Chapter 3 Digital Transmission Fundamentals Digital Representation of Information Why Digital Communications? Digital Representation of Analog Signals Characterization of Communication Channels Fundamental Limits in Digital Transmission Line Coding Modems and Digital Modulation Properties of Media and Digital Transmission Systems Error Detection and Correction Digital Networks z Digital transmission enables networks to support many services TV E-mail Telephone Questions of Interest z How long will it take to transmit a message? z How many bits are in the message (text, image)? z How fast does the network/system transfer information? z Can a network/system handle a voice (video) call? z How many bits/second does voice/video require? At what quality? z How long will it take to transmit a message without errors? z How are errors introduced? z How are errors detected and corrected? z What transmission speed is possible over radio, copper cables, fiber, infrared, …? Chapter 3 Digital Transmission Fundamentals Digital Representation of Information Bits, numbers, information z Bit: number with value 0 or 1 z n bits: digital representation for 0, 1, … , 2n z Byte or Octet, n = 8 z Computer word, n = 16, 32, or 64 z n bits allows enumeration of 2n possibilities z n-bit field in a header z n-bit representation of a voice sample z Message consisting of n bits z The number of bits required to represent a message is a measure of its information content z More bits → More content Block vs. Stream Information Block Stream z Information that occurs z Information that is in a single block produced & transmitted z Text message continuously z Data file z Real-time voice z JPEG image z Streaming video z MPEG file z Size = Bits / block z Bit rate = bits / second or bytes/block z 1 kbps = 103 bps 6 z 1 kbyte = 210 bytes z 1 Mbps = 10 bps 9 bps z 1 Mbyte = 220 bytes z 1 Gbps =10 z 1 Gbyte = 230 bytes Transmission Delay z L number of bits in message z R bps speed of digital transmission system z L/R time to transmit the information z tprop time for signal to propagate across medium z d distance in meters z c speed of light (3x108 m/s in vacuum) Delay = tprop + L/R = d/c + L/R seconds Use data compression to reduce L Use higher speed modem to increase R Place server closer to reduce d Compression z Information usually not represented efficiently z Data compression algorithms z Represent the information using fewer bits z Noiseless: original information recovered exactly z E.g. zip, compress, GIF, fax z Noisy: recover information approximately z JPEG z Tradeoff: # bits vs. quality z Compression Ratio #bits (original file) / #bits (compressed file) Color Image W W W W Red Green Blue Color component component component H image =++H image H image H image Total bits = 3 × H × W pixels × B bits/pixel = 3HWB bits Example: 8×10 inch picture at 400 × 400 pixels per inch2 400 × 400 × 8 × 10 = 12.8 million pixels 8 bits/pixel/color 12.8 megapixels × 3 bytes/pixel = 38.4 megabytes Examples of Block Information Type Method Format Original Compressed (Ratio) Text Zip, ASCII Kbytes- (2-6) compress Mbytes Fax CCITT A4 page 256 5-54 kbytes Group 3 200x100 kbytes (5-50) pixels/in2 Color JPEG 8x10 in2 photo 38.4 1-8 Mbytes Image 4002 pixels/in2 Mbytes (5-30) Stream Information z A real-time voice signal must be digitized & transmitted as it is produced z Analog signal level varies continuously in time Th e s p ee ch s i g n al l e v el v a r ie s w i th t i m(e) Digitization of Analog Signal z Sample analog signal in time and amplitude z Find closest approximation Original signal Sample value 7Δ/2 Approximation 5Δ/2 3Δ/2 Δ/2 −Δ/2 −3Δ/2 3 bits / sample −5Δ/2 −7Δ/2 Rs = Bit rate = # bits/sample x # samples/second Bit Rate of Digitized Signal z Bandwidth Ws Hertz: how fast the signal changes z Higher bandwidth → more frequent samples z Minimum sampling rate = 2 x Ws z Representation accuracy: range of approximation error z Higher accuracy → smaller spacing between approximation values → more bits per sample Example: Voice & Audio Telephone voice CD Audio z Ws = 4 kHz → 8000 z Ws = 22 kHertz → 44000 samples/sec samples/sec z 8 bits/sample z 16 bits/sample z Rs=8 x 8000 = 64 kbps z Rs=16 x 44000= 704 kbps per audio channel z Cellular phones use z MP3 uses more powerful more powerful compression algorithms: compression 50 kbps per audio algorithms: 8-12 kbps channel Video Signal z Sequence of picture frames z Each picture digitized & compressed z Frame repetition rate z 10-30-60 frames/second depending on quality z Frame resolution z Small frames for 30 fps videoconferencing z Standard frames for conventional broadcast TV z HDTV frames Rate = M bits/pixel x (WxH) pixels/frame x F frames/second Video Frames 176 QCIF