Chapter 2 Wireless Communication Technology (Part Two in textbook)

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Chapter 2 Wireless Communication
Technology(Part Two in textbook)
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Outline

• 2.1Antennas and Propagation(?????)
• 2.2 Signal Encoding Techniques(??????)
• 2.3 Spread Spectrum(??)
• 2.4 Coding and Error Control(????)

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2.1Antennas and Propagation
Reading material 1Antenna
Tutorial2Chapter 5 in textbook
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2.1.1 Classifications of Transmission Media (2.4
in textbook)

• Transmission Medium(????)
• Physical path between transmitter and receiver
• Guided Media(????)
• Waves are guided along a solid medium
• E.g., copper twisted pair, copper coaxial cable,
  optical fiber
• Unguided Media
• Provides means of transmission but does not guide
  electromagnetic signals
• Usually referred to as wireless transmission
• E.g., atmosphere, outer space

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Unguided Media

• Transmission and reception are achieved by means
  of an antenna
• Configurations for wireless transmission
• Directional
• Omnidirectional

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?????????
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General Frequency Ranges

• Microwave frequency range
• 1 GHz to 40 GHz
• Directional beams possible
• Suitable for point-to-point transmission
• Used for satellite communications
• Radio frequency range
• 30 MHz to 1 GHz
• Suitable for omnidirectional applications
• Infrared frequency range
• Roughly, 3x1011 to 2x1014 Hz
• Useful in local point-to-point multipoint
  applications within confined areas

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???????
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ISM
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???(1)
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???(2)
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???(3)
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???????

• ??--LF (Low Frequency)
• ????--?????,?????
• ???????????????,?????????????????,???? ?
• ????????????,??? ,???? ,???? ,????
• ??????????

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Broadcast Radio

• Description of broadcast radio antennas
• Omnidirectional
• Antennas not required to be dish-shaped
• Antennas need not be rigidly mounted to a precise
  alignment
• Applications
• Broadcast radio
• VHF and part of the UHF band 30 MHZ to 1GHz
• Covers FM radio and UHF and VHF television

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Microwave
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Microwave System
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Terrestrial Microwave

• Description of common microwave antenna
• Parabolic "dish", 3 m in diameter
• Fixed rigidly and focuses a narrow beam
• Achieves line-of-sight transmission to receiving
  antenna
• Located at substantial heights above ground level
  
• Applications
• Long haul telecommunications service
• Short point-to-point links between buildings

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Satellite Microwave

• Description of communication satellite
• Microwave relay station
• Used to link two or more ground-based microwave
  transmitter/receivers
• Receives transmissions on one frequency band
  (uplink), amplifies or repeats the signal, and
  transmits it on another frequency (downlink)
• Applications
• Television distribution
• Long-distance telephone transmission
• Private business networks

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???
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??????(Multiplexing)(1)
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??????(2)
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??????(3)
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??????(4)
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??????(5)
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??????(6)
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2.1.2 Introduction to Antennas

• ?????????????????(An antenna is an electrical
  conductor or system of conductors)
• Transmission - radiates electromagnetic energy
  into space
• Reception - collects electromagnetic energy from
  space
• ???????????????????????(In two-way communication,
  the same antenna can be used for transmission and
  reception)

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????(Radiation Patterns)

• ?????????????,?????????????????????????????????
• ????(Radiation pattern)
• ?????????????
• ?????????????????(cross section)
• ???????????
• ??????(????)?????
• ????(Reception pattern)
• Receiving antennas equivalent to radiation
  pattern

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????(Radiation Patterns)
??????(????) ????
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????(Types of Antennas)

• ??????? (idealized)
• Radiates power equally in all directions
• ????(Dipole antennas)
• ?????? (or ????)
• 1/4????? (or ?????)??????????????????
• ??????

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????(Dipole antennas)

• ??????????????????????????8????????
  ????????????????????

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????(Dipole antennas)

• ??????????
• ????????
• ????????????

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??????(parabolic reflective)

• ?????? ?????????,???????????
• ?????????????????????????????????????????(focus),?
  ??????(directrix)

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??????WL-ANT150????

• ???

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??????WL-ANT150????

• ????

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??????WL-ANT168????

• ????

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??????WL-ANT168????

• ??????

