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Communication Systems IK1500. Anders Västberg [email protected] 08-790 44 55. IK1500 Communication Systems. TEN1: 7,5 hec. Seminars Active participation in the seminars gives the grade E. For higher grades or if you missed the seminars then you can write the exam. Required reading: - PowerPoint PPT Presentation
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HT08/P1 IK1500 2
IK1500 Communication Systems
• TEN1: 7,5 hec. • Seminars
– Active participation in the seminars gives the grade E. For higher grades or if you missed the seminars then you can write the exam.
• 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/HT09-1
HT08/P1 IK1500 3
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
HT08/P1 IK1500 4
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/
HT08/P1 IK1500 5
Course Overview
HT08/P1 IK1500 6
HT08/P1 IK1500 7
HT08/P1 IK1500 8
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
HT08/P1 IK1500 9
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!
HT08/P1 IK1500 10
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
HT08/P1 IK1500 11
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
HT08/P1 IK1500 12
Example: Efficient Transport of Packet Voice Calls
Voice coderand packetizer
Voice coderand packetizer
Voice coderand packetizer
Depacketizervoice decoder
Depacketizervoice decoder
Depacketizervoice 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
HT08/P1 IK1500 13
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.
HT08/P1 IK1500 14
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
HT08/P1 IK1500 15
Design alternatives• Bit-dropping at the multiplexer
– If the buffer level would exceed B, then drop excess bits
– Same as 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
HT08/P1 IK1500 16
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
HT08/P1 IK1500 18
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]
HT08/P1 IK1500 19
Input-queued (IQ) switch
4 X 4Switch
time
a1b3c4
f1 e1 d1
g2h2
j3 i2
f a e d
ghi
jb
c
3
4
2
1
4
3
2
1
HT08/P1 IK1500 20
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).
HT08/P1 IK1500 21
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
HT08/P1 IK1500 22
Saturation throughputN Saturation throughput1 1.00002 0.75003 0.68254 0.65535 0.63996 0.63027 0.62348 0.6184
Converges 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
HT08/P1 IK1500 23
Virtual Output Queuing
• A virtual output queue at input i for output j and is denoted by VOQij
• Maximum-weight matching algorithm
2 2VOQ21
VOQ12
VOQ11Q111 1Q12
Q22
2 x 2switch Q21
VOQ22