Lecture Series in Mobile Telecommunications and Networks (1583KB)

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From wireless networks to sensor networks and onward to networked embedded contrtol information? In fact, if you are sending this information over multiple paths to your destination, then perhaps it is only the case that the end-point has sufficient signal strength to decode the information, and not the intermediate points. Thus, this architecture of decoding and treating interference as noise limits itself from the start. As Shakespeare said, through Hamlet, the world is extremely complicated. The fundamental question is, what is the best architecture for wireless networks? The point is that the design space is infinite-dimensional and there are so many sophisticated things we could do. To get to the bottom of this, we have to seek answers with information theory. Network information theory As many of you know, information theory was invented by Claude Shannon in 1948, about 60 years ago. A very celebrated formula, for example, is the capacity for Gaussian channel which says that, if you have a spectrum of bandwidth (B), signal strength (S) and noise strength (N), then this is the absolute limit on the number of bits per second of information that you can transmit. So, for example, if you have a telephone wire and you tell me how much noise there is on it, Shannon tells us exactly how much throughput that wire can take. That kind of fundamental result allows for any mode of operation: no matter what you do, you cannot beat this formula. This is fundamentally good because, once you have some kind of law of thermodynamics, you have some limit, then you know when you are close to it that you can quit trying. Information theory has had much success in point-to-point communication: point-to-point means one person talking to another. However, we are in the world of networks and not just one transmitter and one receiver, but we have a whole bunch of people co-operating to transmit information to each other. So how should we do it? Here is the result, which is a theoretical one which says the following, under some assumptions. It says that if your path loss is sufficient, then multi-hopping is indeed the order of real architecture. That is the way that the present design efforts have been going, and that is indeed the right choice. So, out of this whole complicated space, what we have been doing is the right thing but, unfortunately, it also means that there is a law of diminishing returns. We cannot beat this limit, even if you throw over the digital revolution and even if you decide to have these other strategies. In-network information processing Let me move on to another theme: in-network information processing. I am now talking about what are called ‘sensor networks’. Instead of just having the facility to communicate and perhaps to local computations on your processor, nodes can also sense their environment, so you can plug in your favourite sensor there. What tasks might be a sensor network be deployed to perform? There is environmental monitoring and so, for example, in some domain you may throw a whole bunch of nodes, all of which measure the temperature. Being extremely simplistic, let us suppose that the n nodes which take the temperature X1 to XM, and that perhaps there is some collector node or a sink – then what the sink is interested in is the average temperature of the domain. You just want to monitor the average temperature. Or, perhaps on an alarm network, perhaps a collector node may be interested in the maximum temperature. Is there a fire, or isn’t there? The point is that sensor networks are not just data networks. You should not think of sensor networks as just good old communication networks where you simply replace files by sensor measurements, for the following The Royal Academy of Engineering 9
easons. In the internet, one never looks inside another person’s packet. For example, I do not look at your packet and say, ‘This is not interesting information – I will drop it.’ However, in a sensor network I may do that. If I see a high temperature, then I may drop a low temperature. So, depending on what I have heard, I may say that this information is uninteresting, or I confuse information and combine information and so on. The point is that in sensor networks, the nodes do not just forward information but they also compute. In other words, they process information in the network – the network itself processes information, and so this whole thing is like a Maxwellian computer, if you will. There are many interesting questions that you can ask and I will say something really simplistic. Let us say that I want to compute a symmetric function in a sensor network. What is a symmetric function? It is one where, if you change the identity of which node has which temperature, the result does not change. For example, the average is invariant to permutations. In fact, most statistical quantities are symmetric