... bandwidth constraint
Nyquist bandwidth constraint:
The theoretical minimum required system bandwidth to
detect Rs [symbols/s] without ISI is Rs/2 [Hz].
Equivalently, a system with bandwidth ...
filter
Equalizing
filter
Threshold
comparison
For bandpass signals
Compensation for
channel induced ISI
Baseband pulse
(possibly distored)
Sample
(test statistic)
Baseband pulse
Received waveform
Step 1 – ... [symbols/s] without ISI.
Bandwidth efficiency, R/W [bits/s/Hz] :
An important measure in DCs representing data
throughput per hertz of bandwidth.
Showing how efficiently the bandwidth resources...
... features of digital communication
systems
Some basic concepts and definitions such as
as signal classification, spectral density,
random process, linear systems and signal
bandwidth.
Lecture ... stream
Format
Format
Digital info.
Textual
info.
Analog
info.
Textual
info.
Analog
info.
Digital info.
source
sink
Formatting and transmission of baseband signal
Lecture 2 21
M-ary pulse modulation
M-ary ... with a digital system
Lecture 2 20
Spectra of PCM waveforms
Lecture 2 10
Encoding (PCM)
A uniform linear quantizer is called Pulse Code
Modulation (PCM).
Pulse code modulation (PCM): Encoding...
... PAM
T
t
)(
1
t
ψ
T
1
0
Digital Communications I:
Modulation andCoding Course
Term 3 - 2008
Catharina Logothetis
Lecture 5
Lecture 5 2
Last time we talked about:
Receiver structure
Impact of AWGN and ISI ... noise vector are i.i.d
Gaussian random variables with zero-mean and
variance . The noise vector pdf is
The elements of observed vector are
independent Gaussian random variables. Its pdf is
), ... to maximize SNR
Matched filter and correlator receiver
Signal space used for detection
Orthogonal N-dimensional space
Signal to waveform transformation and vice versa
Lecture 5 7
Detection...
... and evaluation of the code.
Block codes are based on algebraic/combinatorial
techniques.
Convolutional codes are based on construction techniques.
Digital Communications I:
Modulation and ... encoder.
Lecture 10 10
Effective code rate
Initialize the memory before encoding the first bit (all-
zero)
Clear out the memory after encoding the last bit (all-
zero)
Hence, a tail of zero-bits is ... of data bits and k=1 is assumed:
data
Encoder
codewordtail
ceff
R
KLn
L
R <
−+
=
)1(
Lecture 10 4
Convolutional codes
Convolutional codes offer an approach to error control
coding substantially...
... ,zzZ
ZZZZ
=
=Z
Channel
Lecture 10 2
Last time, we talked about:
Channel coding
Linear block codes
The error detection and correction capability
Encoding and decoding
Hamming codes
Cyclic codes
Lecture 10 ... design and evaluation of the code.
Block codes are based on algebraic/combinatorial
techniques.
Convolutional codes are based on construction techniques.
Digital Communications I:
Modulation and ... specified by
three parameters or
where
is the coding rate, determining the
number of data bits per coded bit.
In practice, usually k=1 is chosen and we
assume that from now on.
K is the constraint...
... error correction coding?
Error performance vs. bandwidth
Power vs. bandwidth
Data rate vs. bandwidth
Capacity vs. bandwidth
(dB) /
0
NE
b
B
P
A
F
B
D
C
E
Uncoded
Coded
Coding gain:
For ... coset
kknknkn
k
k
22
2
22
2
2222
2
21
UeUee
UeUee
UUU
⊕⊕
⊕⊕
−−−
L
MOLM
L
L
zero
codeword
coset
coset leaders
kn
i
−
=
2, ,3,2
n
V
i
e
th:i
Digital Communications I:
Modulation andCoding Course
Period 3 - 2007
Catharina Logothetis
Lecture 9
Lecture 9 36
Cyclic ... detection and correction codes
Lecture 9 28
Linear block codes – cont’d
Standard array
For row , find a vector in of minimum
weight which is not already listed in the array.
Call this pattern and...
... information provides the decoder with a
measure of confidence for the decision.
Digital Communications I:
Modulation andCoding Course
Period 3 - 2007
Catharina Logothetis
Lecture 12
... each state, and keeps
only the path with the largest metric, called the
survivor, together with its metric.
Lecture 12 6
Soft and hard decision decoding …
ML soft-decisions decoding rule:
Choose ... code uses two levels on coding, an
inner code and an outer code (higher rate).
Popular concatenated codes: Convolutional codes with
Viterbi decoding as the inner code and Reed-Solomon codes...
... levels.
Decoding based on soft-bits, is called the
“soft-decision decoding”.
On AWGN channels, 2 dB and on fading
channels 6 dB gain are obtained by using
soft-decoding over hard-decoding.
Lecture ...
state
101
010
11
011
100
10
001
110
01
111
000
00
0
S
1
S
2
S
3
S
0
S
2
S
0
S
2
S
1
S
3
S
3
S
1
S
0
S
1
S
2
S
3
S
1/11
1/00
1/01
1/10
0/11
0/00
0/01
0/10
Input
Output
(Branch word)
Modulation, Demodulation and
Coding Course
Period 3 - 2007
Catharina Logothetis
Lecture 11
... level) which are called “hard-
bits”.
Decoding based on hard-bits is called the
“hard-decision decoding”.
