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### Ii Communications Channel

1. 1. COMMUNICATION CHANNELS INTRODUCTION TO SIGNALS F A cycle is the part of the signal that repeats itself. Not all signals have cycles. v t cycle F Signals with cycles are called periodic signals while signals which do not have cycles are called aperiodic signals. F The period (τ) of a periodic signal is the length of time of its cycle. Communications Channels 1
2. 2. F The frequency (f) of a signal is the number of cycles per unit time of the signal. Frequency is measured in cycles per second or hertz (Hz). Example: If a cycle is 0.4 ms long, then its frequency is: 1 cycle f= -3 = 2,500 cycles/second or Hz 0.4 x 10 sec F The frequency of a signal is therefore the reciprocal of its period. ( f = 1 / τ ). Example: If the period of signal is 6 µs long, then its frequency is: 1 1 f= = τ 6 x 10 - 6 = 166,666.67 Hz or 166.67 KHz Communications Channels 2
3. 3. F The frequency of a signal can also be computed by: f= v λ where: v velocity of signal movement through the channel in meters per second λ wavelength or the length of one cycle in meters Example: If the velocity of the signal is 250,000 km/sec and its wavelength is 0.25 m, then its frequency is: v 250,000 x 10 3 f= = λ 0.25 = 1 x 109 Hz or 1 GHz Communications Channels 3
4. 4. COMMUNICATION SYSTEMS F A communication system is a group of hardware (and possibly software) that can facilitate communication. F Shannon Block Diagram of a Communication System: Information Transmitter Channel Receiver Destination Source modulation demodulation encoding decoding encryption decryption Noise Source INFORMATION SOURCE F The communication system exists to communicate a message. This message comes from the information source F In electronic communication systems, what is important is the quantity of the information being transmitted, not the quality. Communications Channels 4
5. 5. TRANSMITTER F The message or information to be transmitted must be electrical in nature. F If it is not yet electrical, then it must be first converted into electrical energy by using the appropriate transducer. A transducer is a device that converts a physical quantity such as force, pressure, sound, level, and temperature into electrical energy. Example: A microphone is a transducer that converts sound into electrical signals. F Most information signals are in the audio (low frequency) frequency range. Examples: Telephone Speech - 300 Hz to 3,400 Hz Natural Speech - 80 Hz to 8,000 Hz Good Quality Music - 50 Hz to 15,000 Hz F Audio signals may be transmitted directly by wire. Communications Channels 5
6. 6. F However, several difficulties are involved in the transmission of audio signals by electromagnetic waves or radio waves (transmission by air). F For sufficient radiation and reception of audio signals, the transmitting and receiving antennas should have dimensions comparable to the wavelength of the signal to be transmitted. λ = v/f All electromagnetic waves propagate at a velocity near the speed of light. v ≈ 300,000 km / s Example: Shortest wavelength of music: λ = v/f = 300,000 x 103 / 15 x 103 = 20,000 m Therefore, to transmit music via electromagnetic transmission, the transmitting and receiving antennas should have dimensions comparable to 20 Km. Communications Channels 6
7. 7. F The solution to this problem is to translate or change the frequency of the audio signal to be transmitted to a much higher value. Example: If f = 15 MHz λ = v/f = 300,000 x 103 / 15 x 106 = 20 m F This process of translation is called modulation. In the process of modulation, some characteristic of a high-frequency sine wave (called the carrier) is varied in accordance with the instantaneous value of the information or message signal (called the modulating signal). Communications Channels 7
8. 8. F General equation of a sine wave: v(t) = V sin (ωt + θ) or v(t) = V sin (2πft + θ) where: V = maximum amplitude ω = angular velocity = 2πf frequency θ = phase angle (with respect to some reference) v(t) V t V T = 1/f period Communications Channels 8
9. 9. F The three characteristics or parameters of a sine wave are amplitude, frequency, and phase angle. Any of these may be varied by the modulating signal, giving rise to amplitude, frequency, and phase modulation. carrier signal 0 1 0 0 1 1 information signal amplitude modulated signal frequency modulated signal phase modulated signal F A modulated signal is just simply the carrier in another form. Communications Channels 9
10. 10. F Another benefit from modulation: If two of more radio stations were able to come up with a 20 Km antenna, they can transmit music without going through the process of modulation. However, since all music is concentrated within the range from 20 Hz to 20 KHz, all signals coming from the different stations would be hopelessly and inseparably mixed up. If each station has its own unique carrier and modulation was used, then each message signal (music) will be translated into different frequencies thus enabling the receiver to separate the transmission of one station from other stations. F Therefore, the two major reasons for needing modulation are: 1. So that a relatively smaller antenna can be used to transmit electromagnetic signals. 2. So that signals with similar frequencies can be transmitted without interference from one another. Communications Channels 10
