Digital Transmission

Digital Transmission Media Error Detection Digital Transmission

Transmitted Received Transmitter Signal Signal Receiver

Communication channel

Transmitter Key questions l Accepts bits from data link l How many bits per second can layer be transmitted reliably across the l Converts bits into digital channel? modulated signal l How much power and Receiver is consumed in the l Recovers bits from received process? signal l How do we control error rate in l Transfers bits to its data link delivered bits? layer Transmission Impairments

Transmitted Received Transmitter Signal Signal Receiver

Communication channel

Communication Channels Transmission Impairments l Pair of copper l Signal attenuation l l Signal distortion l Radio l Spurious noise l Light in l Interference from other l Light in air signals l Infrared Digital Binary Signal

1 0 1 1 0 1 +A

0 T 2T 3T 4T 5T 6T -A

Bit rate = 1 bit / T seconds For a given communications medium: l How do we increase transmission speed? l How do we achieve reliable communications? l Are there limits to speed and reliability? Pulse Transmission Rate

l Objective: Maximize pulse rate through a channel, that is, make T as small as possible

??? Channel

T t t

l If input is a narrow pulse, then typical output is a spread-out pulse with ringing l Question: How frequently can these pulses be transmitted without interfering with each other?

l Answer: 2 x Wc pulses/second

where Wc is the bandwidth of the channel Multilevel Pulse Transmission l If channel bandwidth Wc, we can transmit 2Wc pulses/sec (without interference) l 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 bps l If amplitudes are from {-A, -A/3, +A/3, +A}, then bit rate is 2 x 2Wc bps l By going to M = 2m amplitude levels, we achieve

Bit Rate = m bits/pulse x 2Wc pulses/sec = 2mWc bps

In the absence of noise, the bit rate can be increased without limit by increasing m Noise & Reliable Communications l All physical systems have noise l Electrons always vibrate randomly at non-zero temperature l Motion of electrons induces noise l Presence of noise limits accuracy of measurement of received signal amplitude l Errors occur if signal separation is comparable to noise level l Bit Error Rate (BER) increases with decreasing signal-to-noise ratio l Noise places a limit on how many amplitude levels can be used in pulse transmission Signal-to-Noise Ratio

Signal Noise Signal + noise High SNR t t t No errors

Signal Noise Signal + noise

Low SNR t t t

Average signal power error SNR = Average noise power

SNR (dB) = 10 log10 SNR Shannon Channel Capacity

C = Wc log2 (1 + SNR) bps l Arbitrarily reliable communications is possible if the transmission rate R < C. l If R > C, then arbitrarily reliable communications is not possible. l Arbitrarily reliable means the BER can be made arbitrarily small through sufficiently complex coding. l C can be used as a measure of how close a system design is to the best achievable performance. l Bandwidth Wc & SNR determine C Example l Find the Shannon channel capacity for a channel with Wc = 3400 Hz and SNR = 10000

C = 3400 log2 (1 + 10000)

= 3400 log10 (10001)/log102 = 45200 bps

Note that SNR = 10000 corresponds to

SNR (dB) = 10 log10(10000) = 40 dB Examples of Channels

Channel Bandwidth Bit Rates

Telephone voice 3-4 kHz 33 kbps channel Copper pair 1 MHz 1-6 Mbps (~1 mile) Coaxial cable 500 MHz 38 Mbps/ channel (6 MHz channels) 5 GHz radio 300 MHz 54 Mbps / channel (IEEE 802.11) (11 channels) Optical fiber Many TeraHertz 40-100 Gbps / wavelength Bit Rates of Digital Transmission Systems

System Bit Rate Observations Telephone 33.6-56 kbps 4 kHz telephone channel copper pair

Ethernet twisted 10 Mbps, 100 Mbps 100 meters of unshielded twisted pair copper pair

Cable modem .5Mbps-38-343Mbps Shared CATV return channel; 6Mz TV channel; 8 combined channels ADSL twisted 64-640 kbps in, 1.536- Coexists with analog telephone pair 6.144 Mbps out signal

FTTC+copper 100Mbps, 1 Gbps Fiber to the curb 2.4 GHz radio 2-11-54 Mbps IEEE 802.11 LAN 28 GHz radio Multi-Gbps mmwave radio in 5G Optical fiber 10-40-100-200-400 Gbps Optical fiber >400Gbps, >petabit/s 1 wavelength; multiple wavelengths Telephone Local Loop Local Loop: l Copper pair from telephone to CO l Pedestal to SAI to Main (MDF) l 2700 cable pairs in a feeder cable l MDF connects Pedestal l voice signal to telephone switch l DSL signal to routers Serving area Local telephone office interface Distribution cable Switch

