Proceedings of Symposia in Applied Mathematics
Volume 31, 1985
P. A. Humblet1
ABSTRACT. These lecture notes are intended as an introduction to the problem
of transmitting digital data on analog channels subject to noise and distortion.
Modulation, detection and coding theories are reviewed to the extent they apply
directly to practical systems. Some non classical problems that arise when a
channel is shared by many users are also treated.
1. INTRODUCTION. The purpose of these notes is to discuss the problem of reliably
transmitting information on analog circuits, like telephone lines, which are subject to noise and
various kinds of distortions.
The need to do this efficiently arose first for defense in the 1950's and grew to the point where
commerce and industry are almost as dependent on efficient and reliable digital communication as
they are on voice communication.
At the outset engineers had all the essential theoretical ingredients at hand: classical detection
theory, Nyquist's work on characterizing waveshapes allowing independent transmissions of a
sequence of digits, and Shannon's information theory. It shows the existence of a maximum rate
at which information can be transmitted as reliably as desired, provided one is willing to build
complex encoders and decoders.
Sections 2, 3 and 4 will give a brief review of these theories, and outline how they are actually
With the recent advent of computer networks, where data is typically generated in a bursty
fashion, it makes economical sense to share communication channels between different "streams" of
traffic. Thus a method must be found to decide what stream can use the channel at a given time,
and addressing information must also be transmitted on the channel. This leads to new problems
that will be described in Section 5.
Supported by NSF Grant ECS 79-19880.
© 1985 American Mathematical Society
0160-7634/85 $1.00 + $.25 per page
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