PROCEEDINGS
OF
THE
I.R.E.
through
the
attenuator
to
the
receiver.
In
this
manner,
the
gain
versus
the
cathode-potential-difference
curve
of
Fig.
17
was
obtained.
This
figure
corresponds
rather
closely
with
the
theoretical
curve
of
propagation
con-
stant
versus
the
inhomogeneity
factor,
shown
in
Fig.
1.
40
-
-
-
I,
I,-
15.ma.
30c1
X2
-2
238.volts
20fC
-
3000
me.
lo
-_
-20
CATHODE
POTENTIAL
DIFFERENCE
(V
-V2)
I~
V
L
o
10
20
30
40
so
60
70
80
90
100
110
§20
Fig.
17-Gain
versus
cathode-potential-difference
characteristics
of
the
two-velocity-type
electron-wave
tube.
At
a
frequency
of
3000
Mc
and
a
total
current
of
15
ma,
a
net
gain
of
46
db
was
obtained,
even
though
no
at-
tempt
was
made
to
match
either
the
input
or
output
circuits.
The
lack
of
appropriate
match
is
responsible
for
the
fact
that
the
gain
curve
assumes
negative
values
when
the
electronic
gain
is
not
sufficient
to
overcome
the
losses
due
to
mismatch.
At
the
peak
of
the
curve,
it
is
estimated
that
the
electronic
gain
is
of
the
order
of
80
db.
The
curves
of
output
voltage
versus
the
potential
of
the
drift
tube
were
shown
in
Figs.
8
and
9.
Fig.
9
shows
this
characteristic
for
the
electron-wave
tube
of
the
space-charge
type
illustrated
in
Fig.
5.
The
shape
of
this
curve
corresponds
rather
closely
with
the
shape
of
the
theoretical
curve
given
in
Fig.
7.
Fig.
8
shows
the
output
voltage
versus
drift-potential
characteristic
for
the
two-
velocity-type
electron-wave
tube.
When
the
drift-tube
voltage
is
high,
the
tube
behaves
like
the
two-cavity
klystron
amplifier.
As
the
drift
voltage
is
lowered
the
gain
gradually
increases,
due
to
the
space-charge
inter-
action
effect,
and
achieves
a
maximum
which
is
ap-
proximately
60
db
higher
than
the
output
achieved
with
klystron
operation.
With
further
reduction
of
the
drift-
tube
potential
the
output
drops
rather
rapidly,
because
the
space-charge
conditions
become
unfavorable;
that
is,
the
inhomogeneity
factor
becomes
too
large.
The
electronic
bandwidth
was
measured
by
measur-
ing
the
gain
of
the
tube
over
a
frequency
range
from
2000
to
3000
Mc
and
retuning
the
input
and
output
cir-
cuits
for
each
frequency.
It
was
observed
that
the
gain
of
the
tube
was
essentially
constant over
this
frequency
range,
thus
confirming
the
theoretical
prediction
of
electronic
bandwidth
of
over
30
per
cent
at
the
gain
of
80
db.
The
electron-wave
tube,
because
of
its
remarkable
property
of
achieving
energy
amplification
without
the
use
of
any
resonant
or
waveguiding
structures
in
the
amplifying
region
of
the
tube,
promises
to
offer
a
satis-
factory
solution
to
the
problem
of
generation
and
amplification
of
energy
at
millimeter
wavelengths,
and
thus
will
aid
in
expediting
the
exploitation
of
that
por-
tion
of
the
electromagnetic
spectrum.
ACKNOWLEDGMENT
The
author
wishes
to
express
his
appreciation
of
the
enthusiastic
support
of
all
his
co-workers
at
the
Naval
Research
Laboratory
who
helped
to
carry
out
this
proj-
ect
from
the
stage
of
conception
to
the
production
and
tests
of
experimental
electron-wave
tubes.
The
untiring
efforts
of
two
of
the
author's
assistants,
C.
B.
Smith
and
R.
S.
Ware,
are
particularly
appreciated.
Communication
in
the
Presence
of
Noise*
CLAUDE
E.
SHANNONt,
MEMBER,
IRE
Summary-A
method
is
developed
for
representing
any
com-
munication
system
geometrically.
Messages
and
the
corresponding
signals
are
points
in
two
"function
spaces,"
and
the
modulation
process
is
a
mapping
of
one
space
into
the
other.
Using
this
repre-
sentation,
a
number
of
results
in
communication
theory
are
deduced
concerning
expansion
and
compression
of
bandwidth
and
the
threshold
effect.
Formulas
are
found
for
the
maxmum
rate
of
trans-
mission
of
binary
digits
over
a
system
when
the
signal
is
perturbed
by
various
types
of
noise.
Some
of
the
properties
of
"ideal"
systems
which
transmit
at
this
maxmum
rate
are
discussed.
The
equivalent
number
of
binary
digits
per
second
for
certain
information
sources
is
calculated.
*
Decimal
classification:
621.38.
Original
manuscript
received
by
the
Institute,
July
23,
1940.
Presented,
1948
IRE
National
Conven-
tion,
New
York,
N.
Y.,
March
24,
1948;
and
IRE
New
York
Section,
New
York,
N.
Y.,
November
12,
1947.
t
Bell
Telephone
Laboratories,
Murray
Hill,
N.
J.
I.
INTRODUCTION
A
GENERAL
COMMUNICATIONS
system
is
shown
schematically
in
Fig.
1.
It
consists
essen-
tially
of
five
elements.
1.
An
information
source.
The
source
selects
one
mes-
sage
from
a
set
of
possible
messages
to
be
transmitted
to
the
receiving
terminal.
The
message
may
be
of
various
types;
for
example,
a
sequence
of
letters
or
numbers,
as
in
telegraphy
or
teletype,
or
a
continuous
function
of
timef(t),
as
in
radio
or
telephony.
2.
The
transmitter.
This
operates
on
the
message
in
some
way
and
produces
a
signal
suitable
for
transmis-
sion
to
the
receiving
point
over
the
channel.
In
teleph-
10
January
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