Serving Distribution frame area Feeder interface cable

lFor interesting pictures of switches & MDF, see lweb.mit.edu/is/is/delivery/5ess/photos.html www.museumofcommunications.org/coe.html Twisted Pair

Twisted pair l Two insulated copper 30 26 gauge wires in regular spiral 24 gauge pattern to minimize interference 24 22 gauge l Various thicknesses, e.g. 0.016 inch (24 gauge) 18 l Low cost 19 gauge l Attenuation increases with distance 12 l Telephone loop from customer to CO Attenuation (dB/mi) 6 l Intra-building wiring closet to desktop f (kHz) 1 10 100 1000

Lower Higher attenuation rate attenuation rate analog telephone for DSL Twisted Pair Bit Rates

l Twisted pairs can provide Table 3.5 Data rates of 24-gauge twisted pair high bit rates at short distances Standard Data Rate Distance l Asymmetric Digital Subscriber Loop (ADSL) T-1 1.544 Mbps 18,000 feet, 5.5 km l Access l Lower 3 kHz for voice DS2 6.312 Mbps 12,000 feet, 3.7 km l Upper band for data 1/4 STS-1 12.960 4500 feet, 1.4 km l 64 kbps inbound Mbps l 640 kbps outbound

1/2 STS-1 25.920 3000 feet, 0.9 km l Much higher rates possible at Mbps shorter distances l Strategy for telephone STS-1 51.840 1000 feet, 300 m companies is to bring fiber Mbps close to home & then twisted pair l Higher-speed access +

Node

Curb

Building

Home Ethernet LANs

In office or home networks l Cat 3 Unshielded twisted pair (UTP): ordinary telephone wires

l l l l l l l Cat 5 UTP: tighter twisting to improve signal quality l Shielded twisted pair (STP): costly l10BASE-T Ethernet l 10 Mbps, Twisted pair l Two Cat3 pairs,100 meters l100BASE-T4 l 100 Mbps, Twisted pair l Four Cat3 pairs, 100 meters l Cat5 & STP provide other options l1000BASE-T GigE l Four Cat5 pairs, 100 meters lMany optical fiber options l 500m – many km Coaxial Cable

Twisted pair l Cylindrical braided outer 35 conductor surrounds 0.7/2.9 mm insulated inner wire 30 conductor l High interference immunity 25 1.2/4.4 mm l Higher bandwidth than twisted pair 20 l Hundreds of MHz 15 l Cable TV distribution l Original Ethernet LAN 10

medium (dB/km) Attenuation 2.6/9.5 mm 5

0.1 1.0 10 100 f (MHz) Cable Modem & TV Spectrum

Downstream Downstream Upstream 42 MHz 42 500 MHz 500 750 MHz 750 550 MHz 550 5 MHz 5 54 MHz 54

l Cable TV network originally unidirectional l Cable plant upgraded to bidirectional l 1 analog TV channel is 6 MHz, can support very high data rates l Cable Modem: shared upstream & downstream l 5-42 MHz upstream into network; 2 MHz channels; 500 kbps to 4 Mbps l >550 MHz downstream from network; 6 MHz channels; 36 Mbps Cable

Upstream fiber Fiber Fiber Head Fiber Fiber end node Downstream fiber

Coaxial distribution plant

= Bidirectional split-band Optical Fiber Properties

Advantages Disadvantages l Very low attenuation l New types of optical signal impairments & dispersion l Noise immunity l Polarization dependence l Extremely high l Wavelength dependence bandwidth l Limited bend radius l Security: Very difficult to l If physical arc of cable too tap without breaking high, light lost or wont l No corrosion reflect l Will break l More compact & lighter than copper wire l Difficult to splice l Mechanical vibration becomes signal noise Very Low Attenuation

100 Water Vapor Absorption 50 (removed in new fiber designs) 10 5

1 Infrared absorption 0.5 Rayleigh scattering Loss (dB/km) Loss

0.1 0.05

0.01 0.8 1.0 1.2 1.4 1.6 1.8 Wavelength (µm)