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????????
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????(Antenna Gain)

• ?????????????
• ????????????????????
• ???????????????????????????
• ???????????????????????,???????????
• ????Effective area
• Related to physical size and shape of antenna

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????(Antenna Gain)

• ?????????
• G antenna gain
• Ae effective area
• f carrier frequency
• c speed of light ( 3 108 m/s)
• ? carrier wavelength

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????(Antenna Gain)

• ??????2m???????,?????12GHz,???????????????
• ???????0.56A,A?????????
• ?
• Api, Ae 0.56A, ??0.025m
• G7pi/(0.0250.025)35186
• Gdbl0lg3518645.46db

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2.1.3 Propagation Modes

• Ground-wave propagation
• Sky-wave propagation
• Line-of-sight propagation

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Ground Wave Propagation
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Ground Wave Propagation

• Follows contour of the earth
• Can Propagate considerable distances
• Frequencies up to 2 MHz
• Example
• AM radio

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Sky Wave Propagation
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Sky Wave Propagation

• Signal reflected from ionized layer of atmosphere
  back down to earth
• Signal can travel a number of hops, back and
  forth between ionosphere and earths surface
• Reflection effect caused by refraction
• Examples
• Amateur radio
• CB radio

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Line-of-Sight Propagation
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Line-of-Sight Propagation

• Transmitting and receiving antennas must be
  within line of sight
• Satellite communication signal above 30 MHz not
  reflected by ionosphere
• Ground communication antennas within effective
  line of site due to refraction
• Refraction bending of microwaves by the
  atmosphere
• Velocity of electromagnetic wave is a function of
  the density of the medium
• When wave changes medium, speed changes
• Wave bends at the boundary between mediums

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Line-of-Sight Equations

• Optical line of sight
• Effective, or radio, line of sight
• d distance between antenna and horizon (km)
• h antenna height (m)
• K adjustment factor to account for refraction,
  rule of thumb K 4/3

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Line-of-Sight Equations

• Maximum distance between two antennas for LOS
  propagation
• h1 height of antenna one
• h2 height of antenna two

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2.1.4 LOS Wireless Transmission Impairments

• ?????(Attenuation and attenuation distortion)
• ??????(Free space loss)
• ??(Noise)
• ????(Atmospheric absorption)
• ??(Multipath)
• ??(Refraction)
• ???(Thermal noise)

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??(Attenuation)

• ????????????????????????
• ??????????????,????????????????
• ?????????????
• ?????,??????????????????????
• ??????????,??????

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??????(Free Space Loss)

• ????????,?????????,??,????????????????,???????????
  
• ??????????,???????????????????????????????????????
  ??
• ??????????????????????????

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??????(Free Space Loss)

• ??????(?????????)
• Pt signal power at transmitting antenna
• Pr signal power at receiving antenna
• ? carrier wavelength
• d propagation distance between antennas
• c speed of light ( 3 10 8 m/s)
• where d and ? are in the same units (e.g., meters)

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Free Space Loss

• Free space loss equation can be recast

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??????(Free Space Loss)

• ??????(???????)
• Gt gain of transmitting antenna
• Gr gain of receiving antenna
• At effective area of transmitting antenna
• Ar effective area of receiving antenna

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Free Space Loss

• Free space loss accounting for gain of other
  antennas can be recast as

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????(Categories of Noise)

• ???(Thermal Noise)
• ????(Intermodulation noise)
• ??(Crosstalk)
• ????(Impulse Noise)

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???(Thermal Noise)

• ????????????????.?????????????????,
  ?????????.??????????????,???????.
• ?????
• ????????????????,??????????????????.

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???(Thermal Noise)

• ?????????1Hz????????
• N0 noise power density in watts per 1 Hz of
  bandwidth
• k Boltzmann's constant 1.3803 10-23 J/K
• T ??,?????(????)??

??T17 ?290K????,?????? No 1.3803 10-23
290410-21(W/Hz) -240(dbw/hz)
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???(Thermal Noise)

• ????????
• ?B???????????????????
• or, ?????

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Noise Terminology

• ??????????????????????,??????????? f1, f2 ,
  f1f2, f1-f2
• ?? ?????????
• ????????????????????,???ISM???,????????
• ???? ???????????????
• ??????,????,??????????
• ??????,??????????

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Expression Eb/N0

• Ratio of signal energy per bit to noise power
  density per Hertz
• The bit error rate for digital data is a function
  of Eb/N0
• Given a value for Eb/N0 to achieve a desired
  error rate, parameters of this formula can be
  selected
• As bit rate R increases, transmitted signal power
  must increase to maintain required Eb/N0

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Other Impairments

• Atmospheric absorption water vapor and oxygen
  contribute to attenuation
• Multipath obstacles reflect signals so that
  multiple copies with varying delays are received
• Refraction bending of radio waves as they
  propagate through the atmosphere

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2.1.5 Fading

• Fading refers to the time variation of received
  signal power caused by changes in the
  transmission medium or path (s).

