Source coding theory has as its goal the characterization of the
optimal performance achievable in idealized communication systems
which must code an information source for transmission over a
digital communication or storage channel for transmission to a
user. The user must decode the information into a form that is a
good approximation to the original. A code is optimal within some
class if it achieves the best possible fidelity given whatever
constraints are imposed on the code by the available channel. In
theory, the primary constraint imposed on a code by the channel is
its rate or resolution, the number of bits per second or per input
symbol that it can transmit from sender to receiver. In the real
world, complexity may be as important as rate. The origins and the
basic form of much of the theory date from Shan non's classical
development of noiseless source coding and source coding subject to
a fidelity criterion (also called rate-distortion theory) [73]
[74]. Shannon combined a probabilistic notion of information with
limit theo rems from ergodic theory and a random coding technique
to describe the optimal performance of systems with a constrained
rate but with uncon strained complexity and delay. An alternative
approach called asymptotic or high rate quantization theory based
on different techniques and approx imations was introduced by
Bennett at approximately the same time [4]. This approach
constrained the delay but allowed the rate to grow large.
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