PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 15, Number 3, July–September, 1979
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CONTENTS

Upper Bounds for Decoding Error Probability in Some Broadcast Channels
B. D. Kudryashov and G. Sh. Poltyrev
pp. 163–174

Abstract—Upper bounds are obtained for the decoding error probabilities of block codes in discrete broadcast channels in the absence of side information for one of the receivers. These estimates are more exact than those obtained earlier by Gallager. It is also shown that it is possible to employ lattice codes in this situation, and estimates are given for their decoding error probabilities.

Boundary of Region of Permissible Rates for Asynchronous Communication over a Binary Adder Channel
A. A. Grigor'ev
pp. 174–178

Abstract—The coding problem is considered for a binary two-input adder channel and asynchronous user operation. A lower bound is obtained for the region of permissible transmission rates. In individual cases, the resultant bound coincides with the known upper bound for this case.

Information Contained in a Sequence of Observations
S. Yu. Efroimovich
pp. 178–189

Abstract—Bounds and asymptotic expressions are given for the Shannon information contained in a sequence of dependent observations relative to an unknown parameter.

Bounds for Codes with Unequal Protection of Two Sets of Messages
L. A. Bassalygo, V. A. Zinov'ev, V. V. Zyablov, M. S. Pinsker, and G. Sh. Poltyrev
pp. 190–197

Abstract—Upper and lower bounds are derived for the transmission rates $R_1$ and $R_2$ for codes with unequal protection of two sets of messages (i.e., codes that correct different numbers of errors depending on the messages).

Codes with Unequal Protection of Information Symbols
V. A. Zinov'ev and V. V. Zyablov
pp. 197–205

Abstract—It is shown that generalized cascade codes of order m make it possible to construct codes with unequal protection of information symbols in relation to independent errors, error bursts, and both of these factors. A decoding algorithm for such codes is considered. The codes in question are simultaneously correcting codes for some broadcast channels. A table of codes is compiled.

On Computation of Efficiency of Maximum-Likelihood Estimate When Observing a Discontinuous Signal in White Noise
G. K. Golubev
pp. 206–212

Abstract—In observing a discontinuous signal in white Gaussian noise with a spectral density of $\varepsilon^2$ the mean-square risk of the best estimate of the shift parameter for $\varepsilon\to\infty$ is of magnitude $C\varepsilon^4/r^4+o(\varepsilon^4)$, where $r^2$ is the sum of the squares of the signal jumps. In this paper, identities linking the quadratic risks of equivariant estimates are used to find the value of the constant $C$.

Asymptotically Optimal Stochastic Approximation Procedure with Continuous Time
E. Kh. Mustafaev and M. B. Nevel'son
pp. 212–223

Abstract—Under extremely broad conditions, the authors investigate the properties of finite-dimensional distributions of the optimal (in the ordinary sense) stochastic approximation procedure with continuous time, described by an Ito stochastic differential equation.

Synchronization Errors in an Adaptive Quantizer
N. I. Pilipchuk
pp. 223–230

Abstract—For an adaptive quantizer with an adjustable range and unequal code-word lengths, formulas are obtained for the probability of incorrect determination of word length at the receiving end of the communications line for redundant and nonredundant coding. The communications channel is assumed to be a binary symmetrical memoryless channel. Redundant coding is achieved by increasing the prefix symbols in the code word and eliminating some words from the code table.

Detection of Poisson Fields
V. I. Fedoseev
pp. 230–234

Abstract—The article considers the problem of detecting one Poisson field against the background of another when the intensities of both fields are random.

Language Recognition Using Finite Probabilistic Multitape and Multihead Automata
R. V. Freivald
pp. 235–241

Abstract—Rabin demonstrated in [Inf. Control, 1963, vol. 6, no. 3, pp. 230–244] that finite probabilistic automata with an isolated section point can recognize only those languages that can be recognized by finite deterministic automata. In this paper for finite automata with many tapes or with many heads on one tape, we prove the opposite result; namely, that there exists a language that can be recognized with probability $1-\varepsilon$ for any $\varepsilon>0$ but which cannot be recognized deterministically.

On One Class of Self-Synchronizing Codes
E. B. Brodskaya
pp. 242–244

Abstract—It is known that no coset of a cyclic $(n,k)$-code is a code that can restore synchronization in one step if $k>(n-1)/3$. It is proved that if $k\le(n-2)/3$ and $n\ge 5$, then the coset $\{1+x^{n-1}\}$ of any cyclic $(n,k)$-code is a code that restores synchronization in one step. Moreover, examples are given that demonstrate that, for $k=(n-1)/3$, the coset $\{1+x^{n-1}\}$ of a cyclic $(n,k)$-code may or may not be a code that restores synchronization in one step.

Obituary Notice: Mikhail Aleksandrovich Gavrilov
pp. 245–246