850 nm 1300 nm Low-cost LEDs Metropolitan Area 1550 nm LANs Networks Long Distance Networks Short Haul Long Haul Huge Available Bandwidth

l Optical range from λ1 to 100 λ1 +Δλ contains bandwidth 50 v v B = f1 – f2 = – 10 λ λ1 + Δλ 1 5 v Δλ / λ1 v Δλ = ≈ 2 λ1 1 + Δλ / λ1 λ1 1 0.5 Loss (dB/km) Loss

0.1 l Example: λ1 = 1450 nm λ1 +Δλ =1650 nm:

2(108)m/s 200nm B = ≈ 19 THz 0.8 1.0 1.2 1.4 1.6 1.8 (1450 nm)2 Fiber to the Home Fiber to the Home Evolution

From CO to Multiprovider Point of Presence Cellular Communications

Two basic concepts: l Frequency Reuse l A region is partitioned into cells l Each cell is covered by base station l Power transmission levels controlled to minimize inter-cell interference l Spectrum can be reused in other cells l Handoff l Procedures to ensure continuity of call as user moves from cell to another l Involves setting up call in new cell and tearing down old one Base station l Transmits to users on forward channels l Receives from users on reverse channels

BSS BSS Mobile Switching MSC Center SS7 HLR STP l Controls connection VLR Wireline EIR terminal setup within cells & AC PSTN to telephone network

AC = authentication center MSC = mobile switching center BSS = base station subsystem PSTN = public switched telephone network EIR = equipment identity register STP = signal transfer point HLR = home location register VLR = visitor location register "Gold" was 5, 20, 95, 0; changed to current 2nd column, 1st para, 5th line: interna-tionaux

imageable 2nd column, 1st para, 10th line: move l'at- to the next line so that there is no hyphenation. area

