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1、1,Chapter 4 Digital Transmission Fundamentals,4.1 Digital Representation of Information4.2 Why Digital Communications?4.3 Digital Representation of Analog Signals4.4 Characterization of Communication Channels4.5 Fundamental Limits in Digital Transmission4.6 Line Coding4.7 Modems and Digital Modulati
2、on4.8 Properties of Media and Digital Transmission Systems4.9 Error Detection and Correction,2,The Seven-Layer OSI Reference Model,ApplicationLayer,PresentationLayer,SessionLayer,TransportLayer,NetworkLayer,Data LinkLayer,PhysicalLayer,ApplicationLayer,PresentationLayer,SessionLayer,TransportLayer,N
3、etworkLayer,Data LinkLayer,PhysicalLayer,NetworkLayer,Application,Application,Data LinkLayer,PhysicalLayer,NetworkLayer,Data LinkLayer,PhysicalLayer,Communicating End Systems,One or More Network Nodes,End-to-End Protocols,3,Physical Layer,Transfers bits across linkDefinition&specification of the phy
4、sical aspects of a communications linkEthernet,DSL,cable modem,telephone modemsTwisted-pair cable,coaxial cable optical fiber,radio,infrared,4,Chapter 4 Digital Transmission Fundamentals,Digital Representation of Information,5,Block vs.Stream Information,BlockInformation that occurs in a single bloc
5、kSize=Bits/blockor bytes/block1 kbyte=210 bytes1 Mbyte=220 bytes1 Gbyte=230 bytes,StreamInformation that is produced&transmitted continuouslyBit rate=bits/second1 kbps=103 bps1 Mbps=106 bps1 Gbps=109 bps,6,Digitization of Analog Signal,Sample analog signal in time and amplitudeFind closest approxima
6、tion,Original signal,Sample value,Approximation,Rs=Bit rate=#bits/sample x#samples/second,3 bits/sample,7,Bit Rate of Digitized Signal,Bandwidth Ws Hertz:Higher bandwidth more frequent samplesMinimum sampling rate=2 x WsRepresentation accuracy:range of approximation errorHigher accuracy smaller spac
7、ing between approximation values more bits per sample,8,Example:Voice&Audio,Telephone voiceWs=4 kHz 8000 samples/sec8 bits/sampleRs=8 x 8000=64 kbpsCellular phones use more powerful compression algorithms:8-12 kbps,CD AudioWs=22 kHertz 44000 samples/sec16 bits/sampleRs=16 x 44000=704 kbps per audio
8、channelMP3 uses more powerful compression algorithms:50 kbps per audio channel,9,Chapter 4 Communication Networks and Services,Why Digital Communications?,10,A Transmission System,Transmitter:Converts information into signal suitable for transmissionInjects energy into communications medium or chann
9、elReceiver:Receives energy from mediumConverts received signal into form suitable for delivery to user,11,Transmission Impairments,Communication ChannelPair of copper wiresCoaxial cableRadio Light in optical fiberLight in airInfrared,Transmission ImpairmentsSignal attenuationSignal distortionSpuriou
10、s noiseInterference from other signals,12,Analog Long-Distance Communications,Each repeater attempts to restore analog signal to its original formRestoration is imperfectDistortion is not completely eliminatedNoise&interference is only partially removedSignal quality decreases with#of repeatersCommu
11、nications is distance-limited,13,Analog vs.Digital Transmission,Analog transmission:all details must be reproduced accurately,Sent,Received,Received,DistortionAttenuation,Digital transmission:only discrete levels need to be reproduced,DistortionAttenuation,Simple Receiver:Was original pulse positive
12、 or negative?,14,Digital Long-Distance Communications,Regenerator recovers original data sequence and retransmits on next segmentCan design so error probability is very smallThen each regeneration is like the first time!Communications is possible over very long distancesDigital systems vs.analog sys
