PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Girth Analysis of Quantum Quasi-Cyclic LDPC Codes
Farzane Amirzade, Daniel Panario, and Mohammad-Reza Sadeghi
pp. 71–89

Abstract—Quantum quasi-cyclic LDPC (QQC LDPC) codes, as CSS (Calderbank, Shor, and Steane) codes, are attracting attention because of their good structure and popular channel coding schemes. Fully connected quasi-cyclic LDPC (QC-LDPC) codes with different girths which result in QQC-LDPC codes are investigated. We analytically prove that QC-LDPC codes with column weight at least 3, which yield a QQC-LDPC code, have girth at most 6. To obtain a QQC-LDPC code from QC-LDPC codes with girth more than 6 we should focus on QC-LDPC codes with column weight 2. We present an efficient and practical method to construct these codes with girth at least 8. Then, we extend our method to construct codes with column weight 2 and girth 12, thus reaching the largest possible girth.

Impact of Modulation Constellation Type on the Finite Signal-to-Noise Ratio Diversity Gain in the Presence of a Multipath Fading Channel
A. S. Gvozdaryev, T. K. Artemova, and A. V. Morkovkin
pp. 90–112

Abstract—The evolution of wireless communication in the presence of multipath fading and shadowing is generally strained by the worsening of propagation conditions. Thus, in order to estimate the achievable improvements of the link quality (due to channel enhancement), such a~parameter as diversity gain is usually used. The diversity gain is classically defined as a limit for infinitely increasing signal-to-noise ratio (SNR) at the receiver input, theoretically attained only in asymptotics, and in practice attained at very high SNR values (e.g., 50–70 dB), which are unrealistic from the practical perspectives for wireless fading channels. In this case, a modified version of the same metric (i.e., the finite-SNR diversity gain; FSDG) was proposed. The presented research performs a comparative analysis of the FSDG for the case of a multipath channel with fading induced by second order scattering and fluctuating line-of-sight (LoS) component (i.e., fluctuating double-Rayleigh with Line-of-Sight; fdRLoS). The signal model included the hexagonal quadrature amplitude modulations (QAM) with regular and irregular constellations. For the considered problem, an exact expression for the FSDG was derived and analyzed as a function of channel parameters (responsible for fading severity and shadowing intensity) and modulation formats. It has been found that the FSDG can exceed the classical (asymptotic) diversity gain by the order of magnitude, and scenarios have been identified where this can occur (for example, the maximum is achieved under conditions of light shadowing and strong line-of-sight component). A nonmonotonic dependence of FSDG on the QAM constellation size (for any type of constellation) was found out: for low-to-moderate average SNR, for extremely weak and extremely strong LoS, the highest FSDG is achieved with smaller constellations, whereas for moderate LoS components, with larger constellations.

Spectral Representation of Two-Sided Signals from $\ell_\infty$ and Applications to Signal Processing
N. G. Dokuchaev
pp. 113–126

Abstract—We study spectral representation as well as predictability and recoverability problems for nonvanishing discrete-time signals from $\ell_\infty$, i.e., for bounded discrete-time signals, including signals that do not vanish at $\pm\infty$. We extend the notions of transfer functions, the spectrum gaps, bandlimitness, and filters to these general type signals. We present some frequency conditions for predictability and data recoverability and propose some prediction and data recovery methods.

Information Diagrams and Their Capabilities for Classifying Weak Signals
V. G. Babikov and A. A. Galyaev
pp. 127–140

Abstract—The paper is devoted to the study of information characteristics which play an important role in solving problems of detection of weak signals and their classification. We formulate and prove lemmas on estimating upper and lower boundaries in statistical and spectral complexity diagrams for different signal-noise mixtures. The obtained theoretical results are verified by numerical experiments, which have confirmed the efficiency of the theoretical estimates. We establish some important laws of the behavior of noise-like and weak signals and the possibilities of their detection in white and blue noise conditions, formulate and prove the corresponding lemmas. Also, we obtain estimates on conditions for the possibility of classifying weak signals by means of information characteristics.