Comp445 data communications and computer networks
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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

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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 = 2norn = 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

Comp445 data communications and computer networks


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

Bipolar ami and pseudoternary

Bipolar-AMI and Pseudoternary

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

Manchester encoding

Manchester Encoding

Differential manchester encoding

Differential Manchester Encoding

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

Modulation rate a note

Modulation Rate(a note)

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

Comp445 data communications and computer networks


  • 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

Comp445 data communications and computer networks


  • High Density Bipolar 3 Zeros

  • Based on bipolar-AMI

  • String of four zeros replaced with one or two pulses

B8zs and hdb3


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)

Modulation techniques

Modulation Techniques

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

Fsk on voice grade line for info

FSK on Voice Grade Line (for info)

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

Qpsk and oqpsk modulators

QPSK and OQPSK Modulators

Examples of qpsf and oqpsk waveforms

Examples of QPSF and OQPSK Waveforms

Digitizing analog data recording your voice and storing in pc

Digitizing Analog Data(recording your voice and storing in PC)

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

Pcm example

PCM Example

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 example

Delta Modulation - example

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

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