Chapter 3 Digital Transmission Fundamentals Chapter Figures

Leon-Garcia/Widjaja Communication Networks H W =++ H W H W H W Color image Red component image Green component image Blue component image Total bits before compression = 3  H  W pixels  B bits/pixel = 3HWB Figure 3.1

Leon-Garcia/Widjaja Communication Networks  /2 3  /2 5  /2 7  /2 -  /2 -3  /2 -5  /2 -7  /2 (a) Original waveform and the sample values  /2 3  /2 5  /2 7  /2 -  /2 -3  /2 -5  /2 -7  /2 (b) Original waveform and the quantized values Figure 3.2

Leon-Garcia/Widjaja Communication Networks (b) Broadcast TV at 30 frames/sec = 10.4 x 10 6 pixels/sec (c) HDTV at 30 frames/sec = 67 x 10 6 pixels/sec (a) QCIF videoconferencing at 30 frames/sec = 760,000 pixels/sec Figure 3.3

Leon-Garcia/Widjaja Communication Networks Receiver Communication channel Transmitter Figure 3.4

Leon-Garcia/Widjaja Communication Networks (a) (b) Sent Received Examples: digital telephone, CD Audio Examples: AM, FM, TV transmission Figure 3.5

Leon-Garcia/Widjaja Communication Networks SourceRepeater Destination Repeater Transmission segment Figure 3.6

Leon-Garcia/Widjaja Communication Networks Attenuated and distorted signal + noise Equalizer Recovered signal + residual noise Repeater Amp Figure 3.7

Leon-Garcia/Widjaja Communication Networks Amplifier equalizer Timing recovery Decision circuit and signal regenerator Figure 3.8

Leon-Garcia/Widjaja Communication Networks Communication channel d meters Figure 3.9

Leon-Garcia/Widjaja Communication Networks (a) Low-pass and idealized low-pass channel f 0 W A(f)A(f) 0W f A(f)A(f) 1 Figure 3.10 Channel t t (b) Maximum pulse transmission rate is 2W pulses/second

Leon-Garcia/Widjaja Communication Networks Figure 3.11 SNR = Average signal power Average noise power SNR (dB) = 10 log 10 SNR Signal Noise Signal + noise High SNR t t t Signal Noise Signal + noise Low SNR t t t

Leon-Garcia/Widjaja Communication Networks 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) Figure 3.12

Leon-Garcia/Widjaja Communication Networks Figure 3.13

Leon-Garcia/Widjaja Communication Networks t 1 ms (a) 1 ms t (b) Figure 3.14

Leon-Garcia/Widjaja Communication Networks (a) Frequency components for (b) Frequency components for Figure 3.15

Leon-Garcia/Widjaja Communication Networks Figure 3.16 s (noisy ) | p (air stopped) | ee (periodic) | t (stopped) | sh (noisy)

Leon-Garcia/Widjaja Communication Networks Figure 3.17 f W X(f) 0

Leon-Garcia/Widjaja Communication Networks T x(t) t x(nT) nT Figure 3.18

Leon-Garcia/Widjaja Communication Networks Sampler t x(t) t x(nT) (a) Interpolation filter t x(t) t x(nT) (b) Figure 3.19

Leon-Garcia/Widjaja Communication Networks Interpolation filter Display or playout 2W samples / sec 2W m bits/sec x(t) Bandwidth W Sampling (A/D) Quantization Analog source 2W samples / sec m bits / sample Pulse generator y(t) Original Approximation Transmission or storage Figure 3.20

Leon-Garcia/Widjaja Communication Networks x(t) and the corresponding quantizer approximations y(nT) t 3.5  2.5  1.5  0.5  -0.5  -1.5  -2.5  -3.5  Figure 3.21 input x(nT) output y(nT ) 0.5  1.5  2.5  3.5  -0.5  -1.5  -2.5  -3.5        Uniform quantizer

Leon-Garcia/Widjaja Communication Networks Figure 3.22 M = 2 m levels, Dynamic Range ( -V, V), Δ = 2V/M... error = y(nT)-x(nT)=e(nT) input...      x(nT) V -V-V Mean Square Error: σ e 2 ≈ Δ 12

Leon-Garcia/Widjaja Communication Networks Channel t t A in cos 2  ftA out cos (2  ft +  (f)) A out A in A(f) = Figure 3.23

Leon-Garcia/Widjaja Communication Networks f 1 A(f) =  2 f 2 (a) f 0  (f) = tan -1 2  f -45 o -90 o 1/ 2  (b) Figure 3.24