The Spectrum The spectrum is divided into a number of fre- Among radio spectrum users are broadcasters, Le spectre Le spectre se compose de bandes de fréquences Parmi les utilisateurs du spectre radioélectrique, Radio waves use the electromagnetic spectrum. quency bands, each possessing characteristics taxis, building and other construction trades, air Les ondes radioélectriques utilisent le spectre possédant chacune des particularités qui en on compte les radiodiffuseurs, les compagnies Industry Industrie peculiar to it which determine the usage appropri- transportation, radio amateurs, marine transporta- déterminent l’utilisation. Chaque bande est attri- de taxi, l’industrie du bâtiment et d’autres secteurs Canada Canada The lowest frequencies have the longest radio électromagnétique. Aux fréquences les plus bas- waves and the highest fre- ate to that band. Each band has been allocated by tion, carriers, electrical power ses correspondent les buée à un ou plusieurs services radio ou à des de la construction, les transporteurs aériens, les quencies have the shortest international agreement at a World Radiocommu- utilities, trucking companies, police, and federal, ondes radio les plus lon- usages déterminés par voie d’accords interna- radioamateurs, les transporteurs maritimes, les radio waves. nication Conference (WRC) to one or more radio provincial, territorial and municipal departments gues et aux fréquences les tionaux signés à une Conférence mondiale des entreprises de télécommunications, les services RADIO services or for specific usages. Sponsored by the and agencies. ATTRIBUTION DES plus élevées, les ondes radiocommunications (CMR). Organisées sous publics d’électricité, les entreprises de camion- Radio waves are character- International Union (a United nage, la police, ainsi que les ministères ou orga- This chart is based on the 2007 Canadian Table radio les plus courtes. l’égide d’un organisme des Nations Unies, l’Union ized according to their fre- Nations agency), WRCs are held to extend, nismes fédéraux, provinciaux, territoriaux et muni- of Frequency Allocations, which was developed internationale des télécommunications, les CMR quency, the unit for which review and revise frequency allocations among Les ondes radio se caract- cipaux. SPECTRUM from decisions of World Radio Conferences, FREQUENCES ont pour but d’étendre, d’étudier et de réviser is the hertz (Hz). The fre- the various uses. érisent par leur fréquence, l’attribution des bandes de fréquences. quency is determined by the including WRC-03. The chart provides a graphic qui se mesure en hertz Ce graphique est fondé sur la version 2007 du number of complete waves After WRC conferences — and when Canada’s representation of Canadian electromagnetic spec- (Hz). La fréquence est À l’issue de chacune de ces conférences et Tableau canadien d’attribution des bandes de ALLOCATIONS propagated through a needs change — Industry Canada allocates spe- trum allocations between 9 Hz and 275 GHz. RADIOELECTRIQUES déterminée par le nombre quand des changements s’imposent au Canada, fréquences, résultant des diverses Conférences cific frequency bands to services to satisfy mondiales des radiocommunications, notamment medium past a fixed point in For further information on spectrum or radio d’ondes complètes fran- Industrie Canada attribue des bandes de fréquen- domestic communications requirements as shown la CMR-03. Il fournit la représentation graphique one second. Thus, the fre- matters, contact the Spectrum and Radio Policy chissant un point fixe d’un ces particulières à certains services, de manière à on this chart. The official regulatory provisions that des attributions de fréquences radioélectriques au IN CANADA quency of a signal where Directorate, Industry Canada, Ottawa (e-mail: AU CANADA support en une seconde. s’adapter aux besoins du pays en matière de pertain to frequency allocations in Canada are Canada, entre 9 et 275 GHz. one wave passes a fixed point in one second [email protected]) or one of its regional offi- On dira donc d’un signal pour lequel une onde communications, comme l’illustre le graphique ci- contained in the Canadian Table of Frequency is one hertz. A kilohertz (kHz) represents ces in Moncton, Montréal, Toronto, Winnipeg or franchit un point fixe en une seconde qu’il a une dessous. Les dispositions officielles de la régle- Pour obtenir plus de renseignements sur le spec- Allocations and the related spectrum policies. 1000 waves passing a point in one second, or Vancouver. fréquence de 1 hertz. Le kilohertz (kHz) équivaut mentation touchant l’attribution des fréquences au tre ou les radiocommunications, veuillez commu- 1000 hertz. One megahertz (MHz) is 1000 kilo- à 1 000 ondes par seconde, soit 1 000 hertz, le Canada figurent dans le Tableau canadien niquer avec la Direction des politiques du spectre hertz and a gigahertz (GHz) is 1000 megahertz. mégahertz, à 1 000 kilohertz et le gigahertz d’attribution des bandes de fréquences et dans et de la radiocommunication d’Industrie Canada (GHz), à 1 000 mégahertz. les politiques connexes d’utilisation du spectre. à Ottawa (courriel: [email protected]), ou avec l’un des bureaux régionaux à Moncton, Omega long range navigation Montréal, Toronto, Winnipeg et Vancouver. Radionavigation à grande distance de type oméga 3 9 14 19.95 20.05 30 1 Aeronautical mobile VLF VLF Service mobile aéronautique Not allocated 2 Aeronautical radionavigation Non attribuée Radionavigation aéronautique 3 Amateur Amateur 3 kHz 30 kHz 4 Broadcasting Radiodiffusion Fixed 5 Fixe Land mobile 70 190 30 90 110 130 160 200 285 300 6 Service mobile terrestre Maritime mobile LF LF 7 Service mobile maritime Maritime radionavigation 8 Radionavigation maritime Meteorological aids 9 Auxiliaires de la météorologie 30 kHz 500 kHz — International radiotelegraph distress 2182 kHz — International 300 kHz Mobile and calling frequency distress and calling frequency 10 500 kHz — Fréquence internationale AM radio 160 metre band 2182 kHz — Fréquence internationale de Service mobile de détresse et d’appel pour radiotélégraphie Radio AM Bande de 160 mètres détresse et d'appel pour radiotéléphonie Radiolocation 11 Radiolocalisation

