Problems of Information Transmission, Vol. 38, No. 3, 2002, pp. 247–248. Translated from Problemy Peredachi Informatsii, No. 3, 2002, pp. 94–95.
Original Russian Text Copyright
2002 by the Editorial Board.
On the 100th Anniversary since the Birth
of Andrei Nikolaevich Kolmogorov
Dear Roland L’vovich,
I have looked through the ﬁrst part of your book
with interest. It is vividly written. I have not
checked its logical strictness, but I am totally conﬁdent in your skill in this case. I am sorry, but
lack of time has not permitted me to make any speciﬁc comment that might have been useful for
Following the publication of your article in Uspekhi Matematicheskikh Nauk,
the question on
issuing a corresponding book was put forth. I do not remember how this matter ended. Of course,
we thought it to be a book with a broad coverage, particularly of the case of continuous messages
and, more generally, of higher knowledge. In any case, the idea of asking you to write a book on
general problems of the Shannon theory seemed natural to me.
You have asked my opinion on issuing separately the ﬁrst part of your book now ready. In light
of all that I said before, I would be ready to support the publication of a book like this as a slightly
altered version of the idea of your book on the Shannon theory for general purposes. I mean that
it should not only be designed for engineers especially interested in knowing everything that is
practically useful for them in coding.
I support the translation of Peterson’s book
as well. There I have found partial answers to
the questions I mentioned to you this fall. This book contains a lot of information on algebraic
coding theory, and further work in this ﬁeld requires profound algebra. It seems to me that it
would be good for someone to write a short article (about two pages long) to attract the attention
of algebraists towards these questions. The article would have to contain everything important that
has been obtained with the use of Galois ﬁelds, a clear explanation of the state of the art concerning
the problem of divergence between upper and lower bounds (see Peterson’s book, Figs. 4.1 and 9.1),
as well as what can be obtained by practically realizable algebraic calculation methods (given in
all details, with numerical data as a possible example of the type of information for constructed
codes, in brief).
From the contents of the further parts of your book (no matter how they will be published), it is
not clear for me whether your collaborators are still planned to master this subject to the extent
that the work of your group
really corresponds to the complete technically applicable knowledge of
We publish here a letter from A.N. Kolmogorov to R.L. Dobrushin and Kolmogorov’s letter of reference
for Dobrushin in support of promoting him to the rank of senior research fellow.—Note by L.E. Filippova.
Since October 1960 Dobrushin had been working on a book that had to contain (in project) a thorough
exposition of mathematical information theory. The ﬁrst (“discrete”) part of the book was given to
Kolmogorov to look through.—L.F.
Dobrushin, R.L., A General Formulation of the Basic Shannon Theorem in Information Theory, Usp. Mat.
Nauk, 1959, vol. 14, no. 6, pp. 3–103 [Rep. Soviet Acad. Sci., 1959, vol. 126, no. 3, pp. 474–477].—L.F.
Peterson, W.W., Error-Correcting Codes, Cambridge: MIT Press, 1961. Translated under the title
Kody, ispravlyayushchie oshibki, Moscow: Mir, 1964 (Russian translation by L.E. Filippova, edited by
Dobrushin was the head of the research group of the statistics laboratory of the probability theory chair,
department of mechanics and mathematics, Moscow State University.—L.F.
2002 MAIK “Nauka/Interperiodica”