Leon-Garcia/Widjaja Communication Networks Figure ms

Leon-Garcia/Widjaja Communication Networks Figure 3.26

Leon-Garcia/Widjaja Communication Networks Channel t 0 t h(t) tdtd Figure 3.27

Leon-Garcia/Widjaja Communication Networks t s(t) = sin(2πWt)/ 2πWt T T T T T T T Figure 3.28

Leon-Garcia/Widjaja Communication Networks Figure A+A -A-A 0 T 2T2T 3T3T 4T4T5T5T t Transmitter Filter Communication Medium Receiver Filter Receiver r(t) Received signal

Leon-Garcia/Widjaja Communication Networks (a) (b) t t TTTTTT TTTTTT Figure 3.30

Leon-Garcia/Widjaja Communication Networks W (1+  )W (1-  )W 0 f Figure 3.31

Leon-Garcia/Widjaja Communication Networks Four signal levelsEight signal levels Typical noise Figure 3.32

Leon-Garcia/Widjaja Communication Networks x 0 Figure 3.33

Leon-Garcia/Widjaja Communication Networks  /2  Figure 3.34

Leon-Garcia/Widjaja Communication Networks Unipolar NRZ NRZ-inverted (differential encoding) Bipolar encoding Manchester encoding Differential Manchester encoding Polar NRZ Figure 3.35

Leon-Garcia/Widjaja Communication Networks Figure 3.36

Leon-Garcia/Widjaja Communication Networks Figure 3.37 f f 2 f 1 f c 0 A(f)A(f)

Leon-Garcia/Widjaja Communication Networks Information T 2T2T 3T3T 4T4T5T5T 6T6T Amplitude Shift Keying +1 Frequency Shift Keying +1 Phase Shift Keying (a) (b) (c) 0 T 2T2T 3T3T 4T4T5T5T 6T6T 0 T 2T2T 3T3T 4T4T5T5T 6T6T t t t Figure 3.38

Leon-Garcia/Widjaja Communication Networks (a) Information (d) 2Y i (t) cos(2  f c t) +2A -2A +A -A (c) Modulated signal Y i (t) 0 T 2T2T 3T3T 4T4T5T5T 6T6T +A -A (b) Baseband signal X i (t) 0 2T2T 3T3T 6T6T 0 T 2T2T 3T3T 4T4T5T5T 6T6T T 4T4T5T5T t t t Figure 3.39

Leon-Garcia/Widjaja Communication Networks (a) AkAk  cos(2  f c t) Y i (t) = A k cos(2  f c t) (b)  2cos(2  f c t) 2A k cos 2 (2  f c t) = A k {1 + cos(2  f c t)} Low-pass filter with cutoff W Hz X i (t) Y i (t) = A k cos(2  f c t) Figure 3.40

Leon-Garcia/Widjaja Communication Networks AkAk  cos(2  f c t) Y i (t) = A k cos(2  f c t) BkBk  sin(2  f c t) Y q (t) = B k sin(2  f c t) +Y(t) Figure 3.41

Leon-Garcia/Widjaja Communication Networks Y(t)  2cos(2  f c t) 2A k cos 2 (2  f c t)+2B k cos(2  f c t)sin(2  f c t) = A k {1 + cos(4  f c t)}+B k {0 + sin(4  f c t)} Low-pass filter with cutoff W/2 Hz AkAk  2sin(2  f c t) 2B k sin 2 (2  f c t)+2A k cos(2  f c t)sin(2  f c t) = B k {1 - cos(4  f c t)}+A k {0 + sin(4  f c t)} Low-pass filter with cutoff W/2 Hz BkBk Figure 3.42

Leon-Garcia/Widjaja Communication Networks AkAk BkBk (a) 4 “levels”/pulse 2 bits/pulse 2W bits/second 2-D signal AkAk BkBk (b) 16 “levels”/ pulse 4 bits/pulse 4W bits/second 2-D signal Figure 3.43

Leon-Garcia/Widjaja Communication Networks AkAk BkBk 4 “levels”/pulse 2 bits/pulse 2W bits/second AkAk BkBk 16 “levels”/pulse 4 bits/pulse 4W bits/second Figure 3.44

Leon-Garcia/Widjaja Communication Networks Frequency (Hz) Wavelength (meters) Power and telephone Broadcast radio Microwave radio Infrared light Visible light Ultraviolet light X-rays Gamma rays Figure 3.45

Leon-Garcia/Widjaja Communication Networks t = 0 t = d/v Communication channel d meters Figure 3.46

