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Communication Systems IK1500 Anders Västberg [email protected] 08-790 44 55 IK1500 1 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/programkurser/kurshemsidor/ict/cos/IK1500/HT08-1 HT08/P1 IK1500 2 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 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/Ma thematica/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 coder and packetizer Depacketizer voice decoder Voice coder and packetizer Depacketizer voice decoder Communication link Router C bits/s Voice coder and packetizer Router Depacketizer voice decoder Problem: Given a link speed of C, maximize the number of simultaneous calls subject to a constraint on voice quality. HT08/P1 IK1500 13 [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. HT08/P1 IK1500 14 Queuing Model B C • 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 HT08/P1 IK1500 15 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 HT08/P1 IK1500 16 Multiplexer Buffer Level bits dropped B 0 time HT08/P1 IK1500 17 Maximum load that can be offered Results 1.2 1 0.8 0.6 0.4 bit-dropping low-bit -rate coding 0.2 0 0 HT08/P1 5 20 15 10 delay bound (in packet transmission times) IK1500 25 30 18 Achievable Throughput in an Input-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 HT08/P1 IK1500 19 [kumar, et. al., 2004] Input-queued (IQ) switch time c4 b3 a1 f1 e1 d1 h2 g2 j3 i2 HT08/P1 1 1 2 2 f a e d i h g 4 X4 3 Switch 4 3 4 IK1500 b j c 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 representation N=2 0.25 0.5 1, 1 0.25 0.25 0.25 Number of states = N 0.25 0.25 N 0.25 0.25 0.25 0.25 0.25 1, 2 2, 1 2, 2 0.5 0.25 HT08/P1 IK1500 22 Saturation throughput N Saturation throughput 1 1.0000 Capacity of a switch is the maximum 2 0.7500 rate at which packets can arrive and be served with a bounded delay. 3 0.6825 4 0.6553 The insight gained: 5 0.6399 capacity ≈ saturation throughput 6 0.6302 7 0.6234 8 0.6184 Converges to: 2 2 0.586 HT08/P1 IK1500 23