Digital Transmission Fundamental

1. Digital Transmission Fundamental

2. Digital Transmission Fundamental Digital Representation of Information

3. Two Categories of Information • Block-oriented information • data files • documents • pictures • Stream information • audio • video

4. Block-oriented information • The normal form in which these files occur can contain a fair amount of statistical redundancy. • Data compression utilities exploit these redundancies. • Lossless compression: the original data can be recovered exactly. • Lossy compression: only an approximation to the original information can be recovered. • Compression ratio: the ratio of the number of bits in the original file to the number of bits in the compressed file.

5. W W W W H H H H Color image Red Component Image Green Component Image Blue Component Image Color Image = + + Total bits before compression = 3xHxW pixels x B bits/pixel = 3HWB

6. Block-oriented information

7. Sampling of a speech signal 7D/2 5D/2 3D/2 D/2 -D/2 -3D/2 -5D/2 -7D/2

8. Stream information

9. (a) QCIF Videoconferencing 144 @ 30 frames/sec = 760,000 pixels/sec 720 (b)Broadcast TV @ 30 frames/sec = 10.4 x 106 pixels/sec 480 1920 (c) HDTV @ 30 frames/sec = 67 x 106 pixels/sec 1080 Video image pixel rates

10. Network requirements • The volume of the delivered information • The accuracy of the delivered information • The timeliness of the delivery

11. The accuracy of the delivery • Different types of information have different degrees of tolerance to transmission errors. • As the compression ratio increases, the importance of the information conveyed by every bit increases.

12. Timeliness requirements • Delay • The time to deliver a block of L bits is d/c + L/R • d is the distance that the information must travel • c is the speed of light • R is the transmission bit rate • Real-time communications requires a maximum delay of about 250 ms to ensure interactivity • Jitter: the variation in the delay between consecutive blocks • The receiver uses a buffer to hold blocks of information until their playback time.

13. Temporal impairments for stream information Original sequence (a) 1 2 3 4 5 6 7 8 9 (b) Jitter due to variable delay 1 2 3 4 5 6 7 8 9 Playout delay (c) 1 2 3 4 5 6

14. Digital Transmission Fundamental Why Digital Transmissions?

15. Transmitter Receiver Communication channel General transmission system

16. Transmission systems • A transmission system makes use of a physical transmission medium or channel that allows the propagation of energy in the form of pulse or variation in voltage, current , or light intensity. • In analog communication the objective is to transmit a waveform, which is a function that varies continuously with time. • In digital communication the objective is to transmit a given symbol that is selected from some finite set of possibilities.

17. Received Sent • e.g. AM, FM, TV transmission Received Sent • e.g digital telephone, CD Audio Analog vs digital transmission Analog transmission: all details must be reproduced accurately Digital transmission: only discrete levels need to be reproduced

18. Typical long-distance link To transmit over long distance, it is necessary to introduce repeaters periodically to regenerate the signal. Transmission segment Destination Source Repeater Repeater

19. Recovered signal + residual noise Attenuated & distorted signal + noise Equalizer Amp. Repeater An analog Repeater • The task of analog repeater is to regenerate a signal that resemble as closely as possible the signal at the input of the repeater. • The repeater is limited in what it can do to deal with noise.

20. Causes of the signal distortion • Different frequency components of a signal are attenuated differently. • In general, high-frequency components are attenuated more than low-frequency components. • The equalizer compensates this by amplifying different frequency components by different amounts. • Different frequency components of a signal are delayed by different amounts. • The equalizer attempts to provide different delays to realign the frequency components.

21. A digital repeater • The sole objective of the digital repeater is to determine with high probability the original binary stream. • It does not need to completely regenerate the original shape of the transmitted signal. • An error occurs when the noise signal is sufficiently large to change the polarity of the original signal at the sampling point. • Digital repeaters eliminate the accumulation of noise and provide for long-distance transmission. Decision Circuit. & Signal Regenerator Amplifier Equalizer Timing Recovery

22. Benefits of digital transmission • Digital transmission systems can operate with lower signal levels or with greater distance between repeaters. • This means lower overall system cost. • The digital networks are suitable for handling many types of information that can be represented in digital form. • Digital transmission allows network to exploit the advances in digital computer technology.

23. A digital transmission system • The purpose of a digital transmission system is to transfer a sequence of 0s and 1s from a transmitter to a receiver. • It uses pulses or sinusoids to transmit binary information over a physical medium. • We are particularly interested in the bit rate as measured in bits/second. d meters 0110101... communication channel 0110101...

24. Factors that affects transmission • How fast can bits be transmitted reliably over a given medium? This depends: • The amount of energy put into transmitting each signal. • The distance that the signal has to traverse. • The amount of noise that the receiver needs to contend with. • The bandwidth of the transmission medium.

25. Transmission channel • A transmission channel can be characterized by its effect on tones of various frequencies. • The ability of the channel to transfer a tone of the frequency f is given by the amplitude-response functionA(f), which is defined as the ratio of the amplitude of the output tone divided by the amplitude of the input tone. • The bandwidth of a channel is the range of frequencies that is passed by a channel. • The rate at which pulses can be transmitted over a channel is proportional to the bandwidth.