11. 11. CHANNEL F The channel is the medium of transmission. It is the physical or non-physical link between transmitter and receiver. Examples: wire (copper) coaxial cable physical fiber optics radio waves non-physical F If the transmission channel used is electromagnetic propagation, the frequency of the carrier used must be specified. Example: DWRT - 99.5 MHz Communications Channels 11
12. 12. F The channel is affected by two factors: 1. Attenuation. Attenuation is the heavily fading of signals. The farther the signal goes away from the transmitter, the weaker it gets. 2. Noise. Noise is any unwanted energy. Noise can actually affect the entire communications system, but it is in the channel where it can do the most damage since this is where the signal is weakest. RECEIVER F After receiving the selected high-frequency modulated signal, the receiver now will apply demodulation to revert the signal to its original form. DESTINATION F The output of the receiver is fed into the circuit of the desired destination. Examples: 1. Picture tube of a television set 2. Speakers of a radio set 3. Computer 4. Telephone handset Communications Channels 12
13. 13. BANDWIDTH F The bandwidth of a signal refers to the width of the band (or range) of frequencies occupied by a particular signal. F Bandwidth is very important in designing communication systems since it dictates the type of channel suitable for the transmission of a particular signal. F If the signal is composed of several sinusoidal signal components, then BW = highest frequency - lowest frequency This equation is good for sinusoidal (sine or cosine) waves only. Example: If the signal to be transmitted is composed of sine waves ranging from 1,000 Hz to 5,000 Hz, then the bandwidth is computed to be: BW = 5,000 - 1,000 = 4,000 Hz Communications Channels 13
14. 14. F However, most information or message signals are complex nonsinusoidal aperiodic waveforms. Example: v(t) t F According to the studies of Jean Fourier, all nonsinusoidal signals can be expressed in terms of its constituent sine waves. In other words, all nonsinusoidal signals actually consist of several sine and/or cosine waves. F These sinusoidal components comprise the frequency spectrum of the signal. Communications Channels 14
15. 15. F Some important points regarding the sinusoidal components: 1. The frequency of each component is unique. 2. The number of frequency components is infinite. 3. In theory, the bandwidth of a nonsinusoidal signal is infinite. 4. As a general rule, the higher the frequency of a component, the lower its amplitude. 5. The higher frequency components will have very small amplitudes such that they may be considered negligible. 6. Therefore, there will be a finite number of significant components. F The bandwidth of complex nonsinusoidal aperiodic waveforms is just the difference between the lowest frequency and the highest significant frequency. Communications Channels 15
16. 16. F Case Study : The Human Voice power shows the sound power a human vocal system can produce at various frequencies freq 2000 4000 6000 8000 12000 This graph shows that the human voice is mainly composed of analog periodic signals ranging from 0 Hz to 12,000 Hz. If a communications channel is to convey the entire frequency range of human sounds, it must have a minimum frequency near zero and a bandwidth of more than 12,000 Hz. Communications Channels 16
17. 17. F The Telephone System Bandwidth Because of technology limitations and cost trade-offs made during the design of the public telephone system, this system can only handle a small part of the total bandwidth of the human voice. Telephone System Bandwidth = 300 Hz to 3,400 Hz The 300 to 3,400 Hz range is sufficient to convey messages to distant listeners. This range is the portion of the voice bandwidth that can produce the greatest power. Communications Channels 17
18. 18. NOISE IN A COMMUNICATION SYSTEM F Noise is any unwanted energy tending to interfere with the signal to be transmitted. Examples: 1. “Confetti” superimposed on the picture of a television broadcast. 2. Hissing sound in a radio transmission. 3. A logic 0 becoming a logic 1 in computer data transmission. F Types of Noise: 1. External Noise. This is noise originating from outside the communication system. 1.1. Atmospheric Noise. This type of noise is mainly due to spurious radio waves that tend to induce unwanted voltages in the antenna. It is also known as static. Example: Lightning discharges during thunderstorms. Atmospheric noise is less disturbing for transmissions using frequencies higher than 30 MHz. Communications Channels 18