functions. Computing symmetric functions: the mean versus max Theorem: The rate at which the Mean can be harvested is – Strategy Tessellate Add locally Sum along a rooted tree of cells Theorem: The rate at which the Max can be harvested is Strategy: Take advantage of Block Coding – First node announces times of max values: ( 1 1 1 ) – Second node announces times of additional max values (1 ) 1 – third node announces of yet more max values: ( ) 1 (Giridhar & K03) 12/34 It turns out that we are very much at the beginning point of developing theories for how to operate such networks. What I would like to illustrate for you is a kind of dichotomy about how you treat different functions. It turns out that the rate at which you can exfiltrate average temperature readings from sensor networks is that - [alpha-1 over log n]. The architecture for that is the commonsense architecture. If you have a bunch of nodes, you break them up into cells and you tessellate them. In each cell, you add up the temperatures, you sum the temperatures, and then you propagate all the sums along an entry route at the collector node, and that is the commonsense thing that anybody would do. However, it turns out that if you want to compute the max temperature, not the average, then you can do it exponentially faster. The rate at which you can do it is [1 over log log n]. I just want to show you how you could take advantage of what you are computing. You can take advantage of what is called block coding. In other words, I do not compute the maximum temperature every day but I gather together a bunch of temperatures and then spew out a bunch of maximum temperatures. Just to show you the idea, let us suppose that all temperatures are binary, 0 or 1. So anybody who has a temperature of 1, has a maximum temperature automatically. Let us also suppose that we are all collocated so that, when I talk, everybody hears, and whenever anybody talks, everybody hears. Then the first node can simply announce the set of times at which it has a max temperature – so at times 10, 15 and 20, it has a temperature of 1. Then the second node can butt in and say, ‘Okay, I have a maximum temperature at these three times.’ Such information can be very efficiently compacted and therefore you can get exponential speed-ups. The way you operate these networks can be quite sophisticated. Knowledge of time important in Cyberphysical systems – However no two clocks agree – How to synchronize clocks in distributed systems? In computer science, beginning with the work of Cook in Canada, that leads to this whole theory of complexity, and we need similar theories of complexity for sensor networks – in fact, for all these cyberphysical systems. Clock synchronization in distributed systems ^ x 01 ^ x 12 ^ x 23 ^ ^ ^ ^ v 3 = x 01 + x 12 + x 23 Std. Dev of Error Can we do better? Let me turn to another theme, that of time and clocks. It turns out that a knowledge of time is important in cyberphysical systems. If computers are just talking to each other, their conversations could be purely event-based – time is irrelevant. However, when you are interacting with physics and physics-based systems, time is important because if of two of us were at the same spot at the same 10 The Royal Academy of Engineering
Page 1 and 2: Lecture Series in Mobile Telecommun
Page 3 and 4: Foreword This compilation brings to
Page 5 and 6: From wireless networks to sensor ne
Page 7 and 8: From wireless networks to sensor ne
Page 9: As far as the routing of packets is
Page 13 and 14: Implementation with laser pointers,
Page 15 and 16: here of laptops, and all these lapt
Page 17 and 18: adds a great deal of discrete compl
Page 19 and 20: Questions & Answers Mike Walker: Th
Page 21 and 22: Human beings will also evolve and w
Page 23 and 24: Welcome and introduction Professor
Page 25 and 26: ComReg Collection - Start 16/Apr/20
Page 27 and 28: evidence that people give in favour
Page 29 and 30: chunks of spectrum where you are in
Page 31 and 32: As an aside, I was reading a few of
Page 33 and 34: Of course, it is not just one mask,
Page 35 and 36: I apologise for hopping between top
Page 37 and 38: Questions & Answers Michael Walker:
Page 39 and 40: Nobody - believe you me, it came ou
Page 41 and 42: The second aspect of my comment is
Page 43 and 44: want to call it - that sits there a
Page 45 and 46: From plain old Telephony to flawles
Page 47 and 48: From plain old Telephony to flawles
Page 49 and 50: You can see that there is much room
Page 51 and 52: 1024, we transmit 10 bits, so to sp
Page 53 and 54: Bandwidth extension with hidden sid
Page 55 and 56: 4 Vision: ambience audio communicat
Page 57 and 58: Questions & Answers Michael Walker:
Page 59 and 60: I said five years ago and what I he
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them and perhaps leave out some of
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Lecture Series in Mobile Telecommunications and Networks (1583KB)

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