300 300 315 315 325 325 335 335 405 405 415 415 495 495 505 505 510 510 525 525 535 535 1 705 1 800 1 850 2 000 2 065 2 107 2 170 2 173.5 2 190.5 2 194 2 495 2 501 2 502 2 505 2 850 3 000 Radionavigation 12 Radionavigation MF MF Standard frequency 13 Fréquences étalon (R)R Earth exploration satellite 1s Exploration de la Terre par satellite Intersatellite service 300 kHz National Research Council time signal Industrial, scientific and medical uses (ISM) 40 metre band 20 metre band General radio service (GRS)/Citizens' band (CB) 3 MHz 2s Service inter-satellites Signaux horaires du Conseil national de recherches Emplois industriels, scientifiques et médicaux (ISM) Bande de 40 mètres Bande de 20 mètres Service de radio général (SRG)/Bande publique (BP) Meteorological satellite 80 metre band HF shortwave broadcasting National Research Council time signal 30 metre band Industrial, scientific and medical (ISM) National Research Council time signal 15 metre band 12 metre band ISM 10 metre band 3s Bande de 80 mètres Radiodiffusion HF sur ondes courtes Signaux horaires du Conseil national de recherches Bande de 30 mètres Industriel, scientific et medical (ISM) Signaux horaires du Conseil national de recherches Bande de 15 mètres Bande de 12 mètres Bande de 10 mètres Météorologie par satellite Radio astronomy 4s Radioastronomie 3 3.025 3.155 3.23 3.4 3.5 4 4.063 4.438 4.65 4.7 4.75 4.85 4.995 5.003 5.005 5.06 5.25 5.45 5.68 5.73 5.9 5.95 6.2 6.525 6.765 7 7.1 7.3 7.4 8.1 8.195 8.815 8.965 9.04 9.4 9.5 9.9 9.995 10.003 10.005 10.1 10.15 11.175 11.275 11.4 11.6 11.65 12.05 12.1 12.23 13.2 13.26 13.36 13.41 13.57 13.6 13.8 13.87 14 14.25 14.35 14.99 15.005 15.01 15.1 15.6 15.8 16.36 17.41 17.48 17.55 17.9 17.97 18.03 18.052 18.068 18.168 18.78 18.9 19.02 19.68 19.80 19.99 19.995 20.01 21 21.45 21.85 21.924 22 22.855 23 23.2 23.35 24 24.89 24.99 25.005 25.01 25.07 25.21 25.55 25.67 26.1 26.175 27.5 28 29.7 30 Radiodetermination satellite HF HF 5s Radiorepérage par satellite O O O O O O Space operations (R) (OR) A (R) (R) O (R) (R) (R) (R) (R) (R) (OR) (R) (R) 6s (R) (R) (R) (R) (R) (R) (R) Exploitation spatiale A A A A A A A A A A A S A A S S S A S A A A S Space research R R R R A AR AR R R R R R R AR R R 7s Recherche spatiale

3 MHz Air traffic control 2 metre band Vessel traffic services 30 MHz Contrôle de la circulation aérienne Bande de 2 mètres Services de trafic maritime Secondary Secondaire ISM Cordless phones 6 metre band TV channels 2– 4 TV channels 5–6 FM radio (100 channels spaced 200 kHz apart) 121.5 MHz — Emergency Low earth orbit satellite (LEO-SAT) LEO-SAT TV channels 7–13 Téléphones sans cordon Bande de 6 mètres Canaux de télévision 2 à 4 Canaux de télévision 5 et 6 Radio MF (100 canaux espacés de 200 kHz) 121,5 MHz — Urgence Satellite orbite basse terrestre (SAT-LEO) SAT-OBT Canaux de télévision 7 à 13 Satellite S Satellite

30 30.005 30.01 37.5 38.25 39.986 40.02 40.98 41.015 50 54 72 73 74.6 74.8 75.2 76 88 108 117.975 137 138 144 146 148 149.9 150.05 156.7625 156.8375 174 216 222 225 300 R Route S S Route

VHF S VHF Off route OR Hors route L L L Uplink S S Liaison montante Downlink 30 MHz Family radio service (FRS/GMRS) TV channels 38–59 Paging Air traffic control radars Mobile satellite service (MSS) Personal communication service (PCS) Advanced wireless service (AWS) Satellite radio networks Wireless communication services (WCS) 300 MHz Liaison descendante Dispositif radio familial Canaux de télévision 38 à 59 Téléappel Radars de contrôle de la circulation aérienne Service mobile par satellite (SMS) Service de communications personnelles (SCP) Services sans fil évolués (SSFE) Réseaux radio par satellite Services de télécommunications sans fil (STSF) Except aeronautical mobile TV channels 14– 36 Cellular/trunked mobile Air-to-ground L-E/S-P Global positioning system (GPS) Digital audio broadcasting (DAB) MSS/SMS AWS/SSFE A Search and rescue satellite (SARSAT) Canaux de télévision 14 à 36 Mobile cellulaire/partage Air-sol Système de positionnement mondial (GPS) Radiodiffusion audionumérique (RAN) WCS/STSF L-E/E-L (Wi-Fi, ISM) Sauf mobile aéronautique Satellite de recherche et sauvetage GPS PCS/SCP MSS/SMS 300 312 315 328.6 335.4 387 390 399.9 400.05 400.15 401 402 403 406 406.1 410 414 415 419 420 430 432 438 450 455 456 459 460 470 608 614 746 806 890 902 928 929 932 932.5 935 941 941.5 942 944 952 956 960 1 164 1 215 1 240 1 300 1 350 1 370 1 400 1 427 1 429 1 452 1 492 1 518 1 525 1 530 1 535 1 559 1 610 1 610.6 1 613.8 1 626.5 1 660 1 660.5 1 668 1 668.4 1 670 1 675 1 700 1 710 1 755 1 850 2 000 2 020 2 025 2 110 2 120 2 155 2 180 2 200 2 290 2 300 2 450 2 483.5 2 500 2 596 2 655 2 686 2 690 2 700 2 850 2 900 3 000 S S S S S A A A A A S S S S S S UHF S A S A UHF S S S S A S S A A A A A A S S S S S S A S S S S S A A A A S A A A A A S

