1. 15-441 Communications and Networking Gregory Kesden

2. Copper Wire l Unshielded twisted pair »Two copper wires twisted, often unshielded »Twisting avoids capacitive coupling – the cause of cross-talk »Grouped into cables: multiple pairs with common sheath »Category 3 versus category 5/5e (more twists) »100 Mbps up to 100 m, 1 Mbps up to a few km l Coax cables. »One connector is placed inside the other connector »Holds the signal in place and keeps out noise »Gigabit up to a km l Signaling processing research pushes the capabilities of a specific technology.

3. 1000 wavelength (nm) loss (dB/km) 1500 0.0 0.5 1.0 tens of THz 1.3  1.55  Light Transmission in Silica Fiber

4. lower index of refraction core cladding (note: minimum bend radius of a few cm) Ray Propagation

5. l Multimode fiber. »62.5 or 50 micron core carries multiple “modes” »used at 1.3 microns, usually LED source »subject to mode dispersion: different propagation modes travel at different speeds, depending on where source reflects bounces within cable – different paths are different lengths »Mode dispersion can be combated with a graded refraction index. Cable has variable refraction index to squeeze things back together. »typical limit: 1 Gbps at 100m l Single mode »Narrow cable so that it holds only “one beam” of light »8 micron core carries a single mode »used at 1.3 or 1.55 microns, usually laser diode source »typical limit: 1 Gbps at 10 km or more »still subject to chromatic dispersion Fiber Types

6. Wireless - Satellite Typically geostationary orbit High latency High bandwidth (500MHz) High latency (240ms – 540ms) Microwave frequencies (10 8 – 10 11 Hz) Interestingly enough, water (rain, &c) absorbs a great deal of microwave energy – that’s why we use it to cook.

7. Radio - terrestrial Below microwave frequency range (10 4 – 10 9 Hz) Still absorbed by water, but less so than microwave Higher frequencies tend to “bounce” off obstacles Lower frequencies tend to be penetrate Lower frequencies can “bounce” off ionosphere. As frequency approaches microwave band, this doesn’t happen. For comparison: Twisted pair 10 4 – 10 6 Hz, Fiber optic 10 14 -10 15 Hz

8. Maximum Data Rate Different media (even assuming no outside interference) have different ability to hold a signal Different media (even assuming no outside interference) have different ability to hold a signal For example, copper tends to be limited by capacitance For example, copper tends to be limited by capacitance Fiber optic media limited by electronics on either side Fiber optic media limited by electronics on either side

9. Bandwidth Bandwidth is literally that – the width of the band, or range of frequencies, supported by the media. Bandwidth is literally that – the width of the band, or range of frequencies, supported by the media. Bandwidth is usually given in terms of a frequency – the number of times per unit time that a recognizable sine wave can be transmitted over the media. Bandwidth is usually given in terms of a frequency – the number of times per unit time that a recognizable sine wave can be transmitted over the media. Depending on the encoding, a different number of bits might be transmitted per cycle. Depending on the encoding, a different number of bits might be transmitted per cycle.

10. An Example Encoding: Sine Waves and Bits 0 1 1 1 01 11 This particular encoding transmits two bits per cycle.

11. Nyquist’s Theorum How is the data rate constrained by bandwidth? How is the data rate constrained by bandwidth?  Maximum data rate(bits/second) = 2 * bandwidth (hz) Nyquist’s Theorum considers only the limit imposed by the bandwidth not noise, encoding, or other factors. Nyquist’s Theorum considers only the limit imposed by the bandwidth not noise, encoding, or other factors. We saw one such encoding on the previous slide We saw one such encoding on the previous slide

12. Nyquist’s Theorum Why Double The Bandwidth? In addition to looking at a signal in the time domain, we can view it in the frequency domain. In addition to looking at a signal in the time domain, we can view it in the frequency domain. In other words, instead of asking the question, “What is the amplitude at time X?”, we can ask the question, “How much energy is present every X units of time?” In other words, instead of asking the question, “What is the amplitude at time X?”, we can ask the question, “How much energy is present every X units of time?” For some signals this is a meaningless measure – but many are periodic. For discrete signals (like data signals), we just assume that they repeat forever. For some signals this is a meaningless measure – but many are periodic. For discrete signals (like data signals), we just assume that they repeat forever. Energy Frequency

13. A (periodic) signal can be viewed as a sum of sine waves of different strengths. A (periodic) signal can be viewed as a sum of sine waves of different strengths. Every signal has an equivalent representation in the frequency domain. Every signal has an equivalent representation in the frequency domain.  What frequencies are present and what is their strength  Similar to radio and TV signals Time Frequency Amplitude The Frequency Domain

14. Nyquist’s Theorum Why Double The Bandwidth? As an analog signal is transmitted through some media, it is filtered by that media. As an analog signal is transmitted through some media, it is filtered by that media. Not only is noise introduced, but energy at certain frequencies is lost – and nearly completely so above and below some threshold frequencies. Not only is noise introduced, but energy at certain frequencies is lost – and nearly completely so above and below some threshold frequencies. As a result, the signal has no harmonics above a certain frequency or below another. As a result, the signal has no harmonics above a certain frequency or below another.

