Том 53, № 3 (2017)

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

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.

We propose a new ensemble of binary low-density parity-check codes with paritycheck 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.

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 Z₄-linear Preparata code to the Z₄-linear perfect code.

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.

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.

We present a method to construct a theoretically fast algorithm for computing the discrete Fourier transform (DFT) of order N = 2ⁿ. We show that the DFT of a complex vector of length N is performed with complexity of 3.76875N log₂N real operations of addition, subtraction, and scalar multiplication.

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.

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.