13、temsLess power,longer distances,lower system costMonitoring,multiplexing,coding,encryption,protocols,15,Digital Binary Signal,For a given communications medium:How do we increase transmission speed?How do we achieve reliable communications?Are there limits to speed and reliability?,Bit rate=1 bit/T
14、seconds,16,Pulse Transmission Rate,Objective:Maximize pulse rate through a channel,that is,make T as small as possible,Channel,t,t,pulse frequently without interfering with each other:2 x Wc pulses/second for lowpass channel Wc pulses/second for bandpass channelWc is the bandwidth of the channel,T,1
15、7,Multilevel Pulse Transmission,If pulses amplitudes are either-A or+A,then each pulse conveys 1 bit,so Bit Rate=1 bit/pulse x 2Wc pulses/sec=2Wc bpsIf amplitudes are from-A,-A/3,+A/3,+A,then bit rate is 2 x 2Wc bpsBy going to M=2m amplitude levels,we achieve Bit Rate=m bits/pulse x 2Wc pulses/sec=2
16、mWc bps,18,Noise&Reliable Communications,All physical systems have noisePresence of noise limits accuracy of measurement of received signal amplitudeErrors occur if signal separation is comparable to noise levelBit Error Rate(BER)increases with decreasing signal-to-noise ratioNoise places a limit on
17、 how many amplitude levels can be used in pulse transmission,19,SNR=,Average signal power,Average noise power,SNR(dB)=10 log10 SNR,Signal-to-Noise Ratio,error,No errors,20,Arbitrarily reliable communications is possible if the transmission rate R C,then arbitrarily reliable communications is not pos
18、sible.“Arbitrarily reliable”means the BER can be made arbitrarily small through sufficiently complex coding.C can be used as a measure of how close a system design is to the best achievable performance.,Shannon Channel Capacity,C=Wc log2(1+SNR)bps,21,Example,Find the Shannon channel capacity for a t
19、elephone channel with Wc=3400 Hz and SNR=10000 C=3400 log2(1+10000)=3400 log10(10001)/log102=45200 bpsNote that SNR=10000 corresponds to SNR(dB)=10 log10(10001)=40 dB,22,Bit Rates of Digital Transmission Systems,23,Examples of Channels,24,Chapter 4 Digital Transmission Fundamentals,Digital Represent
20、ation of Analog Signals,25,Interpolationfilter,(a),(b),Nyquist:Perfect reconstruction if sampling rate 1/T 2Ws,Sampling Theorem,26,Digital Transmission of Analog Information,27,Quantization error:“noise”=x(nT)y(nT),Quantizer maps inputinto closest of 2mrepresentation values,Quantization of Analog Sa
21、mples,28,W=4KHz,so Nyquist sampling theorem 2W=8000 samples/second8 bits/samplePCM(“Pulse Code Modulation”)Telephone Speech:Bit rate=8000 x 8 bits/sec=64 kbps,Example:Telephone Speech,29,Chapter 4 Digital Transmission Fundamentals,Characterization of Communication Channels,30,Communications Channel,
22、Signal Bandwidthtransfer data faster,a signal varies more quickly.Channel BandwidthA channel or medium has an inherent limit on how fast the signals it passes can vary,Transmission ImpairmentsSignal attenuationSignal distortionSpurious noiseInterference from other signals,Transmitted Signal,Received
23、 Signal,Receiver,Communication channel,Transmitter,31,Ideal Low-Pass Filter,Ideal filter:all sinusoids with frequency fWc are passed without attenuation and delayed by t seconds;sinusoids at other frequencies are blocked,Amplitude Response,Wc,y(t)=Aincos(2ft-2ft)=Aincos(2f(t-t)=x(t-t),32,Example:Low
24、-Pass Filter,Simplest non-ideal circuit that provides low-pass filtering,33,Bandpass Channel,Some channels pass signals within a band that excludes low frequenciesTelephone modems,radio systems,Channel bandwidth is the width of the frequency band that passes non-negligible signal power,34,Chapter 4
25、Digital Transmission Fundamentals,Fundamental Limits in Digital Transmission,35,Noise distribution,Noise is characterized by probability density of amplitude samplesNoise distribution is Gaussian(bell-shaped)as below,t,PrX(t)x0=?,PrX(t)x0=Area undergraph,x0,x0,s2=Avg Noise Power,36,Probability of Er