Leon-Garcia/Widjaja Communication Networks Attenuation (dB/mi) f (kHz) 19 gauge 22 gauge 24 gauge 26 gauge Figure 3.47

Leon-Garcia/Widjaja Communication Networks Figure 3.48

Leon-Garcia/Widjaja Communication Networks Dielectric material Braided outer conductor Outer cover Center conductor Figure 3.49

Leon-Garcia/Widjaja Communication Networks Attenuation (dB/km) f (MHz) 2.6/9.5 mm 1.2/4.4 mm 0.7/2.9 mm Figure 3.50

Leon-Garcia/Widjaja Communication Networks Head end = Unidirectional amplifier Figure 3.51

Leon-Garcia/Widjaja Communication Networks Head end Upstream fiber Downstream fiber Fiber node Coaxial distribution plant Fiber node = Bidirectional split-band amplifier Fiber Figure 3.52

Leon-Garcia/Widjaja Communication Networks Downstream 54 MHz 500 MHz (a) Current allocation 550 MHz 750 MHz Upstream Downstream 5 MHz 42 MHz 54 MHz 500 MHz (b) Proposed hybrid fiber- coaxial allocation Proposed downstream Figure 3.53

Leon-Garcia/Widjaja Communication Networks Core Cladding Jacket Light (a) Geometry of optical fiber cc (b) Reflection in optical fiber Figure 3.54

Leon-Garcia/Widjaja Communication Networks Wavelength (  m) Loss (dB/km) Infrared absorption Rayleigh scattering Figure 3.55

Leon-Garcia/Widjaja Communication Networks (a) Multimode fiber: multiple rays follow different paths Direct path Reflected path (b) Single-mode fiber: only direct path propagates in fiber Figure 3.56

Leon-Garcia/Widjaja Communication Networks Optical fiber Optical source Modulator Electrical signal Receiver Electrical signal Figure 3.57

Leon-Garcia/Widjaja Communication Networks RRRRRRRR (a) Single signal per fiber with 1 regenerator per span …… R R R R … R R R R … R R R R … R R R R … (b) DWDM composite signal per fiber with 1 regenerator per span Optical amplifier R Regenerator OA DWDM multiplexer … (c) DWDM composite signal with optical amplifiers … R R R R … R R R R OA … … Figure 3.58

Leon-Garcia/Widjaja Communication Networks Frequency (Hz) Wavelength (meters) Satellite and terrestrial microwave AM radio FM radio and TV LF MF HF VHF UHF SHF EHF 10 4 Cellular and PCS Wireless cable Figure 3.59

Leon-Garcia/Widjaja Communication Networks Channel Encoder User information Pattern checking All inputs to channel satisfy pattern or condition Channel output Deliver user information or set error alarm Figure 3.60

Leon-Garcia/Widjaja Communication Networks Calculate check bits Channel Recalculate check bits Compare Information bits Received information bits Sent check bits Information accepted if check bits match Received check bits Figure 3.61

Leon-Garcia/Widjaja Communication Networks o x = codewordso = noncodewords x x x x x x x o o o o o o o o o o o o x x x x x x x o o o o o o o o o o o A code with poor distance properties A code with good distance properties (a) (b) Figure 3.62

Leon-Garcia/Widjaja Communication Networks Bottom row consists of check bit for each column Last column consists of check bits for each row Figure 3.63

Leon-Garcia/Widjaja Communication Networks Arrows indicate failed check bits Two errors One error Three errors Four errors Figure 3.64

Leon-Garcia/Widjaja Communication Networks unsigned short cksum(unsigned short *addr, int count) { /*Compute Internet Checksum for “count” bytes *beginning at location “addr”. */ register long sum = 0; while ( count > 1 ) { /* This is the inner loop*/ sum += *addr++; count -=2; } /* Add left-over byte, if any */ if ( count > 0 ) sum += *addr; /* Fold 32-bit sum to 16 bits */ while (sum >>16) sum = (sum & 0xffff) + (sum >> 16) ; return ~sum; } Figure 3.65

Leon-Garcia/Widjaja Communication Networks Addition: Multiplication: Division: x 3 + x + 1 ) x 6 + x 5 x 3 + x 2 + x x 6 + x 4 + x 3 x 5 + x 4 + x 3 x 5 + x 3 + x 2 x 4 + x 2 x 4 + x 2 + x x = q(x) quotient = r(x) remainder divisor dividend 35 ) Figure 3.66

