Lecture Outline (Week 15, lecture 1)
Review of Digital Communication
Reading:
Focus on these notes.
1. Basic Elements of Digital Communication
•
Basic block diagram of a digital communication system.
•
Basic equation governing source: Nyquist sampling and entropy rate of source
)
(
X
H
R
=
•
Basic equation governing channel: Shannon’s formula
)
1
(
log
0
2
W
N
P
W
C
+
=
(Bits/sec)
•
Channel: Power and interference budgets. Channel impairments. Multiple access.
2. Elements of Source Encoding
•
Digitizing of an analog source includes:
•
Sampling at twice the highest frequency of signal, i.e.
W
T
f
s
2
/
1
≥
=
.
•
Nyquist sampling theorem, signal can reconstructed by
∑


=
n
nT
t
T
nT
t
T
nT
x
t
x
)
(
1
))
(
1
sin(
)
(
)
(
~
•
Quantizing samples into
v
bits with quantization error for uniform quantization:
8
.
4
02
.
6
]
[
log
10
2
10
+
+
=
v
X
E
SQNR
dB where
max
x
X
X
=
•
May use nonuniform quantizer such as
μ
law compander.
•
After digitization, we perform data compression:
•
Universal data compression such as LempelZiv codes
•
Optimal Huffman Codes achieves close to
)
(
X
H
R
=
1
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3. Modulation Techniques and Signal Space Representation.
•
Digital modulation techniques:
•
Pulse Amplitude Modulation(PAM)
∑
∞
∞
=

=
n
n
nT
t
h
a
t
x
)
(
)
(
, 4PAM:
}
3
,
,
,
3
{
A
A
A
A
a
n
+
+


∈
•
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 Spring '09
 Hui
 signal space, Signal Space Representation. • Digital, signal point, dB more signal, Signal Space Representation.

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