26、ror,Error occurs if noise value exceeds certain magnitudeProb.of large values drops quickly with Gaussian noiseTarget probability of error achieved by designing system so separation between signal levels is appropriate relative to average noise power,PrX(t)d,37,Chapter 4 Digital Transmission Fundame
27、ntals,Line Coding,38,What is Line Coding?,Mapping of binary information sequence into the digital signal that enters the channelEx.“1”maps to+A square pulse;“0”to A pulseLine code selected to meet system requirements:Low frequency content:Some channels block low frequencieslong periods of+A or of A
28、causes signal to“droop”Waveform should not have low-frequency content,39,Line code selected to meet system requirements,Transmitted power:Power consumption=$Bit timing:Transitions in signal help timing recoveryBandwidth efficiency:Excessive transitions wastes bandwidth.Complexity/cost:Is code implem
29、entable in chip at high speed?Error detection:Ability to detect errors helps,40,Unipolar&Polar Non-Return-to-Zero(NRZ),Unipolar NRZ“1”maps to+A pulse“0”maps to no pulseHigh Average Power0.5*A2+0.5*02=A2/2Long strings of A or 0Poor timingLow-frequency contentSimple,Polar NRZ“1”maps to+A/2 pulse“0”map
30、s to A/2 pulseBetter Average Power0.5*(A/2)2+0.5*(-A/2)2=A2/4Long strings of+A/2 or A/2Poor timing Low-frequency contentSimple,Unipolar NRZ,Polar NRZ,41,Bipolar Code,Three signal levels:-A,0,+A“1”maps to+A or A in alternation“0”maps to no pulseEvery+pulse matched by pulse so little content at low fr
31、equenciesString of 1s produces a square waveSpectrum centered at T/2Long string of 0s causes receiver to lose synchZero-substitution codes,Bipolar Encoding,42,Manchester code&mBnB codes,“1”maps into A/2 first T/2,-A/2 last T/2“0”maps into-A/2 first T/2,A/2 last T/2Every interval has transition in mi
32、ddleTiming recovery easyUses double the minimum bandwidthSimple to implementUsed in 10-Mbps Ethernet&other LAN standards,mBnB line codeMaps block of m bits into n bitsManchester code is 1B2B code4B5B code used in FDDI LAN8B10b code used in Gigabit Ethernet64B66B code used in 10G Ethernet,Manchester
33、Encoding,43,Differential Coding,Errors in some systems cause transposition in polarity,+A become A and vice versaAll subsequent bits in Polar NRZ coding would be in errorDifferential line coding provides robustness to this type of error“1”mapped into transition in signal level“0”mapped into no trans
34、ition in signal levelSame spectrum as NRZErrors occur in pairsAlso used with Manchester coding,NRZ-inverted(differentialencoding),DifferentialManchesterencoding,44,Line coding examples,45,Spectrum of Line codes,Assume 1s&0s independent&equiprobable,NRZ has high content at low frequenciesBipolar tigh
35、tly packed around T/2Manchester wasteful of bandwidth,46,Chapter 4 Digital Transmission Fundamentals,Modems and Digital Modulation,47,Bandpass Channels,Bandpass channels pass a range of frequencies around some center frequency fcRadio channels,telephone&DSL modemsDigital modulators embed information
36、 into waveform with frequencies passed by bandpass channelSinusoid of frequency fc is centered in middle of bandpass channelModulators embed information into a sinusoid,fc Wc/2,fc,0,fc+Wc/2,48,Information,+1,-1,AmplitudeShiftKeying,+1,-1,FrequencyShiftKeying,t,t,Amplitude Modulation and Frequency Mo
37、dulation,Map bits into amplitude of sinusoid:“1”send sinusoid;“0”no sinusoidDemodulator looks for signal vs.no signal,Map bits into frequency:“1”send frequency fc+d;“0”send frequency fc-d Demodulator looks for power around fc+d or fc-d,49,Phase Modulation,Map bits into phase of sinusoid:“1”send A co
