Communication Systems IK1500

1. Communication SystemsIK1500 Anders Västberg vastberg@kth.se 08-790 44 55 IK1500

2. 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 IK1500

3. Teachers • Anders Västberg • vastberg@kth.se • 08-790 44 55 • Göran Andersson • goeran@kth.se • 08-790 44 28 • Bengt Lärka • bengan@kth.se • 08-790 44 47 IK1500

4. 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 IK1500

5. 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/ IK1500

6. Course Overview IK1500

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9. 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 IK1500

10. 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! IK1500

11. Modelling • Models have limited areas of validity • The assumptions about input parameters and the systemmust 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 IK1500

12. 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 IK1500

13. Voice coder Depacketizer and packetizer voice decoder Depacketizer Voice coder voice decoder and packetizer Communication link Router Router Voice coder Depacketizer and packetizer voice decoder Example: Efficient Transport of Packet Voice Calls C bits/s Problem: Given a link speed of C, maximize the number of simultaneous calls subject to a constraint on voice quality. IK1500 [Kumar, et. al., 2004]

14. 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. IK1500

15. 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 IK1500

16. 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 IK1500

17. Multiplexer Buffer Level IK1500

18. Results Maximum load that can be offered IK1500

19. 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 IK1500 [kumar, et. al., 2004]

20. time 1 1 f a e d c4 b3 a1 g 2 2 i h f1 e1 d1 4 X 4 Switch 3 3 b j h2 g2 4 4 c j3 i2 Input-queued (IQ) switch IK1500

21. 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). IK1500

22. Number of states Markov chain representationN=2 IK1500

23. Converges to: Saturation throughput N Saturation throughput 1 1.0000 2 0.7500 3 0.6825 4 0.6553 5 0.6399 6 0.6302 7 0.6234 8 0.6184 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 IK1500