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Multipath Propagation

• ??(Reflection) - occurs when signal encounters a
  surface that is large relative to the wavelength
  of the signal
• ??(Diffraction) - occurs at the edge of an
  impenetrable body that is large compared to
  wavelength of radio wave
• ??(Scattering) occurs when incoming signal hits
  an object whose size in the order of the
  wavelength of the signal or less

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??
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??
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??
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Multipath Propagation
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The Effects of Multipath Propagation

• Multiple copies of a signal may arrive at
  different phases
• If phases add destructively, the signal level
  relative to noise declines, making detection more
  difficult
• Intersymbol interference (ISI)
• One or more delayed copies of a pulse may arrive
  at the same time as the primary pulse for a
  subsequent bit

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???????
???????
???????
???????
???????
???????????????????????,????????????????????????.
???????,???????????????????????
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Types of Fading

• Fast fading
• Slow fading
• Flat fading
• Selective fading
• Rayleigh fading
• Rician fading

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??????(Error Compensation Mechanisms)

• ????(Forward error correction)
• ?????(Adaptive equalization)
• ????(Diversity techniques)

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????(Forward Error Correction)

• ???????????????????????????????????
• ???????????????????????????????
• Transmitter adds error-correcting code to data
  block
• Code is a function of the data bits
• Receiver calculates error-correcting code from
  incoming data bits
• If calculated code matches incoming code, no
  error occurred
• If error-correcting codes dont match, receiver
  attempts to determine bits in error and correct

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????(Forward Error Correction)

• ????????????????
• ????????,??????????????????23??
• ?????,????????????????????

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?????( Adaptive Equalization)

• Can be applied to transmissions that carry analog
  or digital information
• Analog voice or video
• Digital data, digitized voice or video
• Used to combat intersymbol interference
• Involves gathering dispersed symbol energy back
  into its original time interval
• Techniques
• Lumped analog circuits
• Sophisticated digital signal processing algorithms

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????( Diversity Techniques)

• Diversity is based on the fact that individual
  channels experience independent fading events
• Space diversity techniques involving physical
  transmission path
• Frequency diversity techniques where the signal
  is spread out over a larger frequency bandwidth
  or carried on multiple frequency carriers
• Time diversity techniques aimed at spreading
  the data out over time

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2.2 Signal Encoding Techniques
Reading material 1Chapter 6 in textbook
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Reasons for Choosing Encoding Techniques

• Digital data, digital signal
• Equipment less complex and expensive than
  digital-to-analog modulation equipment
• Analog data, digital signal
• Permits use of modern digital transmission and
  switching equipment

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Reasons for Choosing Encoding Techniques

• Digital data, analog signal
• Some transmission media will only propagate
  analog signals
• E.g., optical fiber and unguided media
• Analog data, analog signal
• Analog data in electrical form can be transmitted
  easily and cheaply
• Done with voice transmission over voice-grade
  lines

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2.2.1 Signal Encoding Criteria

• What determines how successful a receiver will be
  in interpreting an incoming signal?
• Signal-to-noise ratio
• Data rate
• Bandwidth
• An increase in data rate increases bit error rate
• An increase in SNR decreases bit error rate
• An increase in bandwidth allows an increase in
  data rate

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Factors Used to CompareEncoding Schemes

• Signal spectrum
• With lack of high-frequency components, less
  bandwidth required
• With no dc component, ac coupling via transformer
  possible
• Transfer function of a channel is worse near band
  edges
• Clocking
• Ease of determining beginning and end of each bit
  position

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Factors Used to CompareEncoding Schemes

• Signal interference and noise immunity
• Performance in the presence of noise
• Cost and complexity
• The higher the signal rate to achieve a given
  data rate, the greater the cost

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2.2.2 Digital data, analog signals
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Basic Encoding Techniques

• Digital data to analog signal
• Amplitude-shift keying (ASK)
• Amplitude difference of carrier frequency
• Frequency-shift keying (FSK)
• Frequency difference near carrier frequency
• Phase-shift keying (PSK)
• Phase of carrier signal shifted

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Basic Encoding Techniques
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Amplitude-Shift Keying

• One binary digit represented by presence of
  carrier, at constant amplitude
• Other binary digit represented by absence of
  carrier
• where the carrier signal is Acos(2pfct)

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Amplitude-Shift Keying

• Susceptible to sudden gain changes
• Inefficient modulation technique
• On voice-grade lines, used up to 1200 bps
• Used to transmit digital data over optical fiber

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Binary Frequency-Shift Keying (BFSK)

• Two binary digits represented by two different
  frequencies near the carrier frequency
• where f1 and f2 are offset from carrier frequency
  fc by equal but opposite amounts

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Binary Frequency-Shift Keying (BFSK)

• Less susceptible to error than ASK
• On voice-grade lines, used up to 1200bps
• Used for high-frequency (3 to 30 MHz) radio
  transmission
• Can be used at higher frequencies on LANs that
  use coaxial cable