Lecture 11 23
Example of Hard decision Viterbi
decoding-cont’d
i=3
0
2
0
1
2
1
0
1
1
0
1
2
2
1
0
2
1
1
1
6
t
1
t
2
t
3
t
4
t
5
t
1
0
2...
...
Input
Output
Linear system
Digital Communication I:
Modulation andCoding Course
Period 3 - 2007
Catharina Logothetis
Lecture 1
Lecture 1 12
Digital versus analog
Advantages of digital communications:
Regenerator ... issues in designing a digital
communication system (DCS):
Utilized techniques
Formatting and source coding
Modulation (Baseband and bandpass signaling)
Channel coding
Equalization
Synchronization
... ergodic in mean and autocorrelation,
if
and
, respectively.
Lecture 1 7
Practical information
Course material
Course text book:
Digital communications: Fundamentals and Applications”...
... variance:
2
Sat
2
Lin
222
)()(})]({[
σσσ
+==−=
∫
∞
∞−
dxxpxexqx
q
E
ll
L
l
l
qxp
q
)(
12
2
12/
0
2
2
Lin
∑
−
=
=
σ
Uniform q.
12
2
2
Lin
q
=
σ
Digital Communications I:
Modulation andCoding Course
Period 3 – 200/
Catharina Logothetis
Lecture 2
Lecture 2 18
PCM waveforms
PCM ... about:
Important features of digital communication
systems
Some basic concepts and definitions as signal
classification, spectral density, random
process, linear systems and signal bandwidth.
Lecture ... NRZ
Lecture 2 21
M-ary pulse modulation
M-ary pulse modulations category:
M-ary pulse-amplitude modulation (PAM)
M-ary pulse-position modulation (PPM)
M-ary pulse-duration modulation (PDM)
M-ary...
... with a digital system
Sampling
Aliasing
Quantization
Uniform and non-uniform
Baseband modulation
Binary pulse modulation
M-ary pulse modulation
M-PAM (M-ay Pulse amplitude modulation)
Lecture ... symbol
Mi ,,1 K
=
M-ary modulation
Lecture 3 13
Baseband and bandpass
Bandpass model of detection process is
equivalent to baseband model because:
The received bandpass waveform is first ... goals.
First, we focus on designing a receiver which
maximizes the SNR.
Digital Communication I:
Modulation andCoding Course
Period 3 - 2007
Catharina Logothetis
Lecture 3
Lecture 3 20
Implementation...
... filters
)()( tTstrz
i
i
−∗=
∗
Mi , ,1
=
), ,,())(), ,(),((
2121 MM
zzzTzTzTz
=
=z
Digital Communications I: Modulation
and Coding Course
Period 3 - 2007
Catharina Logothetis
Lecture 4
Lecture 4 11
Signal ... A
0
1
s
2
s
T
A
T
A−
0
0
Tt
)(
1
t
ψ
T
1
0
0)()()()(
)()()(),(
/)(/)()(
)(
122
0
1212
1111
0
2
2
11
=−−=
−=>=<
==
==
∫
∫
tAtstd
Adtttstts
AtsEtst
AdttsE
T
T
ψ
ψψ
ψ
1
2
Lecture 4 3
Receiver job
Demodulation and sampling:
Waveform recovery and preparing the received
signal for detection:
Improving the signal ...
filter
Equalizing
filter
Threshold
comparison
For bandpass signals
Compensation for
channel induced ISI
Baseband pulse
(possibly distored)
Sample
(test statistic)
Baseband pulse
Received waveform
Step 1 –...
... PAM
T
t
)(
1
t
ψ
T
1
0
Digital Communications I:
Modulation andCoding Course
Period 3 - 2007
Catharina Logothetis
Lecture 5
Lecture 5 20
Eb/No figure of merit in digital
communications
SNR ... noise vector are i.i.d
Gaussian random variables with zero-mean and
variance . The noise vector pdf is
The elements of observed vector are
independent Gaussian random variables. Its pdf is
), ... liesPr()(
)(1)(
icie
mPmP
−
=
i
m
i
s
z
i
Z
sent) and
ˆ
Pr()(
iiie
mmmmP
≠
=
Lecture 5 16
Union bound
Let denote that the observation vector is closer to
the symbol vector than , when is transmitted.
depends only on and .
Applying...
... Polytechnic Institute and State University
Blacksburg, Virginia
Multi-Carrier Digital Communications: Theory and Applications of OFDM
Ahmad R. S. Bahai and Burton R. Saltzberg
Principles of Digital Transmission: ... publisher.
Multi-Carrier
Digital Communications
Theory and Applications of OFDM
Introduction to DigitalCommunications 11
(illustrated in Figure 1.6). Unlike the non-bandlimited OFDM, each carrier
must ... the modulation and
demodulation processes [7]. Fortunately, this occurred at the same time
digital signal processing techniques were being introduced into the design of
Multi-Carrier
Digital Communications
Theory...
... Industry and Economics
The UNEP Division of Technology, Industry and Economics (DTIE) helps governments, local authorities and
decision-makers in business and industry to develop and implement ...
The economic and social context for sustainability
communications
1. CSR and communication : regulation, controls and voluntary
initiatives
a) Definitions: legalistic and voluntaristic ... Economics and Management 43(3), 339-359
See the bibliography on sustainable development and on Communicationsand Sustainable Development
30
3 - Sustainable development and its...