38、s(2pft),i.e.phase is 0“0”send A cos(2pft+p),i.e.phase is pEquivalent to multiplying cos(2pft)by+A or-A“1”send A cos(2pft),i.e.multiply by 1“0”send A cos(2pft+p)=-A cos(2pft),i.e.multiply by-1We will focus on phase modulation,Information,50,Modulator&Demodulator,51,Information,BasebandSignal,Modulate
39、dSignal x(t),Example of Modulation,A cos(2pft),-A cos(2pft),52,RecoveredInformation,Basebandsignal discernable after smoothing,After multiplicationat receiverx(t)cos(2pfct),+A,-A,0,T,2T,3T,4T,5T,6T,Example of Demodulation,A 1+cos(4pft),-A 1+cos(4pft),53,Chapter 4 Digital Transmission Fundamentals,Pr
40、operties of Media and Digital Transmission Systems,54,Fundamental Issues in Transmission Media,Information bearing capacityAmplitude response n=2.0 x 108 m/sec in optical fiber,55,Electromagnetic Spectrum,56,Electromagnetic Spectrum,Frequency of communications signals,Analog telephone,DSL,Cell phone
41、,WiFi,Optical fiber,57,Wireless Media,Signal energy propagates in space,limited directionalityInterference possible,so spectrum regulatedLimited bandwidthSimple infrastructure:antennas&transmittersNo physical connection between network&userUsers can move,58,Wired Media,Signal energy contained&guided
42、 within mediumSpectrum can be re-used in separate media(wires or cables),more scalableExtremely high bandwidthComplex infrastructure:ducts,conduits,poles,right-of-way,59,Attenuation,Attenuation varies with mediaWired media has exponential dependenceReceived power at d meters proportional to 10-kd At
43、tenuation in dB=k d,where k is dB/meterWireless media has logarithmic dependenceReceived power at d meters proportional to d-n Attenuation in dB=n log d,where n is path loss exponent;n=2 in free space,60,Twisted Pair,Two insulated copper wires arranged in a regular spiral pattern to minimize interfe
44、renceLow costTelephone subscriber loop from customer to CO,Lower attenuation rate analog telephone,Higher attenuation ratefor DSL,61,Twisted Pair Bit Rates,Data rates of 24-gauge twisted pair,62,Ethernet LANs,Category 3 unshielded twisted pair(UTP):ordinary telephone wiresCategory 5 UTP:tighter twis
45、ting to improve signal qualityShielded twisted pair(STP):to minimize interference;costly10BASE-T Ethernet100BASE-T4 Fast EthernetCat5&STP provide other options,63,Coaxial Cable,Cylindrical braided outer conductor surrounds insulated inner wire conductorHigh interference immunityHigher bandwidth than
46、 twisted pairHundreds of MHz,64,Optical Fiber,Light sources(lasers,LEDs)generate pulses of light that are transmitted on optical fiberVery long distances(1000 km)Very high speeds(40 Gbps/wavelength)Nearly error-free(BER of 10-15)Profound influence on network architecture,65,Geometry of optical fiber
47、,Total Internal Reflection in optical fiber,Transmission in Optical Fiber,Core has higher index of refraction than claddingLight rays incident at less than critical angle qc is completely reflected back into the core,66,Multimode:Thicker core,Rays on different paths interfere causing dispersion&limi
48、ting bit rateSingle mode:Very thin core,More expensive lasers,but achieves very high speeds,Multimode&Single-mode Fiber,67,Optical Fiber Properties,AdvantagesVery low attenuationNoise immunityExtremely high bandwidthSecurity:Very difficult to tap without breakingNo corrosionMore compact&lighter than
49、 copper wireDisadvantagesNew types of optical signal impairments&dispersionLimited bend radiusDifficult to splice,68,Very Low Attenuation,850 nmLow-cost LEDsLANs,1300 nmMetropolitan Area Networks“Short Haul”,1550 nmLong Distance Networks“Long Haul,Water Vapor Absorption(removed in new fiber designs)
50、,69,Huge Available Bandwidth,Optical range from 1 to 1+contains bandwidth,Example:1=1450 nm 1+=1650 nm:,B=19 THz,70,Wavelength-Division Multiplexing,Different wavelengths carry separate signalsMultiplex into shared optical fiberEach wavelength like a separate circuitA single fiber can carry 160 wave