19. 19. 1.2. Extraterrestrial Noise. This noise comes from outer space. Extraterrestrial Noise is divided into two groups: Solar Noise. Noise due to the intense heat from the sun. This is most severe during corona flares or sunspots. Cosmic Noise or Blackbody Noise. This is noise due to the distant stars. What they lack in distance, they made up for it in numbers. Extraterrestrial noise is less noticeable at frequencies below 20 MHz. 1.3. Man-Made Noise or Industrial Noise. This noise is produced by man-made devices such as automotive ignition, electrical motors, fluorescent lights, and radiation from high- voltage lines. Communications Channels 19
20. 20. 2. Internal Noise. This is noise originating from within the communication system. 2.1. Thermal Agitation Noise or Johnson Noise or White Noise. This noise is due to the random and rapid movement of electrons in any resistive component. Electrons “bump” with each other. 2.2. Shot Noise. This noise is due to active devices present in any communication system. It is caused by the random fluctuations in the arrival of electrons or holes at the collector of transistors. When amplified, shot noise will sound like lead shot falling over a metal surface. 2.3. Transit-time Noise. This noise is generated in active devices. If the travel time of electrons flowing from the emitter to the collector becomes comparable to the period of the signal, then some of these electrons are diffused back to the collector. This would cause the random noise to be generated at the input of the device. Communications Channels 20
21. 21. 2.4. Partition Noise. This noise is due to current being divided between two or more paths. The random variations in the division process can cause fluctuations in current thus generating noise. 2.5. Flicker Noise or Modulation Noise. This noise is due to variations in current density in semiconductors. This would cause fluctuations in the conductivity of the device which in turn would produce a varying voltage drop when direct current flows. Flicker noise is usually in the lower- frequency range (a few KHz). F Noise is fundamental. They are physically part of nature and little can be done to totally eradicate them. They can however, be minimized. F In the study of noise, it is not important to know the absolute value of noise. Even if the power of the noise is very small, it may have a significant effect if the power of the signal is also small. F What is important is a comparison between noise and the signal. Communications Channels 21
22. 22. F The signal-to-noise ratio (SNR) or noise figure is the ratio of signal power to noise power. SNR = Ps / P n Example: Ps1 = 5 w Ps2 = 50,000 w Pn1 = 50 mw Pn2 = 50 w SNR1 = 5 / 50 x 10-3 SNR2 = 50,000 / 50 = 1,000 = 1,000 Both systems have the same performance. F Ideally, SNR = ∞ (when Pn = 0). In practice, SNR should be high as possible. F An SNR ≥ 1,000 is acceptable. Communications Channels 22
23. 23. F SNR can also be expressed in terms of voltage or current. Ps = V2s / Rs Pn = V2n / Rn 2 Vs Ps R SNR = = 2 s Pn Vn Rn If Rs = Rn (which is true all the time), then: antenna resistance 2 V  SNR =  s   Vn    For current: 2 I  SNR =  s   In    Communications Channels 23
24. 24. THE COMMUNICATIONS CHANNEL F A communications channel is the physical or non- physical connection between a transmitter and receiver. F A communications channel moves electromagnetic energy between a source and one or more destination points while retaining the information contained in the energy when it leaves the source. F Characteristics of an ideal channel: 1. It is a perfect vacuum. Therefore, there are no physical objects that can reduce the level of energy sent out by the transmitter. In other words, there is no loss of signal strength. 2. There are no errors. 3. Signals would travel at the speed of light (300,000 km per second). F The ideal channel does not exist. Communications Channels 24
25. 25. F Types of Channels 1. Analog Channels. These channels can carry analog or continuous signals. An analog signal goes through all values within its range. v v t t Examples: telephone system, commercial radio system 2. Digital Channels. These channels can carry digital or discrete signals. A digital signal can not assume all of the possible values within its range. v v t t Example: computer communications Communications Channels 25
26. 26. COMMUNICATIONS CHANNEL CHARACTERISTICS F Signal Attenuation Attenuation is the fading of an electrical signal or decrease in signal strength. This is primarily due to the internal resistance of the channel. F Electronic Noise Electronic noise is any unwanted signal or voltage that tends to interfere with the proper and easy reception and reproduction of wanted signals. Noise can distort signals beyond recognition. F Channel Capacity This refers to the quantity of information the channel can convey over a given period. Communications Channels 26
