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COMP445 Data Communications and Computer Networks. Concepts in Signal Encoding Techniques. Monday, February 4 , 2013. Useful Terms; must know. Unipolar All signal elements have same sign 0, +1 Bipolar One logic state represented by positive voltage the other by negative voltage -1, +1

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comp445 data communications and computer networks

COMP445 Data Communications and Computer Networks

Concepts in

Signal Encoding Techniques

Monday, February 4, 2013

useful terms must know
  • Unipolar
    • All signal elements have same sign 0, +1
  • Bipolar
    • One logic state represented by positive voltage the other by negative voltage -1, +1
  • Data rate
    • Rate of data transmission in bits per second
  • Duration or length of a bit
    • Time taken for transmitter to emit the bit
  • Mark and Space
    • Mark 1
    • Space 0
b it rate
B it Rate

The Nyquist Theorem & Noiseless Channels

  • Baud Rate: the frequency with which components change
  • Each bit string is composed of n bits, and hence the signal component may have up to 2ndifferent amplitudes (one for each unique combination for b1, b2, …bn)
  • Are bit rate and baud rate the Same?
  • No, bit rate depends on the number of bits (n) as well as the baud rate; more precisely:

Bit Rate = n * Baud Rate

  • Bit rate can then be increased by either increasing the baud rate or n; however only up to a point
b it rate continued
B it Rate (continued...)
  • This result is surprisingly old, back to 1920s, when Harry Nyquist developed his classic theory
  • Nyquist theory showed that if f is the maximum frequency a medium can transmit, then the receiver can reconstruct the signal by sampling it 2f times per second
  • For example, if the maximum frequency is 4000 Hz, then the receiver can completely construct it by sampling it at a rate of 8000 per second
  • Assuming that the transmitter baud rate is 2 f , in other words changes signal each 1 / 2f intervals, we can state

Bit Rate = n * Baud Rate = n * 2 * f

  • This can also be stated based on component; if B is the number of different components, then

B = 2n or n = log2(B)

  • Hence,

Bit Rate = 2 * f * log2(B)

b it rate continued1
B it Rate (continued...)

Noisy Channels

  • More components mean subtler change among them
  • Channels are subject to noise
    • The transmitted signal can be distorted due to the channel noise
    • If distortion is too large, the receiver may not be able to reconstruct the signal at all
b it rate continued2
B it Rate (continued...)

Shannon’s Result

  • How much noise is bad? This depends on its ratio to the signal
  • We define S/N (Signal-to-Noise-Ratio)
  • A higher S/N (less significant noise) indicates higher quality
  • Because S >> N, the ratio is often scaled down as

R = log10(S/N) bels // bels is the measurement unit

For example,

If S is 10 times larger than N, then

R = log10(10N/N) = 1 bel

If S is 100 times larger than N, then

R = log10(100N/N) = 2 bels

Perhaps, a more familiar measurement is the decibel (dB)

1 dB = 0.1 bel

b it rate continued3
B it Rate (continued...)

Shannon’s Result

  • In 1940, Claude Shannon went beyond Nyquist’s results and considered noisy channels
  • Shannon related the maximum bit rate not only to the frequency but also to the S/N ratio; specifically he showed that:

Bit Rate = Bandwidth * log2(1 + S/N) bps

  • The formula states that a higher BW and S/N ratio allow higher bit rate
  • Hence, for the telephone system, which has a frequency of about 4000 Hz and S/N ≈ 35 dB, or 3.5 bels, Shannon’s result yields the following

3.5 = log10(S/N)  S = 103.5N  S≈ 3162 N  S/N≈ 3162

Bit Rate = Bandwidth * log2(1 + S/N)

= 4000 * log2(1 + 3162)

