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```Communication Systems
IK1500
Anders Västberg
[email protected]
08-790 44 55
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IK1500 Communication Systems
• TEN1: 7,5 hec.
• Problem assignments
– Each assignment covers one problem of the exam. If you
complete the problem assignment successfully, then you will get
the full points for the corresponding problem on the exam
(only for the ordinary exam – not for any makeup exam
(“omtenta”)).
– Kumar, Manjunath, & Kuri, Communication Networking, Elsevier,
2004.
– G. Blom, et.al., Sannolikhetsteori och statistikteori med
tillämpningar, Studentlitteratur, 2005
• Course Webpage:
– http://www.kth.se/student/programkurser/kurshemsidor/ict/cos/IK1500/HT08-1
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Teachers
• Anders Västberg
– [email protected]
– 08-790 44 55
– [email protected]
– 08-790 44 28
• Bengt Lärka
– [email protected]
– 08-790 44 47
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Supplementary rules for
examination
• Rule 1: All group members are responsible for
group assignments
• Rule 2: Document any help received and all
sources used
• Rule 3: Do not copy the solutions of others
• Rule 4: Be prepared to present your solution
• Rule 5: Use the attendance list correctly
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Mathematica
– http://progdist.ug.kth.se/public/
• General introduction to Mathematica
– http://www.cos.ict.kth.se/~goeran/archives/Ma
thematica/Notebooks/General/
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Course Overview
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Course Aim
• Gain insight into how communication
systems work (building a mental model)
model and what to model
• Use mathematical modelling to analyse
models of communication networks
• Learning how to use power tools
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Modelling
• Find/built/invent a model of some specific system
• Why?
characteristics and behaviour.
• Alternative: Do measurements!
– However, this may be:
• too expensive: in money, time, people, …
• too dangerous: physically, economically, …
– or the system may not exist yet (a very common cause)
• Often because you are trying to consider which system to build!
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Modelling
• Models have limited areas of validity
• The assumptions about input parameters
and the system must be valid for the
model to give reliable results.
• Models can be verified by comparing the
model to the real system
give insight about what to measure
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Use of models
• Essential as input to simulations
• Use models to detect and analyse errors
– Is the system acting as expected?
– Where do I expect the limits to be?
• Model-based control systems
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Example: Efficient Transport of
Packet Voice Calls
Voice coder
and packetizer
Depacketizer
voice decoder
Voice coder
and packetizer
Depacketizer
voice decoder
Router
C bits/s
Voice coder
and packetizer
Router
Depacketizer
voice decoder
Problem: Given a link speed of C, maximize
the number of simultaneous calls subject
to a constraint on voice quality.
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[Kumar, et. al., 2004]
Voice Quality
• Distortion
– The voice is sampled and encoded by, for example, 4
bits.
– At least a fraction a of the coded bits must be
received for an acceptable voice quality.
Example: If a=0.95, then at least 3.8 bits per sample
must be delivered.
• Delay
– Packets arrive at the link at random, only one packet
can be transmitted at a time, this will cause queuing
of packets, which will lead to variable delays.
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Queuing Model
B
C
• B bits: The level of the multiplexer buffer that should
seldom be exceeded.
• C bits/s: Speed of the link
 Leads to the delay bound B/C (s) to be rarely exceeded
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Design alternatives
• Bit-dropping at the multiplexer
– If the buffer level would exceed B, then drop excess
bits
– Buffer adaptive coding (the queue length controls the
source encoder)
 Closed loop control
• Lower bit-rate coding at the source coder
– Lower the source encoder bit rate
– The probability of exceeding buffer level B is less than
a small number (e.g. 0.001).
 Open loop control
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Multiplexer Buffer Level
bits dropped
B
0
time
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Maximum load that can be offered
Results
1.2
1
0.8
0.6
0.4
bit-dropping
low-bit -rate coding
0.2
0
0
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delay bound (in packet transmission times)
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Achievable Throughput in an
Input-Queuing Packet Switch
• N input ports and N output ports
• More than one cell with the same output
destination can arrive at the inputs
• This will cause destination conflicts.
• Two solutions:
– Input-queued (IQ) switch
– Output –queued (OQ) switch
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[kumar, et. al., 2004]
Input-queued (IQ) switch
time
c4 b3 a1
f1 e1 d1
h2 g2
j3 i2
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1
2
2
f
a e d
i
h g
4 X4
3
Switch
4
3
4
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j
c
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Output – queued (OQ) switch
• All of the input cells (fixed size small
packets) in one time slot must be able to
be switched to the same output port.
• Can provide 100% throughput
• If N is large, then this is difficult to
implement technically (speed of memory).
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Markov chain representation
N=2
0.25
0.5
1, 1
0.25
0.25
0.25
Number of states = N
0.25
0.25
N
0.25
0.25
0.25
0.25
0.25
1, 2
2, 1
2, 2
0.5
0.25
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Saturation throughput
N Saturation throughput
1 1.0000
Capacity of a switch is the maximum
2 0.7500
rate at which packets can arrive and be
served with a bounded delay.
3 0.6825
4 0.6553
The insight gained:
5 0.6399
capacity ≈ saturation throughput
6 0.6302
7 0.6234
8 0.6184
Converges to: 2  2  0.586
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