Leon-Garcia/Widjaja Communication Networks Steps: 1.Multiply i(x) by x n-k (puts zeros in (n-k) low order positions) 2.Divide x n-k i(x) by g(x) 3.Add remainder r(x) to x n-k i(x) (puts check bits in the n-k low order positions): Quotient Remainder Transmitted codeword b(x) = x n-k i(x) + r(x) x n-k i(x) = g(x) q(x) + r(x) Figure 3.67

Leon-Garcia/Widjaja Communication Networks Generator polynomial: g(x)= x 3 + x + 1 Information: (1,1,0,0) i(x) = x 3 + x 2 Encoding: x 3 i(x) = x 6 + x 5 Transmitted codeword: b(x) = x 6 + x 5 + x b = (1,1,0,0,0,1,0) 1011 ) x 3 + x + 1 ) x 6 + x 5 x 3 + x 2 + x x 6 + x 4 + x 3 x 5 + x 4 + x 3 x 5 + x 3 + x 2 x 4 + x 2 x 4 + x 2 + x x Figure 3.68

Leon-Garcia/Widjaja Communication Networks ClockInputReg 0Reg 1Reg = i = i = i = i Check bits:r 0 = 0r 1 = 1r 2 = 0 r(x) = x Reg 0 ++ Encoder for Reg 1 Reg 2 Figure 3.69

Leon-Garcia/Widjaja Communication Networks b(x) e(x) R(x) + (Receiver) (Transmitter) Error pattern Figure 3.70

Leon-Garcia/Widjaja Communication Networks 1. Single errors: e(x) = x i 0  i  n-1 If g(x) has more than 1 term, it cannot divide e(x) 2. Double errors: e(x) = x i + x j 0  i < j  n-1 = x i (1 + x j-i ) If g(x) is primitive, it will not divide (1 + x j-i ) for j-i  2 n-k  1 3. Odd number of errors: e(1) =1 if number of errors is odd. If g(x) has (x+1) as a factor, then g(1) = 0 and all codewords have an even number of 1s. Figure 3.71

Leon-Garcia/Widjaja Communication Networks 4. Error bursts of length b: e(x) = x i d(x) where deg(d(x)) = L-1 g(x) has degree n-k; g(x) cannot divide d(x) if deg(g(x))> deg(d(x)) L = (n-k) or less: all will be detected L = (n-k+1): deg(d(x)) = deg(g(x)) i.e. d(x) = g(x) is the only undetectable error pattern, fraction of bursts which are undetectable = 1/2 L-2 L > (n-k+1): fraction of bursts which are undetectable = 1/2 n-k L ith position error pattern d(x) Figure 3.72

Leon-Garcia/Widjaja Communication Networks b e r + (Receiver) (Transmitter) Error pattern b e r + (Receiver) (Transmitter) Error pattern (a) Single bit input (b) Vector input Figure 3.73

Leon-Garcia/Widjaja Communication Networks s = H e = = Single error detected s = H e = = + = Double error detected s = H e = = + + = Triple error not detected Figure 3.74

Leon-Garcia/Widjaja Communication Networks s = H r = He s = 0 No errors in transmission Undetectable errors Correctable errors Uncorrectable errors (1–p) 7 7p37p3 1–3p 3p3p 7p7p 7p(1–3p) 21p 2 Figure 3.75

Leon-Garcia/Widjaja Communication Networks t = 2 b1b1 b2b2 oooo Set of all n-tuples within distance t Set of all n-tuples within distance t Figure 3.76

Leon-Garcia/Widjaja Communication Networks b1b1 b2b2 b3b3 b4b4 b L-3 b L-2 b L-1 bLbL... L codewords written vertically in array; then transmitted row by row b1b1 b2b2 b3b3 b4b4 b L-3 b L-2 b L-1 bLbL... A long error burst produces errors in two adjacent rows Figure 3.77

Leon-Garcia/Widjaja Communication Networks DTEDCE Protective Ground (PGND) Transmit Data (TXD) Receive Data (RXD) Request to Send (RTS) Clear to Send (CTS) Data Set Ready (DSR) Ground (G) Carrier Detect (CD) Data Terminal Ready (DTR) Ring Indicator (RI) (b) 13 (a)                          Figure 3.78

Leon-Garcia/Widjaja Communication Networks Start bit Stop bit Data bits Line idle 3T/2TTTTTTT Receiver samples the bits Figure 3.79

Leon-Garcia/Widjaja Communication Networks f 0 W X(f) -W 1T1T … f 0W X(f)X(f – 1/T)X(f + 1/T) –W … 1T1T – … f 0W X(f)X(f – 1/T) –W … X(f + 1/T) Figure 3.80