1 ik1500 communication systems ik1500 anders västberg [email protected] 08-790 44 55
TRANSCRIPT
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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”)).
• Required reading:– 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/program-kurser/kurshemsidor/ict/cos/IK1500/HT08-1
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Teachers
• Anders Västberg – [email protected]– 08-790 44 55
• Göran Andersson– [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
• Download the program from:– http://progdist.ug.kth.se/public/
• General introduction to Mathematica– http://www.cos.ict.kth.se/~goeran/archives/
Mathematica/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)
• Develop your intuition about when to 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?
– We want to answer questions about the system’s 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
• Models help you not only with design, but 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
Voice coder
and packetizer
Voice coderand packetizer
Depacketizervoice decoder
Depacketizer
voice decoder
Depacketizer
voice decoder
Communication link
Router Router
Problem: Given a link speed of C, maximize the number of simultaneous calls subject to a constraint on voice quality.
[Kumar, et. al., 2004]
C bits/s
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Voice Quality
• Distortion– The voice is sampled and encoded by, for example, 4
bits.– At least a fraction of the coded bits must be
received for an acceptable voice quality.Example: If 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 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
B C
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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
B
bits dropped
time0
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Results
0 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
1.2
delay bound (in packet transmission times)
bit-droppinglow-bit-rate coding
Max
imum
load
that
can
be
offe
red
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Achievable Throughput in anInput-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
[kumar, et. al., 2004]
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Input-queued (IQ) switch
4 X 4
Switch
time
a1b3c4
f1 e1 d1
g2h2
j3 i2
f a e d
ghi
jb
c
3
4
2
1
4
3
2
1
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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 representationN=2
0.25
0.25
0.25
0.25
0.25
0.25
0.5
0.250.25
0.25
0.25
0.5
0.25
0.25
1,1 1,2
2,22,1
Number of states NN
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Saturation throughputN Saturation throughput
1 1.0000
2 0.7500
3 0.6825
4 0.6553
5 0.6399
6 0.6302
7 0.6234
8 0.6184Converges to: 586.022
Capacity of a switch is the maximum rate at which packets can arrive and be served with a bounded delay.
The insight gained: capacity ≈ saturation throughput