PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 6, Number 2, April–June, 1970

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** New Results in the Theory of
Simultaneous Optimum Detection and Estimation of Signals in Noise
**

D. Middleton and R. Esposito

pp. 93–106

**Abstract**—Earlier work of the authors [*IEEE Trans. Inf.
Theory*, 1968, vol. 14, no. 3, pp. 434–444] is
extended to the sequential or adaptive decision-making processes involving
optimum signal detection and extraction, when exact knowledge as to the
signal’s presence is unavailable at any given stage. In particular, the
uncoupled cases are developed, and extension to the coupled cases is
considered. These problems are typical of many “multidecision”
situations occurring in adaptive processing, unsupervised learning, and
pattern recognition. Explicit development of the theory here is restricted to
time-invariant parameters and deterministic signal waveforms. An improved
approach to the single-decision problem of joint detection and estimation is
also given, and illustrated by an example of coherent signal detection, and
amplitude estimation, in which optimum and sub-optimum performance is
compared. Various distinctions between different classes of estimators that
are possible in the adaptive case are explicitly discussed, including their
convergence properties. The paper concludes with a summary of the results
obtained and suggestions for future work.

** Comments on Automata in Random Media
**

M. E. Hellman and T. M. Cover

pp. 107–114

**Abstract**—In this paper several approaches are presented to the
problem of optimizing the design of a finite automaton for the hypothesis
testing problem and the related two-armed bandit problem. It is noted that
the two-armed bandit formulation is equivalent to a fundamental question
raised by Tsetlin and his colleagues concerning the unknown optimal design of
automata in random media. A solution of this problem is given by appropriate
application of other work which is presented in condensed and unified form
here. Closely related problems involving Markov switching hypotheses and
multiple hypotheses remain unsolved.

** Retention and Maximization of
Information in Data Reduction
**

I. Vajda

pp. 115–121

**Abstract**—This paper considers the following problem: to
minimize, with respect to a class of reductions satisfying some requirements
as regards “capacities,” etc., the Bayesian or average risk which
increases in data reduction, or to find a simple criterion allowing us to
decide whether the drop in the quality of the solution for a given reduction
is permissible. The paper offers an estimate of the increase in the average
risk due to data reduction in terms of the average number of observations and
the generalized Shannon entropy of individual observations.

** Asymptotic Behavior of the Capacity of
a Continuous Channel with a Large Amount of Noise
**

V. V. Prelov

pp. 122–135

**Abstract**—We consider a channel with independent additive noise, whose
output signal $\eta=\xi+\zeta$, where $\xi$ is the input signal and $\zeta$ is the
noise. Assuming that the average power of the input signal tends to zero
$M|\xi|^2\leq\varepsilon\to 0$, and with certain conditions imposed on the
distribution density of the noise $\zeta$, we determine the asymptotic behavior of
the channel capacity. We also obtain the form of the asymptotically optimum
distribution at the channel input.

** Low-Capacity Channels and
Symbol-by-Symbol Transmission
**

R. Z. Khas'minskii

pp. 136–143

**Abstract**—Symbol-by-symbol transmission over channels with
large amounts of additive noise and feedback is considered. The
asymptotically optimum transmission method is constructed for the case of
fairly regular noise.

** Efficiency of Channel Use in
Asynchronous Address Systems with Code Address
**

G. Tartara

pp. 144–147

**Abstract**—In this note we consider the efficiency of channel
use in asynchronous address systems with many outputs, when binary code words
are used as addresses of various output subchannels.

** Encoding and Decoding Cyclic Code Groups
**

N. Abramson

pp. 148–154

**Abstract**—In this paper we show that the product of two cyclic
codes with block lengths relatively prime can be described in terms of two
interlaced codes. Using this description we provide an improved
characterization of the generating polynomial of the product code in terms of
the generating polynomials of the two original codes. We then show that the
product code and seven other codes related to the product code (called a code
group) can all be obtained from four canonical polynomials which may be
calculated using the Euclidean Algorithm. These results then lead to simple
encoder realizations for cyclic code groups and to a decoding algorithm,
called cascade decoding.

** Analysis of a Decision-Directed
Receiver for a Markov Sequence with Unknown Transition Probabilities
**

S. C. Schwartz and L. D. Davisson

pp. 155–158

**Abstract**—In many applications, such as in video transmission,
the data can be modeled as a Markov sequence and the performance of the
detector improved through incorporation of the transition probabilities into
the threshold. The difficulty in implementation is that the transition
probabilities are often unknown or known imprecisely. In this paper, a
decision-directed receiver (DDR) is analyzed which estimates these transition
probabilities. This is an extension of recently reported work where the data
consisted of an independent sequence with unknown priors.

** Upper Bounds for the Error Probability
for Channels with Feedback
**

K. Sh. Zigangirov

pp. 159–163

**Abstract**—The author derives upper bounds for the attainable
error probability in block transmission over binary symmetrical and Gaussian
channels with feedback.

** Lower Bounds for the Reliability of
Block Codes in Binary Channels with Noisy Feedback
**

V. N. Koshelev

pp. 164–168

**Abstract**—The author compares the reliability of information
transmission in a repeat-request scheme and in a scheme with control
feedback, assuming that the capacity of the reverse channel is
restricted.

** One Method of Describing Random Fields
with a Discrete Argument
**

M. B. Averintsev

pp. 169–175

**Abstract**—The article considers a method of describing a random
field by using conditional probabilities written in the form of exponents
similar to the Gibbs distributions of statistical physics. It is shown that
this method is applicable to Markov fields with positive conditional
probabilities.

** Optimum Noncoherent Reception in
Channels with Fluctuation and Concentrated Noise
**

A. A. Sikarev

pp. 176–184

**Abstract**—The author obtains and analyzes the decision rules
for one-shot noncoherent reception in discrete-information transmission
systems; the rules are optimum under the action of fluctuation noise and
concentrated interference which can be approximated by the interfering-signal
model. Primary attention is given to the case of Rayleigh fading of signal
and noise. Expressions are obtained for the error probability, and the noise
stability of such systems is compared with that of a system which is optimum
for a channel with only normal fluctuation noise.

** Error-Correcting Codes in Channels with
Relative Phase Manipulation
**

A. E. Neifakh

pp. 185–190

**Abstract**—The article proposes a method of analysis which makes
it possible to allow for the effect of error multiplication in RPM and to
select derivative codes whose correcting capacity can be effectively used in
communications channels. Encoding and decoding procedures are developed for
derivative codes, which are of approximately the same degree of complexity as
the corresponding procedures for cyclic codes. Conditions are determined
under which the code corrects the same number of single errors and of
combinations of double adjacent errors.