26. Typical amplitude-response function (a) Lowpass and idealized lowpass channel A(f) A(f) 1 f f 0 W 0 W (b) Maximum pulse transmission rate is 2W pulses/second Channel t t

27. Nyquist rate • If a channel has bandwidth W, then the narrowest pulse that can be transmitted over the channel has width  = 1/2W seconds. • The fastest rate at which pulses can be transmitted into the channel is the Nyquist rate: rmax = 2W pulses/second. • If we use multilevel transmission pulses that can take on M = 2m amplitude levels, we can transmit at a bit rate: R = 2W pulses/sec  m bits/pulse = 2Wm bits/sec

28. Noise • In the absence of noise, the bit rate can be increased without limit by increasing the number of signal levels. • Noise consists of extraneous signal that are added to the desired signal. • The presence of noise limits the reliability with which the receiver can correctly determine the information that was transmitted.

29. Signal-to-noise ratio Average Signal Power SNR (dB) = 10 log10 SNR SNR = Average Noise Power signal + noise signal noise High SNR t t t noise signal + noise signal Low SNR t t t

30. Channel capacity • The channel capacity is the maximum rate at which bits can be transferred reliably. • Shannon derived an expression for it: C = W log2 (1 + SNR) bps • Ex: consider a telephone channel with W = 3.4 kHz and SNR = 40 dB. The channel capacity is then 40 dB = 10 log10 10000 C = 3400 log2 (1 + 10000) = 44.8 kbps

31. Bit rates of digital transmission systems

32. Digital Transmission Fundamental Characterization of Communication Channels

33. Frequency domain characterization x(t) = cos 2ft y(t) = A(f) cos (2ft + (f)) Channel t t A(f): the amplitude-response function (f): the phase shift

34. Effect of the channel bandwidth • Many signals can be represented as the sum of sinusoidal signals: x(t) = akcos(2fkt) • The output signal of the linear channel is y(t) =  akA(fk)cos(2fkt+(fk)) • As bandwidth is decreased, the precision with which the pulses can be identified is reduced.

35. 1 0 0 0 0 0 0 1 . . . . . . t 1 ms Example effect of the channel bandwidth x(t) = -0.5+ 4/{ sin(/4)cos(21000t) + sin(2/4)cos(22000t) + sin(3/4)cos(23000t) + …}

36. Time domain characterization h(t) Channel t t 0 td s(t) = sin(2Wt)/ 2Wt t T T T T TT T T T TT T TT

37. Impulse response • The width of T is an indicator of how quickly the output follows the input. • As the bandwidth increases, the width of the T decreases, suggesting that pulses can be input into the system more closely spaced, that is at a higher rate.

38. Digital Transmission Fundamentals Line Coding

39. Line coding • Line coding: the method for converting a binary information sequence into a digital signal in a digital communication system. • Design considerations: • Maximizing the bit rate • Timing recovery • Built-in error detecting • Better immunity to noise and interference • The complexity and cost of implementation

40. Line coding methods 0 1 0 1 1 1 1 0 0 Unipolar NRZ Polar NRZ NRZ-Inverted (Differential Encoding) Bipolar Encoding Manchester Encoding Differential Manchester Encoding

41. Spectra consideration • Some communication channel does not pass low frequencies.

42. Timing recovery • The timing recovery circuit in the receiver monitors the transitions at the edge of the bit intervals to determine the boundary between bits. • Long strings of 0s and 1s may cause the timing circuit to lose synchronization because of the absence of transitions. • To address this problem, the bipolar line codes used in telephone systems place a limit on the maximum number of 0s that may be encoded into digital signal. • Whenever a sequence of N consecutive 0s occurs, the string is encoded into a special binary sequence that contains 0s and 1s. • The sequence is encoded so that the mapping in the bipolar line code is violated.

43. Differential encoding • Differential encoding: the binary value is determined by the transition at the beginning of each interval. • Avoiding systematic error in polarity • Errors tends to occur in pairs.

44. mBnB code • mBnB code: m information bits are mapped into n (>m) encoded bits. • The encoded bits are selected so that they provide enough pulse for timing recovery and limit the number of pulses of the same level.

45. Example uses of codes • Bipolar code: long distance transmission • Manchester code: Ethernet and token-ring • Differential Manchester code: token-ring • 4B5B code: FDDI

46. Digital Transmission Fundamentals Modems and Digital Modulation

47. Modulation • Band-pass channels pass power in some frequency range from f1 to f2. • The basic function of the modulation is to produce a signal that occupies frequencies in the range passed by the channel. f f2 f1 0 fc

48. Digital modulation • Digital modulation involves imbedding the binary information sequence into the transmitted signal by varying, or modulating, some attribute of the carrier signal. • A modem is a device that carries out this basic function.

49. Information 1 0 1 1 0 1 +1 (a) Amplitude Shift Keying t 6T 6T 6T 2T 2T 4T 4T 5T 5T 2T 4T 5T 3T 3T 3T T T T 0 0 0 -1 +1 Frequency Shift Keying (b) t -1 +1 (c) Phase Shift Keying t -1 ASK, FSK, and PSK

50. 1 0 1 1 0 1 (a) Information +A +A (b) Baseband Signal Xi(t) (c) Modulated Signal Yi(t) t 6T 2T 4T 5T T 3T 0 6T 2T 4T 5T 3T T 0 -A -A t 6T 2T 4T 5T 3T T 0 +2A (d) 2Yi(t) cos(2fct) t -2A Modulating a signal