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Multiple Frequency-Shift Keying (MFSK)

• More than two frequencies are used
• More bandwidth efficient but more susceptible to
  error
• f i f c (2i 1 M)f d
• f c the carrier frequency
• f d the difference frequency
• M number of different signal elements 2 L
• L number of bits per signal element

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Multiple Frequency-Shift Keying (MFSK)

• To match data rate of input bit stream, each
  output signal element is held for
• TsLT seconds
• where T is the bit period (data rate 1/T)
• So, one signal element encodes L bits

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Multiple Frequency-Shift Keying (MFSK)

• Total bandwidth required
• 2Mfd
• Minimum frequency separation required 2fd1/Ts
• Therefore, modulator requires a bandwidth of
• Wd2L/LTM/Ts

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Multiple Frequency-Shift Keying (MFSK)
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Phase-Shift Keying (PSK)

• Two-level PSK (BPSK)
• Uses two phases to represent binary digits

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Phase-Shift Keying (PSK)

• Differential PSK (DPSK)
• Phase shift with reference to previous bit
• Binary 0 signal burst of same phase as previous
  signal burst
• Binary 1 signal burst of opposite phase to
  previous signal burst

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Phase-Shift Keying (PSK)

• Four-level PSK (QPSK)
• Each element represents more than one bit

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Phase-Shift Keying (PSK)

• Multilevel PSK
• Using multiple phase angles with each angle
  having more than one amplitude, multiple signals
  elements can be achieved
• D modulation rate, baud
• R data rate, bps
• M number of different signal elements 2L
• L number of bits per signal element

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Performance

• Bandwidth of modulated signal (BT)
• ASK, PSK BT(1r)R
• FSK BT2?F(1r)R
• R bit rate
• 0 lt r lt 1 related to how signal is filtered
• ?F f2-fcfc-f1

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Performance

• Bandwidth of modulated signal (BT)
• MPSK
• MFSK
• L number of bits encoded per signal element
• M number of different signal elements

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Quadrature Amplitude Modulation

• QAM is a combination of ASK and PSK
• Two different signals sent simultaneously on the
  same carrier frequency

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Quadrature Amplitude Modulation
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2.2.3 Analog data, analog signals
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Reasons for Analog Modulation

• Modulation of digital signals
• When only analog transmission facilities are
  available, digital to analog conversion required
• Modulation of analog signals
• A higher frequency may be needed for effective
  transmission
• Modulation permits frequency division multiplexing

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Basic Encoding Techniques

• Analog data to analog signal
• Amplitude modulation (AM)
• Angle modulation
• Frequency modulation (FM)
• Phase modulation (PM)

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Amplitude Modulation

• Amplitude Modulation
• cos2?fct carrier
• x(t) input signal
• na modulation index
• Ratio of amplitude of input signal to carrier
• a.k.a (also known as) double sideband transmitted
  carrier (DSBTC)

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Spectrum of AM signal
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Amplitude Modulation

• Transmitted power
• Pt total transmitted power in s(t)
• Pc transmitted power in carrier

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Single Sideband (SSB)

• Variant of AM is single sideband (SSB)
• Sends only one sideband
• Eliminates other sideband and carrier
• Advantages
• Only half the bandwidth is required
• Less power is required
• Disadvantages
• Suppressed carrier cant be used for
  synchronization purposes

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Angle Modulation

• Angle modulation
• Phase modulation
• Phase is proportional to modulating signal
• np phase modulation index

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Angle Modulation

• Frequency modulation
• Derivative of the phase is proportional to
  modulating signal
• nf frequency modulation index

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Angle Modulation

• Compared to AM, FM and PM result in a signal
  whose bandwidth
• is also centered at fc
• but has a magnitude that is much different
• Angle modulation includes cos(? (t)) which
  produces a wide range of frequencies
• Thus, FM and PM require greater bandwidth than AM

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Angle Modulation

• Carsons rule
• where
• The formula for FM becomes

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2.2.4 Analog data, digital signals
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Basic Encoding Techniques

• Analog data to digital signal
• Pulse code modulation (PCM)
• Delta modulation (DM)

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Analog Data to Digital Signal

• Once analog data have been converted to digital
  signals, the digital data
• can be transmitted using NRZ-L
• can be encoded as a digital signal using a code
  other than NRZ-L
• can be converted to an analog signal, using
  previously discussed techniques

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Pulse Code Modulation

• Based on the sampling theorem
• Each analog sample is assigned a binary code
• Analog samples are referred to as pulse amplitude
  modulation (PAM) samples
• The digital signal consists of block of n bits,
  where each n-bit number is the amplitude of a PCM
  pulse