27. 27. ANALOG CHANNEL CAPACITY F An aperiodic analog signal actually has several periodic (sinusoidal) component signals called frequency components. Each of these frequency components has a different frequency and amplitude or signal strength. The frequency of a component is inversely proportional to its signal strength. In other words, the higher the frequency of a component, the lower is its signal strength and vice-versa. Some frequency components (particularly the ones with very high frequency) have very small amplitudes that they are already considered insignificant. F The bandwidth of a signal is the difference between the lowest and highest significant frequency of a single analog signal. F The bandwidth of a channel is the difference between the lowest and highest frequency an analog channel can convey to a distant receiver that the receiver can understand. F A broadband channel is a channel with a wide bandwidth while a baseband channel is a channel with a narrow bandwidth. F THE CAPACITY OF AN ANALOG CHANNEL IS ITS BANDWIDTH. Communications Channels 27
28. 28. F Case Study : The Human Voice power shows the sound power a human vocal system can produce at various frequencies freq 2000 4000 6000 8000 12000 This graph shows that the human voice is mainly composed of analog periodic signals ranging from 0 Hz to 12,000 Hz. If a communications channel is to convey the entire frequency range of human sounds, it must have a minimum frequency near zero and a bandwidth of more than 12,000 Hz. Communications Channels 28
29. 29. F The Telephone System Bandwidth Because of technology limitations and cost trade-offs made during the design of the public telephone system, this system can only handle a small part of the total bandwidth of the human voice. Telephone System Bandwidth = 300 Hz to 3,400 Hz The 300 to 3,400 Hz range is sufficient to convey messages to distant listeners. This range is the portion of the voice bandwidth that can produce the greatest power. Communications Channels 29
30. 30. DIGITAL CHANNEL CAPACITY F In general, digital signals have two states (bits): 1. Logic 1 (mark) - 5 volts 2. Logic 0 (space) - 0 volt or -5 volts F A communications channel that conveys a digital signal has limitations that determine how often the signal can change state over a given period. F These limitations establish the maximum rate at which data can flow through the channel. F Channel Bit Rate The capacity of a digital channel is the number of digital values the channel can convey in one second. It is usually measured in bits per second (bps). Communications Channels 30
31. 31. F The bit period (or bit time) of a digital signal is the length of 1 bit in seconds. +v 1 0 1 1 0 0 1 t -v Bit Period F The bit rate of a digital signal is the reciprocal of its bit period (bit rate = 1 / bit period). Example: If the bit period of a digital signal is 0.208 ms, then its bit rate is: 1 1 bit r ate = = bit period 0.208 x 10- 3 bit rate = 4,800 bps Communications Channels 31
32. 32. RELATIONSHIP BETWEEN BANDWIDTH AND DATA RATE F Digital signals consist of a large number of frequency components. If digital signals are transmitted over a channel with a limited bandwidth, only those components that are within the bandwidth of the transmission medium are received. 0 1 1 0 0 0 1 0 1 rms amplitude 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time 1 1 Component 0 1 1 2 Components 0 1 2 1 4 Components 0 1 2 3 4 1 8 Components 0 1 2 3 4 5 6 7 8 Communications Channels 32
33. 33. F The faster the data rate of a digital signal, the higher the bandwidth will be required since the frequency components will be spaced farther apart. F Therefore, a limited bandwidth will also limit the data rate that can be used for transmission F Nyquist derived a formula that determines the maximum data rate of a transmission medium as a function of its bandwidth: 2Blog (M ) C= 10 log 2 10 where C is the maximum data transfer rate of the system in bits per second, B is the bandwidth of the system in Hz, and M is the number of levels per signalling element. Communications Channels 33
34. 34. Example: A digital signal that uses 2 levels per signalling element is to be transmitted over a channel with a bandwidth of 3000 Hz (similar to that of the analog telephone system). What is the maximum data rate that the system can have? Solution: B = 3,000 Hz M = 2 2(3,000)log 2 C = 10 log 2 10 C = 6,000 bps In practice, the data transfer rate will be less than this because of other effects such as noise. Communications Channels 34
35. 35. TRANSMISSION MEDIA F Transmission channels can be classified as either bounded or unbounded. F In bounded channels, signals are confined to the medium and do not leave it. F In unbounded channels, the signals (electromagnetic signals or radio waves) originated by the source travel freely into the medium and spread throughout the medium. F Examples of bounded media: 1. Wire Pairs. This is the earliest and simplest type of bounded media which provides a go and return path for electrical signals. Wire pairs have low attenuation of voice frequencies due to the large size of the wire and the large distance between the two wires when mounted on the crossarm of a utility pole. Example: A 104 mil (0.104 inch) diameter open wire line has a typical attenuation of 0.07 dB per mile. Communications Channels 35
