Preliminaries
In this section we summarize some basic definitions and relations which will be used freely in the sequel: the simple proofs will be sketched only.
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L E C T U R E S - No 29
IMRE CSISZAR MATHEMATICAL INSTITUTE HUNGARIAN ACADEMY OF SCIENCES, BUDAPEST
CHANNEL CODING THEORY
COURSE HELD AT THE DEPARTMENT FOR AUTOMATION AND INFORMATION JULY 1970
UDJNE 1970
SPRINGER-VERLAG WIEN GMBH
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All rights are reserved, whether the whole or part of the m-aterial is concerned
specifically those of translation, reprinting, re-uae of illustration&, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1972 by Springer-Verlag Wien
Originally published by Springer-Verlag
ISBN 978-3-211-81089-7
Wien-New York
in 1972
ISBN 978-3-7091-2724-7 (eBook)
DOI 10.1007/978-3-7091-2724-7
P R E F A C E Mathematical information theory has been developed in order to investigate the possibilities of reliable communication over chann~ls subject to noise. Although at present the scope of information theory is considerably wider than that 3 the study of the above problem still keeps to be its central part. If the characteristics of the channel are given 3 the only way of increasing the efficiency and reliability of communication is to use proper encoding and decoding methods. As a rule 3 the first step is to represent the output of the information source in some standard form (source coding}; then 3 before en~ering ~he channel~ the messages are encoded in order to be protected against noise (channel coding}.At the output of the channel 3 the corresponding decoding operations are performed. As regards to channel coding 3 the knowledge of the optimum performance of such techniques and of how to implement encoding and decoding such as to perform not much worse than the theoretical optimum are both important. In the sequel 3 we shall concentrate on the first problem~ outlining the main existence theorems of channel coding theory for discrete cne-way channels.
Preface
4
These notes represent the material of the author's lectures at the CISM's Summer course in Udine,19?0. The author is indebted to Prof. L. Sobrero,
Secr~tary
General of CISM,
for having invited
him to give these lectures and also to Prof. G. Longo whose enthusiastic work in organizing this information theory course was a main factor of its success.
Udine, July 19?0
Preliminaries In this section we summarize some basic definitions and relations which will be used freely in the sequel : the simple proofs will be sketched only. The term "random variable" will be abbreviated as RV ; for the sake of simplicity, attention will be restricted to the case of discrete RV's,i.e., to RV's with values in a finite or countably infinite set. ~.~.~will
denote RV 1 s with values in the
(finite or countably infinite) sets X, Y, Z . All random variables considered at the same time will be assumed to be defined on the same probability space. Recall that a probability space is a triplet(~.~~P) where Q is a set (the set of all conceivable outcomes of an experiment), Tis a
~-algebra
of subsets of !l (the class of observable events) and
P is a measure (n
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