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Pulse Code Modulation
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Pulse Code Modulation

• By quantizing the PAM pulse, original signal is
  only approximated
• Leads to quantizing noise
• Signal-to-noise ratio for quantizing noise
• Thus, each additional bit increases SNR by 6 dB,
  or a factor of 4

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Delta Modulation

• Analog input is approximated by staircase
  function
• Moves up or down by one quantization level (?) at
  each sampling interval
• The bit stream approximates derivative of analog
  signal (rather than amplitude)
• 1 is generated if function goes up
• 0 otherwise

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Delta Modulation
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Delta Modulation

• Two important parameters
• Size of step assigned to each binary digit (?)
• Sampling rate
• Accuracy improved by increasing sampling rate
• However, this increases the data rate
• Advantage of DM over PCM is the simplicity of its
  implementation

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Reasons for Growth of Digital Techniques

• Growth in popularity of digital techniques for
  sending analog data
• Repeaters are used instead of amplifiers
• No additive noise
• TDM is used instead of FDM
• No intermodulation noise
• Conversion to digital signaling allows use of
  more efficient digital switching techniques

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2.3 Spread Spectrum
Reading material 1Chapter 7 in textbook
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2.3.1 The Concept of Spread Spectrum
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??????
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Spread Spectrum

• Input is fed into a channel encoder
• Produces analog signal with narrow bandwidth
• Signal is further modulated using sequence of
  digits
• Spreading code or spreading sequence
• Generated by pseudonoise, or pseudo-random number
  generator
• Effect of modulation is to increase bandwidth of
  signal to be transmitted

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Spread Spectrum

• On receiving end, digit sequence is used to
  demodulate the spread spectrum signal
• Signal is fed into a channel decoder to recover
  data

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Spread Spectrum
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Spread Spectrum

• What can be gained from apparent waste of
  spectrum?
• Immunity from various kinds of noise and
  multipath distortion
• Can be used for hiding and encrypting signals
• Several users can independently use the same
  higher bandwidth with very little interference

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?????????(1)

• ?????????????1941????????Hedy Lamarr ????George
  Antheil????
• 1949????????????????????????,Derosa?Rogoff????????
  ???????????????,??????New Jersey?California???????
  ??
• 1950?Basore?????????????NOMACS(Noise Modulation
  and Correlation Detection System)??????????????
• 1951???,??????????MIT???????????NOMACS??,?????????
  ???????????????????MIT???????
• 1952??????????P9D?NOMACS ??,???????

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?????????(2)

• 1955??????????????,??????????????????,???????Phat
  om(??,??)? Hush-Up(??),???????Blades(??),????
  ?????????
• 1976??????????????Spread Spectrum Systems???
• 1978??????????????????(CCIR)??????????????

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?????????(3)

• 1982??????????????????????????????,???????????????
  ???,?????????????
• ???????????????Coherent Spread Spectrum ???
• 1985??????????????
• ?????,??????????????????,??????????????????????

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2.3.2 Frequency Hopping Spread Spectrum
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Frequency Hoping Spread Spectrum (FHSS)

• Signal is broadcast over seemingly random series
  of radio frequencies
• A number of channels allocated for the FH signal
• Width of each channel corresponds to bandwidth of
  input signal
• Signal hops from frequency to frequency at fixed
  intervals
• Transmitter operates in one channel at a time
• Bits are transmitted using some encoding scheme
• At each successive interval, a new carrier
  frequency is selected

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Frequency Hoping Spread Spectrum

• Channel sequence dictated by spreading code
• Receiver, hopping between frequencies in
  synchronization with transmitter, picks up
  message
• Advantages
• Eavesdroppers hear only unintelligible blips
• Attempts to jam signal on one frequency succeed
  only at knocking out a few bits

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Frequency Hoping Spread Spectrum
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FHSS Using MFSK

• MFSK signal is translated to a new frequency
  every Tc seconds by modulating the MFSK signal
  with the FHSS carrier signal
• For data rate of R
• duration of a bit T 1/R seconds
• duration of signal element Ts LT seconds
• Tc ? Ts - slow-frequency-hop spread spectrum
• Tc lt Ts - fast-frequency-hop spread spectrum

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FHSS Performance Considerations

• Large number of frequencies used
• Results in a system that is quite resistant to
  jamming
• Jammer must jam all frequencies
• With fixed power, this reduces the jamming power
  in any one frequency band

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2.3.3 Direct Sequence Spread Spectrum
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Direct Sequence Spread Spectrum (DSSS)

• Each bit in original signal is represented by
  multiple bits in the transmitted signal
• Spreading code spreads signal across a wider
  frequency band
• Spread is in direct proportion to number of bits
  used
• One technique combines digital information stream
  with the spreading code bit stream using
  exclusive-OR (Figure 7.6)

