IK15001

Communication SystemsIK1500

Anders Västbergvastberg@kth.se

08-790 44 55

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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

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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 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

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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

– 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

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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 4Switch

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 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

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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