36. 36. A decibel is simply a ratio of two powers. Decibel = 10 log10 (P 2/P1) where: P2 = output power P1 = input power If a decibel value is positive, there is power gain (amplification). If it is negative, there is power loss (attenuation). Example: Attenuation = 0.07 dB per mile -0.07 = 10 log10 (P 2/P1) -0.007 = log10 (P 2/P1) P2 / P 1 = 0.984 P2 = 0.984 P 1 (after 1 mile) If the transmitted power (P1) is 1 W, then the power at the receiving side (P2) will be 0.984 W. The main problems associated with wire pairs are interference from electromagnetic radiation and crosstalk due to capacitive coupling. Wire pairs can have a data rate not greater than 19.2 Kbps over a distance of about 50 m. Communications Channels 36
37. 37. 2. Twisted Pair Lines. This consists of two insulated copper wires (typically 1 mm thick) twisted together in a helical form so that each wire faces the same amount of interference. The twisting minimizes electromagnetic interference to similar pairs close by and therefore reduces noise. The more twists, the less noise. Twisted pair wires come in a wide range of gauges. Example: A 19-gauge wire has a diameter of 0.03584 inch while a 26-gauge wire has a diameter of 0.01594 inch. Most twisted pair wires consist of wire pairs twisted together and made up into cables of 4 to 3,000 pairs. Communications Channels 37
38. 38. The major problem of twisted-pair lines is that it suffers from skin effect. As the frequency of the signal being transmitted is increased, the signal current tends to flow only on the outside portion or surface of the wire. This is the same as if the line resistance has been increased at higher frequencies causing such signals to be attenuated. Twisted pair lines can have bit rates in the order of several Mbps over a distance of a few kilometers. There are two types of twisted pair wires: 1. Unshielded Twisted Pair (UTP) There is no physical shielding, just an outer jacket. Therefore, more twists are needed to reduce noise. This is the same type of cable used in telephone lines. It has a relatively small size thus making it easy to install. Communications Channels 38
39. 39. Category 3 UTP consist of two insulated wires gently twisted together. Four such pairs are typically grouped together in a plastic sheath for protection and to keep the eight wires together. Starting at around 1988, the more advanced Category 5 UTP were introduced. They are similar to CAT 3 UTP, but with more twists per centimeter and Teflon insulation, which results in less crosstalk and a better quality signal over longer distances, making them more suitable for high-speed computer communication. 2. Shielded Twisted Pair (STP) This cable has an added shield of copper braid around all the wire pairs. The entire STP cable is also shielded (less noise but more expensive than UTP). STP has a large outside diameter which makes it difficult to install. STP can support faster data rates and longer range than UTP. This type of cable was introduced by IBM for its token ring network. Communications Channels 39
40. 40. 3. Coaxial Cable. The ground and reference wires take the form of a solid conductor running concentrically (coaxially) inside a solid outer circular conductor. The space between the two conductors should ideally be filled with air, but in practice it is normally filled with a dielectric insulating material. Braided Protective Insulating outer plastic Copper conductor material covering core Due to its geometry, the center conductor is effectively shielded from external interference signals and also only minimal losses occur due to electromagnetic radiation and the skin effect (self-shielding). Coax cables work well with frequencies from 100 KHz to 2 GHz (or even up to 10 GHz). Because of the larger bandwidth, a faster data rate is possible (up to 1 Gbps). Communications Channels 40
41. 41. 4. Fiber Optic Cables. These cables carry the transmitted information in the form of a fluctuating beam of light in a glass fiber. Since it does not use electricity, there is no electromagnetic radiation (good security). They are essentially free from crosstalk and electrical interference. There is minimal attenuation since fiber optic cables have low transmission losses which allows a much greater separation between repeaters. Light has a much higher frequency of operation (800 THz). This higher bandwidth allows data transmission rates of 20 Gbps and above and over distances up to 30 Km. Communications Channels 41
42. 42. Three (3) main components: 1. Transmission Medium. Ultra-thin fiber of glass or fused silica. 2. Light Source. LED (Light Emitting Diode) or laser diode which emit light pulses when an electrical current is applied to it 3. Detector. Photodiode which generates an electrical pulse when light falls on it Fiber cable types: 1. Multimode Fiber. This was designed to trap light rays internally through light refraction at different angles of incidence. Multimode fiber uses LEDs. 2. Single Mode Fiber. This was designed to be thin enough (one wavelength) to avoid refraction (no bouncing) and thus allowing a single light ray to pass. Single mode fiber uses laser diode for better focus resulting in higher efficiency and longer reaches. The main problems of fiber optics are its cost and difficulty in installation. Communications Channels 42
