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Communication Systems and Information Theory

1. Communication Theory.Communication theory deals primarily
with systems for transmitting information or data form one point to another
A rather general block diagram for visualizing the behavior of such systems
is given in Fig. 4.1. The source output might represent, for example, a voice
waveform, a sequence of binary digits form a magnetic tape, the output of a
set of sensors in a space probe, a sensory input to a biological organism,
or a target in a radar system. The channel might represent, for example, a
telephone line, a high frequency radio link, a space communication link, a
storage medium, or a biological organism (for the case where the source
output is a sensory input to that organism). The channel is usually
subjected to various types of noise disturbances, which on a telephone line,
for example, might take the form of a time-varying frequency response,
crosstalk from other lines, thermal noise, and impulsive switching noise.
The encoder in Fig. 4.1. represents any processing of the source output
performed prior to transmission. The processing might include, for
example, any combination of modulation, data reduction, and insertion of
redundancy to combat the channel noise. The decoder represents the
processing of the channel output with the objective of producing at the
destination an acceptable replica of (or response to) the source output.

2. Information Theory.In the early 1940's a mathematical theory, for
dealing with the more fundamental aspects of communication systems, was
developed. The distinguishing characteristics of this theory are, first, a
great emphasis on probability theory and, second, a primary concern with
the encoder and decoder, both in terms of their functional roles and in
terms of the existence (or nonexistence) of encoders and decoders that
achieve a given level of performance. In the past 20 years, information
theory has been made more precise, has been extended, and brought to
the point where it is being applied in practical communication systems.

As in any mathematical theory, the theory deals only with mathematical models and not with physical sources and physical channels. One would think, therefore, that the appropriate way to begin the development of the theory would be with a discussion of how to construct appropriate mathematical models for physical sources and channels. This, however, is not the way that theories are constructed, primarily because physical reality is rarely simple enough to be precisely modeled by mathematically tractable models. The procedure will be rather to start by studying the simplest classes of mathematical models of sources and channels, using the insight and the results gained to study progressively more complicated classes of models. Naturally, the choice of classes of models to study will be influenced and motivated by the more important aspects of real sources and channels, but the view of what aspects are important will be modified by the theoretical results. Finally, after understanding the theory, it can be found to be useful in the study of real communication systems in two ways. First, it will provide a framework within which to construct detailed models of real sources and channels. Second, and more important, the relationships established by the theory provide an indication of the types of tradeoffs that exist in constructing encoders and decoders for given systems. While the above comments can be applied to almost any mathematical theory, they are particularly necessary here because quite an extensive theory must be developed before the more important implications for the design of communication systems will become apparent.

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