300 MHz Fixed wireless access (FWA) C Band Fixed satellite service (FSS) C Band Ku Band Direct broadcasting satellite (DBS) Ku Band Ka Band Local multipoint communication systems (LMCS) Ka Band 3 GHz Accès fixe sans fil (AFSF) Bande C Services fixe par satellite (SFS) Radio (R-LAN) Bande C Bande Ku Satellite de radiodiffusion directe (SRD) Bande Ku Bande Ka Systemes de télécommunications multipoint locaux (STML) Bande Ka Please note: The space allotted to the Reseaux local sans fil Domestic satellites ISM Domestic satellites RADAR satellite Domestic satellites Domestic satellites Multimedia satellite ISM LMCS/STML Multimedia satellite services in the spectrum segments shown FWA/AFSF Satellites domestiques L-E/S-P (Wi-Fi, R-LAN) Satellites domestiques Satellite RADAR Satellites domestiques DBS/SRD Satellites domestiques DBS/SRD Satellite multimédia Large bande Satellite multimédia is not proportional to the actual amount of spectrum occupied. 3 3.1 3.3 3.45 3.5 4.2 4.4 4.5 4.8 4.825 4.835 4.95 4.99 5 5.01 5.03 5.15 5.25 5.35 5.46 5.47 5.57 5.65 5.725 5.85 5.925 6.7 7.075 7.145 7.235 7.25 7.3 7.45 7.55 7.75 7.85 7.9 7.975 8.025 8.175 8.215 8.4 8.5 8.55 8.65 8.75 8.85 9 9.2 9.3 9.5 9.8 10 10.45 10.5 10.55 10.6 10.68 10.7 11.7 12.2 12.7 12.75 13.25 13.4 13.75 14 14.47 14.5 15.35 15.4 15.43 15.63 15.7 16.6 17.1 17.2 17.3 17.7 17.8 18.1 18.4 18.6 18.8 19.3 19.7 20.2 21.2 21.4 22 22.21 22.5 22.55 23.55 23.6 24 24.05 24.25 24.45 24.65 24.75 25.05 25.25 25.5 27 27.5 29.5 30 S A A A A A S S S S S S S S S S Veuillez noter que l’espace attribué aux SHF S S SHF S S S S services dans les segments du spectre S S A S S S n’est pas proportionnel aux plages réelles S S S S S S S S S S S S S S S S S S S S S des fréquences occupées. S S S S S S S S S S A S S S S S 3 GHz 30 GHz

Broadband/Large bande ISM ISM Cat. No. Co22-33/2001-IN 123 30 31 31.3 31.8 32 32.3 33 33.4 34.2 34.7 35.2 35.5 36 37 37.5 38 39.5 40 40.5 41 42.5 43.5 47 47.2 50.2 50.4 51.4 52.6 54.25 55.78 58.2 59 59.3 64 65 66 71 74 76 77.5 78 79 84 86 92 94 95 100 102 105 109.5 111.8 114.25 116 122.25 130 134 136 141 148.5 151.5 158.5 164 167 174.5 174.8 182 185 190 191.8 200 209 217 226 231.5 232 235 238 240 241 248 250 252 265 275 300 81 94.1 155.5 ISBN 0-662-65588-5 S S S 53299 B S S S S S S EHF S S S S S S EHF S S S S S S S S S See email Smith.Peter Feb23, 2001 S S S Not allocated S S S S S S S S S S S S Non attribuée S A S S S S A S S S S S S S S S S S A S S S S S S S S S S S S 30 GHz 300 GHz Wavelength 3x108 m 3x107 m 3000 km 300 km 30 km 3 km 300 m 30 m 3 m 30 cm 3 cm 0.3 cm 0.03 cm 3x105 Å 3x104 Å 3x103 Å 3x102 Å 3x10 Å 3 Å 3x10-1 Å 3x10-2 Å 3x10-3 Å 3x10-4 Å 3x10-5 Å 3x10-6 Å 3x10-6 Å 3x10-7 Å Wavelength Longueur d’onde Longueur d’onde Infra-sonics Audible Range Ultra-sonics Microwave Infrared Visible Ultraviolet Gamma Ray Cosmic Ray Infracoustique Fréquences audibles Ultracoustique Micro-ondes Infrarouge Visible Ultraviolet X-Ray Rayons gamma Rayons cosmiques VLF LF MF HF VHF UHF SHF EHF Rayons X Frequency Frequency Fréquence 1 Hz 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1 THz 1013 Hz 1014 Hz 1015 Hz 1016 Hz 1017 Hz 1018 Hz 1019 Hz 1020 Hz 1021 Hz 1022 Hz 1023 Hz 1024 Hz 1025 Hz 1026 Hz Fréquence RADIO SPECTRUM (represented in chart above) SPECTRE DES RADIOFRÉQUENCES (représenté dans le graphique ci-dessus)