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DSSS Using BPSK

• Multiply BPSK signal,
• sd(t) A d(t) cos(2? fct)
• by c(t) takes values 1, -1 to get
• s(t) A d(t)c(t) cos(2? fct)
• A amplitude of signal
• fc carrier frequency
• d(t) discrete function 1, -1
• At receiver, incoming signal multiplied by c(t)
• Since, c(t) x c(t) 1, incoming signal is
  recovered

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DSSS Using BPSK
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2.3.4 Code Division Multiple Access
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Code-Division Multiple Access (CDMA)

• Basic Principles of CDMA
• D rate of data signal
• Break each bit into k chips
• Chips are a user-specific fixed pattern
• Chip data rate of new channel kD

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CDMA Example

• If k6 and code is a sequence of 1s and -1s
• For a 1 bit, A sends code as chip pattern
• ltc1, c2, c3, c4, c5, c6gt
• For a 0 bit, A sends complement of code
• lt-c1, -c2, -c3, -c4, -c5, -c6gt
• Receiver knows senders code and performs
  electronic decode function
• ltd1, d2, d3, d4, d5, d6gt received chip pattern
• ltc1, c2, c3, c4, c5, c6gt senders code

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CDMA Example

• User A code lt1, 1, 1, 1, 1, 1gt
• To send a 1 bit lt1, 1, 1, 1, 1, 1gt
• To send a 0 bit lt1, 1, 1, 1, 1, 1gt
• User B code lt1, 1, 1, 1, 1, 1gt
• To send a 1 bit lt1, 1, 1, 1, 1, 1gt
• Receiver receiving with As code
• (As code) x (received chip pattern)
• User A 1 bit 6 -gt 1
• User A 0 bit -6 -gt 0
• User B 1 bit 0 -gt unwanted signal ignored

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CDMA for Direct Sequence Spread Spectrum
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2.3.5 Generation of Spreading Sequences
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Categories of Spreading Sequences

• Spreading Sequence Categories
• PN sequences
• Orthogonal codes
• For FHSS systems
• PN sequences most common
• For DSSS systems not employing CDMA
• PN sequences most common
• For DSSS CDMA systems
• PN sequences
• Orthogonal codes

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PN Sequences

• PN generator produces periodic sequence that
  appears to be random
• PN Sequences
• Generated by an algorithm using initial seed
• Sequence isnt statistically random but will pass
  many test of randomness
• Sequences referred to as pseudorandom numbers or
  pseudonoise sequences
• Unless algorithm and seed are known, the sequence
  is impractical to predict

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Important PN Properties

• Randomness
• Uniform distribution
• Balance property
• Run property
• Independence
• Correlation property
• Unpredictability

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Linear Feedback Shift Register Implementation
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Properties of M-Sequences

• Property 1
• Has 2n-1 ones and 2n-1-1 zeros
• Property 2
• For a window of length n slid along output for N
  (2n-1) shifts, each n-tuple appears once, except
  for the all zeros sequence
• Property 3
• Sequence contains one run of ones, length n
• One run of zeros, length n-1
• One run of ones and one run of zeros, length n-2
• Two runs of ones and two runs of zeros, length
  n-3
• 2n-3 runs of ones and 2n-3 runs of zeros, length 1

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Properties of M-Sequences

• Property 4
• The periodic autocorrelation of a 1
  m-sequence is

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Definitions

• Correlation
• The concept of determining how much similarity
  one set of data has with another
• Range between 1 and 1
• 1 The second sequence matches the first sequence
• 0 There is no relation at all between the two
  sequences
• -1 The two sequences are mirror images
• Cross correlation
• The comparison between two sequences from
  different sources rather than a shifted copy of a
  sequence with itself

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Advantages of Cross Correlation

• The cross correlation between an m-sequence and
  noise is low
• This property is useful to the receiver in
  filtering out noise
• The cross correlation between two different
  m-sequences is low
• This property is useful for CDMA applications
• Enables a receiver to discriminate among spread
  spectrum signals generated by different
  m-sequences

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Gold Sequences

• Gold sequences constructed by the XOR of two
  m-sequences with the same clocking
• Codes have well-defined cross correlation
  properties
• Only simple circuitry needed to generate large
  number of unique codes
• In following example (Figure 7.16a) two shift
  registers generate the two m-sequences and these
  are then bitwise XORed

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Orthogonal Codes

• Orthogonal codes
• All pairwise cross correlations are zero
• Fixed- and variable-length codes used in CDMA
  systems
• For CDMA application, each mobile user uses one
  sequence in the set as a spreading code
• Provides zero cross correlation among all users
• Types
• Welsh codes
• Variable-Length Orthogonal codes

