PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Evaluation of the Asymptotics of the Summarized Capacity of an $M$-Frequency $T$-User Noiseless Multiple-Access Channel
L. A. Bassalygo and M. S. Pinsker
pp. 91–97

Abstract—The best known estimates for the asymptotics of the summarized capacity of an $A$-channel are given. It is shown that the uniform input distribution is asymptotically optimal for a unique value of the parameter $\lambda$ ($T={\lambda}M$, $0<\lambda<\infty$), namely, $\lambda=\ln 2$, and is not such in all other cases.

On the Comparative Complexity of Algorithms for Constructing the Syndrome Trellis of a Linear Block Code
A. V. Trushkin
pp. 98–105

Abstract—We consider the question of the complexity of an algorithm for constructing a block code trellis, as distinct from the complexity of the trellis itself. We state that a lower bound on the complexity of constructing a trellis is determined by the total number of its edges. We show that for the minimal (syndrome) trellis of a linear block code, a simple (but not described earlier) algorithm is asymptotically optimal. The algorithm employs the parity-check matrix in the echelon form and addresses the vertices of the trellis at every level in the basis of the corresponding linear space, which is isomorphic to the space of partial syndromes of the parity-check matrix.

A Novel Construction of High-Rate Unit-Memory Codes
U. K. Sorger and J. Winter
pp. 106–113

Abstract—We present a new construction of a class of unit-memory (UM) codes based on two different $(n,k)$ block codes ${\cal C}_0\ne {\cal C}_1$. This construction is aimed at optimizing not only the free distance but also the extended row distance of a code. In particular, for nonbinary alphabets, we obtain codes with free distance $d_f>d_H({\cal C}_0)+d_H({\cal C}_1)$, where $d_H({\cal C})$ denotes the minimum Hamming distance of a code ${\cal C}$. This improves the results of [1–3]. This approach mainly applies to high-rate UM codes over large alphabets. Hereby, a drastic increase of the free distance is achieved, as compared to known constructions [1,2,4].

Comparative Study of Two Wavelet Bases
V. N. Malozemov and S. M. Masharsky
pp. 114–124

Abstract—Two simple wavelet bases are considered which generate discrete Haar transforms with frequency and time scaling. For these bases, analogs of sampling theorems are obtained. The notion of a log-autoreverse spectrum is introduced. A relation is established between signals with equal spectra in the considered wavelet bases on condition that this spectrum is log-autoreverse.

Adaptive Design for Estimation of Unknown Parameters in Linear Systems
A. I. Ovseevich, R. Z. Khasminskii, and P. L. Chow
pp. 125–153

Abstract—We consider a linear autonomous system of differential equations, where the coefficients depend on an unknown parameter $\theta$, and the input signal has a constrained specific power. We observe the solution perturbed by an additive white noise. In this case we study the asymptotic (for large observation time) design problem of the input signal, which gives us the optimal estimator of $\theta$. We suggest an adaptive algorithm for the design and an asymptotically optimal estimator of $\theta$ with respect to the quadratic risk.

Asymptotic Behavior of the Thermodynamical Limit for Symmetric Closed Queueing Networks
F. I. Karpelevich and A. N. Rybko
pp. 154–179

Abstract—We study the thermodynamical limit for a mean-field model describing how a closed symmetric queueing network operates. The Markov process under consideration is invariant under the action of a certain symmetry group $G$ in the phase space. We prove that the quotient process on the space of orbits of the $G$-action converges to a limit deterministic dynamical system.

Two-Point Jitter in a Network with Periodic Flows under Maximal Load
A. Yu. Privalov
pp. 180–194

Abstract—A method is proposed for the analysis of probabilistic characteristics of a two-point jitter in an ATM network with an initially periodic flow. The network is considered as a system with discrete time. All other flows in the network, which compete for the transmission with the flow studied, are assumed to be periodic. The traffic load at each node of the network is assumed to be equal to $1$. The service discipline is FCFS for packets arriving in different time slots and random for packets arriving within the same slot. Expressions are presented for the jitter probability distribution, jitter variance, and maximum and minimum jitter values.