Effective, error-free transmission of a sequence of bits—a
bit stream
b0b1…
b0
b1
…
—is the goal here. We found that
analog schemes, as represented by amplitude modulation, always
yield a received signal containing noise as well as the message
signal when the channel adds noise. Digital communication
schemes are very different. Once we decide how to represent
bits by analog signals that can be transmitted over wireline
(like a computer network) or wireless (like digital cellular
telephone) channels, we will then develop a way of tacking on
communication bits to the message bits that will reduce
channel-induced errors greatly. In theory, digital
communication errors can be zero, even though the channel adds
noise!
We represent a bit by associating one of two specific analog
signals with the bit's value. Thus, if
bn=0
b
n
0
, we transmit the signal
s
0
t
s
0
t
; if
bn=1
b
n
1
, send
s
1
t
s
1
t
. These two signals comprise the signal
set for digital communication and are designed with the
channel and bit stream in mind. In virtually every case, these
signals have a finite duration TT
common to both signals; this duration is known as the
bit interval. Exactly what signals we use
ultimately affects how well the bits can be received.
Interestingly, baseband and modulated signal sets can yield
the same performance. Other considerations determine how
signal set choice affects digital communication performance.
What is the expression for the signal arising from a
digital transmitter sending the bit stream
bn
bn,
n=…−101…
n
…
1
0
1
…
using the signal set
s
0
t
s
0
t
,
s
1
t
s
1
t
, each signal of which has duration
T
T?
xt=∑n=−∞∞
s
b
(
n
)
t−nT
x
t
n
s
b
(
n
)
t
nT
.
"Electrical Engineering Digital Processing Systems in Braille."