Scale point Chapter 3 Digital Transmission Fundamentals

Error Detection and Correction Error Control l Data applications require error- transfer l Voice & video applications tolerate some errors l Error control provides an acceptable error rate l Two basic approaches: l Error detection & retransmission (ARQ) l Forward error correction (FEC) Key Idea

l All transmitted data blocks (codewords) satisfy a pattern l If received block doesnt satisfy pattern, it is in error l Redundancy: Only a subset of all possible blocks can be codewords l Blindspot: when channel transforms a codeword into another codeword

All inputs to channel Channel satisfy pattern or condition output Deliver user Pattern User Encoder Channel information or checking information set error alarm Single Parity Check l Append an overall parity check to k information bits

Info Bits: b1, b2, b3, …, bk

Check Bit: bk+1= b1+ b2+ b3+ …+ bk modulo 2

Codeword: (b1, b2, b3, …, bk,, bk+!)

l All codewords have even # of 1s l Receiver checks to see if # of 1s is even l All error patterns that change an odd # of bits are detectable l All even-numbered patterns are undetectable l Parity bit used in ASCII code Example of Single Parity Code l Information (7 bits): (0, 1, 0, 1, 1, 0, 0) l Parity Bit: b8 = 0 + 1 +0 + 1 +1 + 0 = 1 l Codeword (8 bits): (0, 1, 0, 1, 1, 0, 0, 1) l If single error in bit 3 : (0, 1, 1, 1, 1, 0, 0, 1) l # of 1s =5, odd l Error detected l If errors in bits 3 and 5: (0, 1, 1, 1, 0, 0, 0, 1) l # of 1s =4, even l Error not detected Checkbits & Error Detection

Information bits Received information bits

Recalculate check bits k bits Channel Calculate Compare check bits Received Sent Information check bits check accepted if bits check bits match n – k bits How good is the single parity check code? l Redundancy: l 1 redundant bit per k information bits: l overhead = 1/(k + 1) l Coverage: l An error pattern is a binary (k + 1)-tuple with 1s where errors occur and 0s elsewhere l All error patterns with odd # of errors can be detected l Of 2k+1 binary (k + 1)-tuples, ½ are odd, so 50% of error patterns can be detected l Is it possible to detect more errors if we add more check bits? l Yes, with the right codes & more check bits What if bit errors are random? l Many transmission channels introduce bit errors at random, independently of each other, and with probability p l Some error patterns are more probable than others:

P[10000000] = p(1 – p)7 = (1 – p)8(p/(1-p)) and

P[11000000] = p2(1 – p)6 = (1 – p)8(p/(1-p))2

l In any worthwhile channel p < 0.5, and so (p/(1 – p) < 1 l It follows that patterns with 1 error are more likely than patterns with 2 errors and so forth l What is the probability that an undetectable error pattern occurs? Single parity check code with random bit errors l Undetectable error pattern if even # of bit errors: P[error detection failure] = P[undetectable error pattern] = P[error patterns with even number of 1s] n n = p2(1 – p)n-2 + p4(1 – p)n-4 + … 2 4 l Example: Evaluate above for n = 32, p = 10-3 32 32 P[undetectable error] = (10-3)2 (1 – 10-3)30 + (10-3)4 (1 – 10-3)28 2 4 ≈ 496 (10-6) + 35960 (10-12) ≈ 4.96 (10-4) l For this example, roughly 1 in 2000 error patterns is undetectable Internet Checksum l Several Internet protocols (e.g. IP, TCP, UDP) use check bits to detect errors in the IP header (or in the header and data for TCP/UDP) l A checksum is calculated for header contents and included in a special field. l Checksum recalculated at every router, so algorithm selected for ease of implementation in software l Let header consist of L, 16-bit words,

b0, b1, b2, ..., bL-1 l The algorithm appends a 16-bit checksum bL Checksum Calculation