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Walsh Codes

• Set of Walsh codes of length n consists of the n
  rows of an n n Walsh matrix
• W1 (0)
• n dimension of the matrix
• Every row is orthogonal to every other row and to
  the logical not of every other row
• Requires tight synchronization
• Cross correlation between different shifts of
  Walsh sequences is not zero

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Typical Multiple Spreading Approach

• Spread data rate by an orthogonal code
  (channelization code)
• Provides mutual orthogonality among all users in
  the same cell
• Further spread result by a PN sequence
  (scrambling code)
• Provides mutual randomness (low cross
  correlation) between users in different cells

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2.4 Coding and Error Control
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Coping with Data Transmission Errors

• Error detection codes
• Detects the presence of an error
• Automatic repeat request (ARQ) protocols
• Block of data with error is discarded
• Transmitter retransmits that block of data
• Error correction codes, or forward correction
  codes (FEC)
• Designed to detect and correct errors

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2.4.1 Error Detection
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Error Detection Probabilities

• Definitions
• Pb Probability of single bit error (BER)
• P1 Probability that a frame arrives with no bit
  errors
• P2 While using error detection, the probability
  that a frame arrives with one or more undetected
  errors
• P3 While using error detection, the probability
  that a frame arrives with one or more detected
  bit errors but no undetected bit errors

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Error Detection Probabilities

• With no error detection
• F Number of bits per frame

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Error Detection Process

• Transmitter
• For a given frame, an error-detecting code (check
  bits) is calculated from data bits
• Check bits are appended to data bits
• Receiver
• Separates incoming frame into data bits and check
  bits
• Calculates check bits from received data bits
• Compares calculated check bits against received
  check bits
• Detected error occurs if mismatch

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Error Detection Process
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Parity Check

• Parity bit appended to a block of data
• Even parity
• Added bit ensures an even number of 1s
• Odd parity
• Added bit ensures an odd number of 1s
• Example, 7-bit character 1110001
• Even parity 11100010
• Odd parity 11100011

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Cyclic Redundancy Check (CRC)

• Transmitter
• For a k-bit block, transmitter generates an
  (n-k)-bit frame check sequence (FCS)
• Resulting frame of n bits is exactly divisible by
  predetermined number
• Receiver
• Divides incoming frame by predetermined number
• If no remainder, assumes no error

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CRC using Modulo 2 Arithmetic

• Exclusive-OR (XOR) operation
• Parameters
• T n-bit frame to be transmitted
• D k-bit block of data the first k bits of T
• F (n k)-bit FCS the last (n k) bits of T
• P pattern of nk1 bits this is the
  predetermined divisor
• Q Quotient
• R Remainder

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CRC using Modulo 2 Arithmetic

• For T/P to have no remainder, start with
• Divide 2n-kD by P gives quotient and remainder
• Use remainder as FCS

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CRC using Modulo 2 Arithmetic

• Does R cause T/P have no remainder?
• Substituting,
• No remainder, so T is exactly divisible by P

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CRC using Polynomials

• All values expressed as polynomials
• Dummy variable X with binary coefficients

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CRC using Polynomials

• Widely used versions of P(X)
• CRC12
• X12 X11 X3 X2 X 1
• CRC16
• X16 X15 X2 1
• CRC CCITT
• X16 X12 X5 1
• CRC 32
• X32 X26 X23 X22 X16 X12 X11 X10
  X8 X7 X5 X4 X2 X 1

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CRC using Digital Logic

• Dividing circuit consisting of
• XOR gates
• Up to n k XOR gates
• Presence of a gate corresponds to the presence of
  a term in the divisor polynomial P(X)
• A shift register
• String of 1-bit storage devices
• Register contains n k bits, equal to the length
  of the FCS

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Digital Logic CRC
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2.4.2 Block Error Correction Codes
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Wireless Transmission Errors

• Error detection requires retransmission
• Detection inadequate for wireless applications
• Error rate on wireless link can be high, results
  in a large number of retransmissions
• Long propagation delay compared to transmission
  time

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Block Error Correction Codes

• Transmitter
• Forward error correction (FEC) encoder maps each
  k-bit block into an n-bit block codeword
• Codeword is transmitted analog for wireless
  transmission
• Receiver
• Incoming signal is demodulated
• Block passed through an FEC decoder

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Forward Error Correction Process
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FEC Decoder Outcomes

• No errors present
• Codeword produced by decoder matches original
  codeword
• Decoder detects and corrects bit errors
• Decoder detects but cannot correct bit errors
  reports uncorrectable error
• Decoder detects no bit errors, though errors are
  present