videoconferencing 144 at 30 frames/sec = 760,000 pixels/sec 720 Broadcast TV at 30 frames/sec = 480 10.4 x 106 pixels/sec 1920 HDTV at 30 frames/sec = 1080 67 x 106 pixels/sec Digital Video Signals Type Method Format Original Compressed Video H.261 176x144 or 2-36 64-1544 Confer- 352x288 pix Mbps kbps ence @10-30 fr/sec Full MPEG 720x480 pix 249 2-6 Mbps Motion 2 @30 fr/sec Mbps HDTV MPEG 1920x1080 1.6 19-38 Mbps 2 @30 fr/sec Gbps Transmission of Stream Information z Constant bit-rate z Signals such as digitized telephone voice produce a steady stream: e.g. 64 kbps z Network must support steady transfer of signal, e.g. 64 kbps circuit z Variable bit-rate z Signals such as digitized video produce a stream that varies in bit rate, e.g. according to motion and detail in a scene z Network must support variable transfer rate of signal, e.g. packet switching or rate-smoothing with constant bit-rate circuit Stream Service Quality Issues Network Transmission Impairments z Delay: Is information delivered in timely fashion? z Jitter: Is information delivered in sufficiently smooth fashion? z Loss: Is information delivered without loss? If loss occurs, is delivered signal quality acceptable? z Applications & application layer protocols developed to deal with these impairments Chapter 3 Communication Networks and Services Why Digital Communications? A Transmission System Transmitter Receiver Communication channel Transmitter z Converts information into signal suitable for transmission z Injects energy into communications medium or channel z Telephone converts voice into electric current z Modem converts bits into tones Receiver z Receives energy from medium z Converts received signal into form suitable for delivery to user z Telephone converts current into voice z Modem converts tones into bits Transmission Impairments Transmitted Transmitter Received Signal Signal Receiver Communication channel Communication Channel Transmission Impairments z Pair of copper wires z Signal attenuation z Coaxial cable z Signal distortion z Radio z Spurious noise z Light in optical fiber z Interference from other z Light in air signals z Infrared Analog Long-Distance Communications Transmission segment Source Repeater . Repeater Destination z Each repeater attempts to restore analog signal to its original form z Restoration is imperfect z Distortion is not completely eliminated z Noise & interference is only partially removed z Signal quality decreases with # of repeaters z Communications is distance-limited z Still used in analog cable TV systems z Analogy: Copy a song using a cassette recorder Analog vs. Digital Transmission Analog transmission: all details must be reproduced accurately Distortion Sent Attenuation Received Digital transmission: only discrete levels need to be reproduced Sent Distortion Received Simple Receiver: Attenuation Was original pulse positive or negative? Digital Long-Distance Communications Transmission segment Source Regenerator . Regenerator Destination z Regenerator recovers original data sequence and retransmits on next segment z Can design so error probability is very small z Then each regeneration is like the first time! z Analogy: copy an MP3 file z Communications is possible over very long distances z Digital systems vs. analog systems z Less power, longer distances, lower system cost z Monitoring, multiplexing, coding, encryption, protocols… Digital Binary Signal 111100 +A 0 T 2T 3T 4T 5T 6T -A Bit rate = 1 bit / T seconds For a given communications medium: z How do we increase transmission speed? z How do we achieve reliable communications? z Are there limits to speed and reliability? Pulse Transmission Rate z Objective: Maximize pulse rate through a channel, that is, make T as small as possible Channel T t t z If input is a narrow pulse, then typical output is a spread-out pulse with ringing z Question: How frequently can these pulses be transmitted without interfering with each other? z Answer: 2 x Wc pulses/second where Wc is the bandwidth of the channel Bandwidth of a Channel X(t) = a cos(2πft) Channel Y(t) = A(f) a cos(2πft) z If input is sinusoid of frequency f, A(f) then 1 z output is a sinusoid of same frequency f f z Output is attenuated by an amount A(f) 0 Wc that depends on f z A(f)≈1, then input signal passes readily Ideal low-pass z A(f)≈0, then input signal is blocked channel z Bandwidth Wc is range of frequencies passed by channel Multilevel Pulse Transmission z Assume channel of bandwidth Wc, and transmit 2 Wc pulses/sec (without interference) z 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 z If amplitudes are from {-A, -A/3, +A/3, +A}, then bit rate is 2 x 2Wc bps z By going to M = 2m amplitude levels, we achieve Bit Rate = m bits/pulse x 2Wc pulses/sec