15. A fundamental theoretical finding is that to reproduce an analog signal accurately at a certain frequency, we must sample it twice as frequently. Otherwise, we could lose information. A fundamental theoretical finding is that to reproduce an analog signal accurately at a certain frequency, we must sample it twice as frequently. Otherwise, we could lose information. If we sample less often, we might miss an event – we sample just before it happens. If we sample less often, we might miss an event – we sample just before it happens. If we sample more often, we just sample the same thing twice – we can’t get more information than is there – and the data has already been limited to a certain bandwidth of information. If we sample more often, we just sample the same thing twice – we can’t get more information than is there – and the data has already been limited to a certain bandwidth of information. Nyquist’s Theorum Why Double The Bandwidth?

16. We need to have two points within the same period to know exactly which sine function we have. More points provide no additional information.

17. Nyquist’s Theorum Why Double The Bandwidth? Reversing this, we find that, given an analog signal of a certain frequency, we can have binary samples at twice the frequency. Reversing this, we find that, given an analog signal of a certain frequency, we can have binary samples at twice the frequency.

18. Better Than Nyquist’s Limit If clocks are synchronized sender and receiver, we only need one point per period. If clocks are synchronized sender and receiver, we only need one point per period. This is because the synchronized starting point counts as one of the two points. This is because the synchronized starting point counts as one of the two points.

19. Noisy Channel Consider ratio of signal power to noise power. Consider ratio of signal power to noise power. Consider noise to be super-imposed signal Consider noise to be super-imposed signal Decibel (dB) = 10 Log (S/N) Decibel (dB) = 10 Log (S/N) S/N of 10 = 10 dB S/N of 10 = 10 dB S/N of 100 = 20 dB S/N of 100 = 20 dB S/N of 1000 = 30 dB S/N of 1000 = 30 dB

20. Shannon’s Theorum Maximum data rate (bits/second) = Maximum data rate (bits/second) = bandwidth (Hz) Log 2 (1 + S/N) As before, this only gives us the limit on the data rate imposed by the noise, itself. As before, this only gives us the limit on the data rate imposed by the noise, itself. It does not consider the encoding or bandwidth limitations. It does not consider the encoding or bandwidth limitations. The bandwidth parameter can be confusing. It is there because it governs the effect that the noise has. More bandwidth either dilutes the noise, or gives the data more places to hide, or both. The bandwidth parameter can be confusing. It is there because it governs the effect that the noise has. More bandwidth either dilutes the noise, or gives the data more places to hide, or both.

21. Increased bandwidth decreases the effects of noise. One way to think of this is that the signal has either more frequency space to call its own, or the noise gets diluted across the frequency space, or some combination of the two. noise signal Shannon’s Theorum

22. Higher Frequency = Higher Energy frequency = frequency = speed of light (m/s)/wavelength (m) Energy (Joules) = frequency * Plank’s constant Energy (Joules) = frequency * Plank’s constant Planck’s constant (Energy in a photon) is 6.626 X 10 –34 Planck’s constant (Energy in a photon) is 6.626 X 10 –34

23. Magnetic Media Hauling a big-rig of DAT along I-79 may appear to be high bandwidth, but how are you going to load them at the other side? Hauling a big-rig of DAT along I-79 may appear to be high bandwidth, but how are you going to load them at the other side? Even if the bandwidth can be achieved, I-79 has a very high latency Even if the bandwidth can be achieved, I-79 has a very high latency

24. Throughput vs. Latency Throughput is the amount of work (data transfer) per unit time Throughput is the amount of work (data transfer) per unit time Latency is the delay before the first unit of work (data) arrives Latency is the delay before the first unit of work (data) arrives Consider highway analogy: Throughput is a function of the number of lanes. Latency is a function of the speed limit. Consider highway analogy: Throughput is a function of the number of lanes. Latency is a function of the speed limit. In networks, throughput is often related to bandwidth. Latency is often related to distance (number of hops across networks). In networks, throughput is often related to bandwidth. Latency is often related to distance (number of hops across networks).

25. Amplitude Modulation

26. Frequency Modulation

27. l Baseband modulation: send the “bare” signal. l Carrier modulation: use the signal to modulate a higher frequency signal (carrier). »Can be viewed as the product of the two signals »Corresponds to a shift in the frequency domain Baseband vs. Carrier Modulation

28. Amplitude Signal Carrier Frequency Amplitude Modulated Carrier Amplitude Carrier Modulation

29. Multiple channels can coexist if they transmit at a different frequency, or at a different time, or in a different part of the space. –Compare with planes: height, (horizontal) space, time Space can be limited using wires or using transmit power of wireless transmitters. Frequency is controlled by standards or law. Supporting Multiple Channels

30. Frequency Division Multiplexing (FDM) Channels shifted to occupy different frequency space Any single channel

31. Time Division Multiplexing (TDM) User 1 User 2User 3

32. Send multiple wavelengths through the same fiber. –Multiplex and demultiplex the optical signal on the fiber Each wavelength represents an optical carrier that can carry a separate signal. –E.g., 16 colors of 2.4 Gbit/second Like radio, but optical and much faster Optical Splitter Frequency Wavelength Division Multiplexing