error exponents for classical and classical-quantum channels.

A Special Class of Quasi-cyclic Low-Density Parity-Check Codes Based on Repetition Codes and Permutation Matrices
F. I. Ivanov
pp. 229–241

Abstract—We propose a new ensemble of binary low-density parity-check codes with parity-check matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.

Nonlinear $q$-ary Codes with Large Code Distance
S. A. Stepanov
pp. 242–250

Abstract—We construct a family of nonlinear $q$-ary codes obtained from the corresponding families of modified complex Butson–Hadamard matrices. Parameters of the codes are quite close to the Plotkin bound and in a number of cases attain this bound. Furthermore, these codes admit rather simple encoding and decoding procedures.

Propelinear Codes Related to Some Classes of Optimal Codes
I. Yu. Mogilnykh and F. I. Solov'eva
pp. 251–259

Abstract—A code is said to be propelinear if its automorphism group contains a subgroup that acts regularly on codewords. We show propelinearity of complements of cyclic codes $C_{1,i}$, $(i,2^m-1)=1$, of length $n=2^m-1$, including the primitive two-error-correcting BCH code, to the Hamming code; the Preparata code to the Hamming code; the Goethals code to the Preparata code; and the $\mathbb{Z}_4$-linear Preparata code to the $\mathbb{Z}_4$-linear perfect code.

Analytical Approach to Multiband Filter Synthesis and Comparison to Other Approaches
A. B. Bogatyrev, S. A. Goreinov, and S. Yu. Lyamaev
pp. 260–273

Abstract—A novel analytical approach to the synthesis of multiband electrical filters is presented. This approach allows to obtain the lowest possible order filters for a wide class of specifications including ones with large number of pass- and stopbands and with narrow transition bands. Comparison of the new approach to direct optimization and composite approaches is provided.

Adaptive Search for One Defective in the Additive Group Testing Model
V. S. Lebedev
pp. 274–278

Abstract—In contrast to the problem of finding all defective elements in group testing, we consider the problem of finding one defective in a set $D$ of defective elements of cardinality $d$. We consider adaptive search algorithms only. A similar problem for the classical and threshold models was solved in [1]. In the present paper we consider the additive testing model. We obtain an optimal answer in the problem of adaptive search of one defective element in this model.

On Projectively Invariant Points of an Oval with a Distinguished Exterior Line
A. M. Balitskii, A. V. Savchik, R. F. Gafarov, and I. A. Konovalenko
pp. 279–283

Abstract—We consider projectively invariant points of an oval with a distinguished exterior line. For this, we introduce a projectively invariant transformation of the line parametrized by the oval. Projectively invariant points are defined as fixed points of this transformation applied twice. We prove that there are at least four such points. For the proof we reduce the problem to an affine problem and construct an extremal area parallelogram circumscribed around the oval.

On the Real Complexity of a Complex DFT
I. S. Sergeev
pp. 284–293

Abstract—We present a method to construct a theoretically fast algorithm for computing the discrete Fourier transform (DFT) of order $N=2^n$. We show that the DFT of a complex vector of length $N$ is performed with complexity of $3.76875N\log_2N$ real operations of addition, subtraction, and scalar multiplication.

Information-Theoretic Method for Classification of Texts
B. Ya. Ryabko, A. E. Gus'kov, and I. V. Selivanova
pp. 294–304

Abstract—We consider a method for automatic (i.e., unmanned) text classification based on methods of universal source coding (or ``data compression''). We show that under certain restrictions the proposed method is consistent, i.e., the classification error tends to zero with increasing text lengths. As an example of practical use of the method we consider the classification problem for scientific texts (research papers, books, etc.). The proposed method is experimentally shown to be highly efficient.

Erratum to: “Remark on Balanced Incomplete Block Designs, Near-Resolvable Block Designs, and $q$-ary Constant-Weight Codes” [Problems of Information Transmission 53, 51 (2017)]
L. A. Bassalygo and V. A. Zinoviev
p. 305

Abstract—The acknowledgment (footnote to the title of the paper) should read as follows:
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

Erratum to: “MDS Codes in Doob Graphs” [Problems of Information Transmission 53, 136 (2017)]
E. A. Bespalov and D. S. Krotov
p. 306

Abstract—The acknowledgment (footnote to the title of the paper) should read as follows:
The research was carried out at the expense of the Russian Science Foundation, project no. 14-11-00555.