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Communication Systems IK1500. Anders Västberg vastberg@kth.se 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:
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Communication SystemsIK1500 Anders Västberg vastberg@kth.se 08-790 44 55 IK1500
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 IK1500
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
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
Course Overview IK1500
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
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
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
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
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]
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
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
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 IK1500
Multiplexer Buffer Level IK1500
Results Maximum load that can be offered IK1500
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]
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
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
Number of states Markov chain representationN=2 IK1500
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
VOQ 11 Q 11 1 1 VOQ Q 12 12 2 x 2 switch Q 21 VOQ 21 2 2 Q 22 VOQ 22 Virtual Output Queuing • A virtual output queue at input i for output j and is denoted by VOQij • Maximum-weight matching algorithm IK1500