The checksum bL is calculated as follows: l Treating each 16-bit word as an integer, find 16 x = b0 + b1 + b2+ ...+ bL-1 modulo 2 -1 l The checksum is then given by: 16 bL = - x modulo 2 -1 Thus, the headers must satisfy the following pattern: 16 0 = b0 + b1 + b2+ ...+ bL-1 + bL modulo 2 -1 l The checksum calculation is carried out in software using ones complement arithmetic Internet Checksum Example

Use Modulo Arithmetic Use Binary Arithmetic l Assume 4-bit words l Note 16 =1 mod15 l Use mod 24-1 arithmetic l So: 10000 = 0001 mod15 l b0=1100 = 12 l leading bit wraps around l b =1010 = 10 1 b0 + b1 = 1100+1010 l b0+b1=12+10=7 mod15 =10110 =10000+0110 l b = -7 = 8 mod15 2 =0001+0110 l Therefore =0111 l b2=1000 =7 Take 1s complement

b2 = -0111 =1000 Polynomial Codes l Polynomials instead of vectors for codewords l Polynomial arithmetic instead of check sums l Implemented using shift-register circuits l Also called cyclic redundancy check (CRC) codes l Most data communications standards use polynomial codes for error detection l Polynomial codes also basis for powerful error-correction methods Binary Polynomial Division

l Division with Decimal Numbers

34 quotient dividend = quotient x divisor +remainder 35 ) 1222 dividend 105 1222 = 34 x 35 + 32 divisor 17 2 140 32 remainder

x3 + x2 + x = q(x) quotient l Polynomial Division x3 + x + 1 ) x6 + x5 x6 + x4 + x3 dividend divisor x5 + x4 + x3 x5 + x3 + x2

Note: Degree of r(x) is less than x4 + x2 degree of divisor x4 + x2 + x x = r(x) remainder Polynomial Coding l Code has binary generating polynomial of degree n–k

n-k n-k-1 2 g(x) = x + gn-k-1x + … + g2x + g1x + 1 l k information bits define polynomial of degree k – 1 k-1 k-2 2 i(x) = ik-1x + ik-2x + … + i2x + i1x + i0

l Find remainder polynomial of at most degree n – k – 1 q(x) g(x) ) xn-k i(x) xn-ki(x) = q(x)g(x) + r(x) r(x) l Define the codeword polynomial of degree n – 1 n-k b(x) = x i(x) + r(x) There are 2k codewords n bits k bits n-k bits Polynomial example: k = 4, n–k = 3 Generator polynomial: g(x)= x3 + x + 1 Information: (1,1,0,0) i(x) = x3 + x2 Encoding: x3i(x) = x6 + x5

x3 + x2 + x 1110 x3 + x + 1 ) x6 + x5 1011 ) 1100000 x6 + x4 + x3 1011

x5 + x4 + x3 1110 x5 + x3 + x2 1011

x4 + x2 1010 x4 + x2 + x 1011

x 010 Transmitted codeword: b(x) = x6 + x5 + x b = (1,1,0,0,0,1,0) The Pattern in Polynomial Coding

l All codewords satisfy the following pattern: b(x) = xn-ki(x) + r(x) = q(x)g(x) + r(x) + r(x) = q(x)g(x) l All codewords are a multiple of g(x)! l To check if an arbitrary polynomial p(x) is a codeword divide it by g(x) and check if remainder is zero Standard Generator Polynomials CRC = cyclic redundancy check l CRC-8: = x8 + x2 + x + 1 ATM l CRC-16: = x16 + x15 + x2 + 1 Bisync = (x + 1)(x15 + x + 1) l CCITT-16: = x16 + x12 + x5 + 1 HDLC, XMODEM, V.41 l CCITT-32: IEEE 802, DoD, V.42 = x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1

See Wikipedia on “cyclic redundancy check” for many more generator polynomials