On April 24, 1995, Prof. Mark S. Pinsker turned 70. In this note we try to describe some of his scientific results. It is impossible to give a comprehensive account of his contributions not only because of his numerous publications but also because his ideas and results were very influential in initiating new scientific branches. Mark studied very natural questions and concepts which, once introduced by him, made one wonder why they had not been addressed before. Mark's principal areas of interest at various times were probability theory, information theory, coding theory, ergodic theory, mathematical statistics, and communication networks.
Some of his papers were written in collaboration with his colleagues and friends. We apologize for not mentioning their names in this short note. We were also forced to leave out many references; the total number of Mark's papers being about 150.
Mark Pinsker began his scientific work at the famous probability school of A. N. Kolmogorov in the 50's, studying stochastic processes. His activity in ergodic theory was inspired by the famous paper of Kolmogorov introducing the notion of entropy of dynamical system. Mark published only one paper on dynamical systems with completely positive and zero entropy [1]. In this classic paper, Mark introduced the maximal partition with zero entropy which later became known as Pinsker's partition and played a very crucial role in the entropy theory of dynamical systems. Mark influenced the work of many others and proved additional results on this topic that he himself did not publish. Some of these results were published later by other authors, sometimes with a reference to him. For example, Mark gave a very beautiful proof of the theorem that, in dynamical systems with continuous time, the entropy of the automorphism belonging to a flow is a linear function of the time. His proof now appears in many textbooks on dynamical systems.
Mark's early work in mathematical statistics
was devoted mostly to the applications of information theory.
In particular, he proposed the concept of
asymptotically sufficient statistics for parameter estimation
based on the Shannon information
about the parameter contained in a sample.
But, Mark's most famous results are related to nonparametric estimation problems.
In the 70's Ibragimov and Hasminskii obtained
nonparametric estimates of a signal in
Gaussian white noise of small intensity when the signal
is known to be contained in a given ellipsoid in a Hilbert space.
These estimates had the asymptotically optimal order of convergence.
A generally shared view at that time almost ruled out the possibility of
more precise results. But in the early 80's, M. Pinsker proposed
an estimator, which was not only asymptotically optimal in order
of convergence of the risk, but also provided the best possible constant of convergence in the 
-norm [2].
This result had great impact on the statistical community and
has become a major theme.
Adaptive nonparametric estimation is yet another important and very popular area that was initiated by Mark's work [3].
In addition to his famous monograph [4], we mention some of M. Pinsker's other contributions to information theory. In a series of important works [5,6], he established the capacity region of a deterministic and semi-deterministic discrete memoryless broadcast channel. He also found the capacity region of a stationary Gaussian broadcast channel, proved converse coding theorems for Gaussian sources with side information, and established the zero-error capacity region of a discrete memoryless multiple-access channel with asymmetric communication.
M. Pinsker obtained several outstanding results in the theory
of switching networks. Most previous work had been concerned with
devising constructions which did not attain known lower bounds
of circuit complexity. Mark proposed a new approach based on combining
the construction with a random choice of some of its elements, which
allowed him to obtain an asymptotically optimal concentrator
with cn switches [7] and nonblocking network
with 
switches. Undoubtedly, these results are among the
most remarkable in this theory.
M. Pinsker was one of the first to precisely formulate
complexity problems in coding theory [8,9].
He also obtained a number of outstanding results related to asymptotic
complexity problems.
In [8], he introduced a concatenated coding scheme
with inner block and outer convolutional codes, for which the
average decoding complexity per symbol is bounded by
a constant independent of the code length for all code rates
less than capacity.
His other results include a proof of the existence of codes whose distance and encoding complexity both grow linearly with
the code length and the existence of codes whose distance grows linearly and decoding complexity grows as 
, and that can correct a linear fraction of errors.
Finally, M. Pinsker constructed
a sequence of codes meeting the Varshamov-Gilbert bound with
nonexponential complexity of the bounded distance decoding.
M. Pinsker initiated several research topics in coding theory, suggesting numerous generalizations of the conventional transmission model with random errors. Mark suggested a novel method of coding, for the situation when the encoder has partial information on the errors in the channel, that is fundamentally different from the standard random choice of codes with minimal distance decoding. This allowed him to prove a very natural though highly nontrivial asymptotic bound on the size of codes that correct errors and defects [10] and an asymptotically tight bound on the size of codes that correct localized errors. These results were very unusual for coding theory. The asymptotic problem for these codes (in the binary case) was solved in all major respects in [11]. In [12], a promising relation between these codes and arbitrarily varying channels is established. Finally, in his most recent paper [13], a formula for the sensitivity of Gaussian channel capacity to non Gaussian noise is obtained.
Happy birthday, Mark!