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Block Code Principles

• Hamming distance for 2 n-bit binary sequences,
  the number of different bits
• E.g., v1011011 v2110001 d(v1, v2)3
• Redundancy ratio of redundant bits to data bits
• Code rate ratio of data bits to total bits
• Coding gain the reduction in the required Eb/N0
  to achieve a specified BER of an error-correcting
  coded system

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Hamming Code

• Designed to correct single bit errors
• Family of (n, k) block error-correcting codes
  with parameters
• Block length n 2m 1
• Number of data bits k 2m m 1
• Number of check bits n k m
• Minimum distance dmin 3
• Single-error-correcting (SEC) code
• SEC double-error-detecting (SEC-DED) code

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Hamming Code Process

• Encoding k data bits (n -k) check bits
• Decoding compares received (n -k) bits with
  calculated (n -k) bits using XOR
• Resulting (n -k) bits called syndrome word
• Syndrome range is between 0 and 2(n-k)-1
• Each bit of syndrome indicates a match (0) or
  conflict (1) in that bit position

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Cyclic Codes

• Can be encoded and decoded using linear feedback
  shift registers (LFSRs)
• For cyclic codes, a valid codeword (c0, c1, ,
  cn-1), shifted right one bit, is also a valid
  codeword (cn-1, c0, , cn-2)
• Takes fixed-length input (k) and produces
  fixed-length check code (n-k)
• In contrast, CRC error-detecting code accepts
  arbitrary length input for fixed-length check code

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BCH Codes

• For positive pair of integers m and t, a (n, k)
  BCH code has parameters
• Block length n 2m 1
• Number of check bits n k mt
• Minimum distancedmin 2t 1
• Correct combinations of t or fewer errors
• Flexibility in choice of parameters
• Block length, code rate

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Reed-Solomon Codes

• Subclass of nonbinary BCH codes
• Data processed in chunks of m bits, called
  symbols
• An (n, k) RS code has parameters
• Symbol length m bits per symbol
• Block length n 2m 1 symbols m(2m 1) bits
• Data length k symbols
• Size of check code n k 2t symbols m(2t)
  bits
• Minimum distance dmin 2t 1 symbols

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Block Interleaving

• Data written to and read from memory in different
  orders
• Data bits and corresponding check bits are
  interspersed with bits from other blocks
• At receiver, data are deinterleaved to recover
  original order
• A burst error that may occur is spread out over a
  number of blocks, making error correction possible

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Block Interleaving
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2.4.3 Convolutional Codes
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Convolutional Codes

• Generates redundant bits continuously
• Error checking and correcting carried out
  continuously
• (n, k, K) code
• Input processes k bits at a time
• Output produces n bits for every k input bits
• K constraint factor
• k and n generally very small
• n-bit output of (n, k, K) code depends on
• Current block of k input bits
• Previous K-1 blocks of k input bits

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Convolutional Encoder
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Decoding

• Trellis diagram expanded encoder diagram
• Viterbi code error correction algorithm
• Compares received sequence with all possible
  transmitted sequences
• Algorithm chooses path through trellis whose
  coded sequence differs from received sequence in
  the fewest number of places
• Once a valid path is selected as the correct
  path, the decoder can recover the input data bits
  from the output code bits

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2.4.4 Automatic Repeat Request
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Automatic Repeat Request

• Mechanism used in data link control and transport
  protocols
• Relies on use of an error detection code (such as
  CRC)
• Flow Control
• Error Control

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Flow Control

• Assures that transmitting entity does not
  overwhelm a receiving entity with data
• Protocols with flow control mechanism allow
  multiple PDUs in transit at the same time
• PDUs arrive in same order theyre sent
• Sliding-window flow control
• Transmitter maintains list (window) of sequence
  numbers allowed to send
• Receiver maintains list allowed to receive

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Flow Control

• Reasons for breaking up a block of data before
  transmitting
• Limited buffer size of receiver
• Retransmission of PDU due to error requires
  smaller amounts of data to be retransmitted
• On shared medium, larger PDUs occupy medium for
  extended period, causing delays at other sending
  stations

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Flow Control
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Error Control

• Mechanisms to detect and correct transmission
  errors
• Types of errors
• Lost PDU a PDU fails to arrive
• Damaged PDU PDU arrives with errors

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Error Control Requirements

• Error detection
• Receiver detects errors and discards PDUs
• Positive acknowledgement
• Destination returns acknowledgment of received,
  error-free PDUs
• Retransmission after timeout
• Source retransmits unacknowledged PDU
• Negative acknowledgement and retransmission
• Destination returns negative acknowledgment to
  PDUs in error

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Go-back-N ARQ

• Acknowledgments
• RR receive ready (no errors occur)
• REJ reject (error detected)
• Contingencies
• Damaged PDU
• Damaged RR
• Damaged REJ

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