≈ 4000 * 11.63 bps

≈ 46,506 bps ≈ 46.5 kbps

encoding schemes
  • Nonreturn to Zero-Level (NRZ-L)
  • Nonreturn to Zero Inverted (NRZI)
  • Bipolar –AMI (Alternate Mark Inversion)
  • Pseudoternary
  • Manchester
  • Differential Manchester
  • B8ZS (Bipolar With 8 Zero Substitution)
  • HDB3 (High Density Bipolar 3 Zeros)
nonreturn to zero level nrz l
Nonreturn to Zero-Level (NRZ-L)
  • Two different voltages for 0 and 1 bits
  • Voltage constant during bit interval
    • no transition I.e. no return to zero voltage
  • e.g. Absence of voltage for zero, constant positive voltage for one
  • More often, negative voltage for one value and positive for the other
  • This is NRZ-L
nonreturn to zero inverted
Nonreturn to Zero Inverted
  • Nonreturn to zero inverted on ones
  • Constant voltage pulse for duration of bit
  • Data encoded as presence or absence of signal transition at beginning of bit time
  • Transition (low to high or high to low) denotes a binary 1
  • No transition denotes binary 0
  • An example of differential encoding
differential encoding
Differential Encoding
  • Data represented by changes rather than levels
  • More reliable detection of transition rather than level
  • In complex transmission layouts it is easy to lose sense of polarity
nrz pros and cons
NRZ pros and cons
  • Pros +’s
    • Easy to engineer
    • Make good use of bandwidth
  • Cons –’s
    • DC component
    • Lack of synchronization capability
  • Used for magnetic recording (outdated)
  • Not often used for signal transmission
multilevel binary
Multilevel Binary
  • Use more than two levels
  • Bipolar-AMI (Alternate Mark Inversion)
    • zero represented by no line signal
    • one represented by positive or negative pulse
    • one pulses alternate in polarity
    • No loss of sync if a long string of ones (zeros still a problem)
    • No net DC component
    • Lower bandwidth
    • Easy error detection
  • One represented by absence of line signal
  • Zero represented by alternating positive and negative
  • No advantage or disadvantage over bipolar-AMI
trade off for multilevel binary
Trade Off for Multilevel Binary
  • Not as efficient as NRZ
    • Each signal element only represents one bit (con)
    • In a 3 level system could represent log23 = 1.58 bits
    • Receiver must distinguish between three levels (+A, -A, 0) (con)
    • Requires approximately 3dB more signal power for same probability of bit error (con)
  • Manchester
    • Transition in middle of each bit period
    • Transition serves as clock and data
    • Low to high represents one
    • High to low represents zero
    • Used by IEEE 802.3
  • Differential Manchester
    • Midbit transition is clocking only
    • Transition at start of a bit period represents zero
    • No transition at start of a bit period represents one
    • Note: this is a differential encoding scheme
    • Used by IEEE 802.5
biphase pros and cons
Biphase Pros and Cons
  • Cons
    • At least one transition per bit time and possibly two
    • Maximum modulation rate is twice NRZ
    • Requires more bandwidth
  • Pros
    • Synchronization on mid bit transition (self clocking)
    • No DC component
    • Error detection
      • Absence of expected transition
scrambling gate to filling
Scrambling;gate to filling
  • Use scrambling to replace sequences that would produce constant voltage
  • Filling sequence
    • Must produce enough transitions to sync
    • Must be recognized by receiver and replace with original
    • Same length as original
  • No DC component
  • No long sequences of zero level line signal
  • No reduction in data rate
  • Error detection capability
  • Bipolar With 8 Zeros Substitution
  • Based on bipolar-AMI
  • If octet of all zeros and last voltage pulse preceding was positive encode as 000+-0-+
  • If octet of all zeros and last voltage pulse preceding was negative encode as 000-+0+-
  • Causes two violations of AMI code
  • Unlikely to occur as a result of noise
  • Receiver detects and interprets as octet of all zeros
  • High Density Bipolar 3 Zeros
  • Based on bipolar-AMI
  • String of four zeros replaced with one or two pulses
digital data analog signal
Digital Data, Analog Signal
  • Public telephone system
    • 300Hz to 3400Hz
    • Use modem (modulator-demodulator)
  • Amplitude shift keying (ASK)
  • Frequency shift keying (FSK)
  • Phase shift keying (PSK)
amplitude shift keying
Amplitude Shift Keying
  • Values represented by different amplitudes of carrier
  • Usually, one amplitude is zero
    • i.e. presence and absence of carrier is used
  • Susceptible to sudden gain changes
  • Inefficient
  • Up to 1200bps on voice grade lines
  • Used over optical fiber
binary frequency shift keying
Binary Frequency Shift Keying
  • Most common form is binary FSK (BFSK)
  • Two binary values represented by two different frequencies (near carrier)
  • Less susceptible to error than ASK
  • Up to 1200bps on voice grade lines
  • High frequency radio
  • Even higher frequency on LANs using co-ax
phase shift keying
Phase Shift Keying
  • Phase of carrier signal is shifted to represent data
  • Binary PSK
    • Two phases represent two binary digits
  • Differential PSK
    • Phase shifted relative to previous transmission rather than some reference signal
differential psk
Differential PSK
  • Is the next bit different than the current bit?
quadrature psk
Quadrature PSK
  • More efficient use by each signal element representing more than one bit
    • e.g. shifts of /2 (90o)
    • Each element represents two bits
    • Can use 8 phase angles and have more than one amplitude
    • 9600bps modem use 12 angles , four of which have two amplitudes
  • Offset QPSK (orthogonal QPSK)
    • Delay in Q stream
pulse code modulation pcm 1
Pulse Code Modulation(PCM) (1)
  • If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal
  • If fs > 2fc OK 
  • Voice data limited to below 4000Hz
  • Requires 8000 samples per second
  • Analog samples (Pulse Amplitude Modulation, PAM)
  • Each sample assigned digital value
pulse code modulation pcm 2
Pulse Code Modulation(PCM) (2)
  • 4 bit system gives 16 levels (24=16)
  • Quantized
    • Quantizing error or noise
    • Approximations mean it is impossible to recover original exactly
  • 8 bit sample gives 256 levels (28=256)
  • Quality comparable with analog transmission
  • 8000 samples per second of 8 bits each gives 64kbps
delta modulation
Delta Modulation
  • Analog input is approximated by a staircase function
  • Move up or down one level () at each sample interval
  • Binary behavior
    • Function moves up or down at each sample interval
delta modulation performance
DeltaModulation - Performance
  • Good voice reproduction
    • PCM - 128 levels (7 bit) (again 27=128)
    • Voice bandwidth 4khz
    • Should be 8000 x 7 = 56kbps for PCM