43. 43. F Examples of unbounded transmission: 1. High-Frequency Radio Transmission. Radio transmission in the frequency band between 3 MHz and 30 MHz is called HF radio. Electromagnetic Spectrum: From To Name 3 KHz 30 KHz VLF 30 KHz 300 KHz LF 300 KHz 3 MHz MF 3 MHz 30 MHz HF 30 MHz 300 MHz VHF 300 MHz 3 GHz UHF 3 GHz 30 GHz SHF 30 GHz 300 GHz EHF Communications Channels 43
44. 44. Propagation Paths of HF Radio Waves: 1. Ground Waves. The signal follows the curvature of the earth’s surface (for lower HF frequencies). 2. Sky Waves. The signal bounces back and forth between the earth’s surface and the various layers of the earth’s ionosphere (for the higher HF frequencies). ionosphere SKY WAVE GROUND WAVE surface of the earth Communications Channels 44
45. 45. 2. Microwave Radio Transmission. Microwave refers to frequencies above the HF region. Microwave signals follow line-of-sight (LOS) propagation, and is therefore highly directional. However, this limits the distance that can be covered. To facilitate beyond-the-horizon propagation, satellite or terrestrial repeaters are used. Communications Channels 45
46. 46. Due to a higher frequency of operation, microwave systems carry large quantities of information. The required antenna is smaller due to shorter wavelength (due to higher frequencies). Take note that the size of the antenna required to transmit a signal is proportional to the wavelength (λ) of the signal. λ = v/f where: f = frequency of the signal v = velocity of signal propagation, usually near the speed of light (3 x 108 m/s ) Example: HF = 15 MHz λ = 3 x 108 / 15 x 106 = 20 m Microwave = 3 GHz λ = 3 x 108 / 3 x 109 = 0.1 m Communications Channels 46
47. 47. Problems with microwave systems: 1. Attenuated by solid objects (including earth) and in addition, the higher frequencies are attenuated by rain, snow and fog. 2. Reflected from flat conductive surfaces (water, metal structures, etc.). 3. Diffracted (split) around solid objects. 4. Refracted (bent) by the atmosphere so that the beam may travel beyond the line-of-sight distance and be picked up by an antenna that is not supposed to receive it. Communications Channels 47
48. 48. INFORMATION THEORY F Information Theory is a quantitative body of knowledge that has been established about information. F Information is assigned a precise value if one is to deal with it scientifically. F The meaning of information is not important as compared to the quantity of information. F Information is a physical quantity such as mass. Example: 1 kg. of gold has the same mass as 1 kg. of garbage. F Information theory is used to establish, precisely and mathematically the rate of information issuing from any source, the information capacity of the channel, system or storage device, and the efficiency of codes. Communications Channels 48
49. 49. F Information is defined as the choice of one message out of set of finite messages. meaning is immaterial more choices means more information when measuring information, it must be taken into account that some choices are more likely than others and therefore contain less information F The simplest possible choice is the one involving two equally likely events. In this case, it is convenient to use the information content of this kind of choice as the basic unit of information. Thus the bit is defined as the quantity of information required to permit the correct selection of one out of a pair of equiprobable events. Communications Channels 49
50. 50. Number of bits of information which must be given to enable the correct selection of one = log2 N event from a set of N equiprobable events If the intelligence (or knowledge) to be communicated can be represented in N equally likely symbols, then the amount of information required per symbol is log2 N bits. Examples: 1. If N = 16, then the number of bits required to represent one of 16 possible choices or events is log2 16 = 4 bits. 2. In ASCII, 7 bits are used which represent one choice out of a total of 128 choices. 3. If the English alphabet is used (26 letters and 1 space character), then log2 27 = 4.76 bits are required to represent one choice or one symbol. Communications Channels 50
51. 51. F Not every symbol is equally likely to be used in a given communication. Example: The letter E is more likely to occur than the letter S. F Any choice that has a high probability of occurring is redundant and contains very little information. Example: The probability of the letter U following a letter Q is almost 1. Therefore U is fully redundant in this case and contains no information. F However, redundancy is desirable in order to raise the chances of receiving a good message when the medium or channel is noisy. Communications Channels 51