PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 27, Number 3, July–September, 1991
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CONTENTS

Construction of Partial-Unit-Memory Convolutional Codes Based on Reed–Muller Codes
V. V. Zyablov and S. I. Portnoi
pp. 189–198

Abstract—The paper describes the construction of partial-unti-memory codes based on Reed–Muller codes. The characteristics of the construction, the decoding algorithms, and the complexity of the decoding algorithms are considered. Examples of the construction and simulation results in a Gaussian channel are reported.

On Existence of Fixed Convolutional Codes of Rate $2/c$ for $c\ge4$ that Attain the Costello Bound
K. Sh. Zigangirov and V. V. Chepyzhov
pp. 199–211

Abstract—We establish lower bounds for the weights of codewords generated by fixed convolutional codes of rate $R=2/c$ with $c\ge 4$. The bounds are derived for three types of input sequences. The results imply the existence of fixed convolutional codes of rate $2/c$ whose free distance $d_{\rm free}$ asymptotically achieves the Costello bound.

List Decoding in a Gaussian Channel
B. D. Kudryashov
pp. 211–218

Abstract—Additive bounds on error probability are computed for list decoding in a channel with additive Gaussian white noise for particular block or convolutional codes. The bounds may be applied to ordinary codes and to Ungerboeck-type signal-code constructions. The notion of list distance is introduced and examples of its computation are described.

Testing of Multialternative Hypotheses under A Priori Uncertainty
V. G. Repin, G. P. Tartakovskii, and A. A. Slepokurov
pp. 219–233

Abstract—An optimal decision rule for testing multialternative hypotheses is constructed for the case where the available information about the a priori probability distribution is limited to knowledge of the admissible region of probability values. The optimality criterion is minimax deviation of the mean risk from the Bayesian risk for a known a priori distribution of the hypotheses. General expressions are derived for the maximum deviation, the structure of the optimal decision rule is determined, and relationships for the choice of decision rule parameters are established. Some examples are considered, many of which produce an optimal decision rule for a whole class of practical problems.

Game-Theoretical Problems of Synthesis of Signal Generation and Reception Algorithms
A. M. Chudnov
pp. 233–240

Abstract—Message transmission in the presence of uncertain interference is considered in the game-theoretical framework. Existence conditions and properties of optimal signal generation and reception algorithms are determined and the least favorable interference distributions are identified. Guaranteed error probability bounds are determined for various classes of signals and interferences defined by energy constraints.

Estimation of Distance Functionals between Density Functions
G. M. Koshkin
pp. 241–246

Abstract—Nonparametric kernel estimators of the type of quasi-$U$-statistics are proposed for the class of functionals describing various distance measures, such as $\chi^2$, Kullback–Leibler, Hellinger, Bhattacharya, etc. The functional estimators are shown to be asymptotically unbiased and the exact asymptotic variances are determined. The distances listed above are considered as examples.

Lower Bound on Delay in a Random Multiple Access System
B. S. Tsybakov and N. B. Likhanov
pp. 247–260

Abstract—We consider a multistation packet transmission network with a Poisson input of intensity $\lambda$. The stations send packets through a shared channel with ternary feedback (success, conflict, empty). A function of $\lambda$ is found such that the mean packet delay is not less than this function for any random multiple access algorithm. The lower-bound function equals $0$ for $\lambda=0$ and $\infty$ for $\lambda=0.587$.

Asymptotic Bit Error Probability for Convolutional Codes
Yu. P. Lobanov
pp. 261–265

Abstract—An exact formula is proposed for bit error probability in a binary symmetric channel using a fix convolutional code of arbitrary rate $b/c$. As a result, an exact asymptotic expression is obtained for the bit error probability in the low noise case. A table of asymptotically good codes is given.

Limit Theorems for Queueing Networks with Multiserver Nodes
M. M. Safarov
pp. 266–270

Abstract—Ergodicity theorems are proved for open and closed queueing networks with multiserver nodes.

Using Group Properties of Discrete and Continuous Filtering Algorithms for Complex Measuring Systems
V. V. Khutortsev
pp. 271–276

Abstract—A unified approach to the synthesis of optimal observation control in complex data-acquisition and measuring systems is proposed on the basis of analysis of the group properties of continuous and discrete filtering algorithms. An example is considered.