N - 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
The Nyquist Theorem & Noiseless Channels
Baud Rate: the frequency with which components change
bit string is composed of n bits, and hence the signal component may have up to
2 different 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
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
Bit Rate = 2 * f * log2(B)
n = log2(B)
B it Rate
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
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
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)
Differential Manchester
B8ZS (Bipolar With 8 Zero Substitution)
HDB3 (High Density Bipolar 3 Zeros)
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 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
• Data represented by changes rather than levels
• More reliable detection of transition rather than
• In complex transmission layouts it is easy to
lose sense of polarity
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
• 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
—No net DC component
—Lower bandwidth
—Easy error detection
• One represented by absence of line signal
• Zero represented by alternating positive and
• No advantage or disadvantage over bipolar-AMI
Bipolar-AMI and Pseudoternary
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
Differential Manchester Encoding
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)
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
• High Density Bipolar 3 Zeros
• Based on bipolar-AMI
• String of four zeros replaced with one or two
B8ZS and HDB3
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
Amplitude Shift Keying
• Values represented by different amplitudes of
• Usually, one amplitude is zero
—i.e. presence and absence of carrier is used
Susceptible to sudden gain changes
Up to 1200bps on voice grade lines
Used over optical fiber
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)
Phase Shift Keying
• Phase of carrier signal is shifted to represent
• Binary PSK
—Two phases represent two binary digits
• Differential PSK
—Phase shifted relative to previous transmission rather
than some reference signal
Differential PSK
• Is the next bit different than the current bit?
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
—9600bps modem use 12 angles , four of which have
two amplitudes
• Offset QPSK (orthogonal QPSK)
—Delay in Q stream
QPSK and OQPSK Modulators
Examples of QPSF and OQPSK Waveforms
Digitizing Analog Data
(recording your
voice and storing in PC)
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)
• 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
PCM Example
Delta Modulation
• Analog input is approximated by a staircase
• Move up or down one level () at each sample
• Binary behavior
—Function moves up or down at each sample interval
Delta Modulation - example
Delta Modulation - 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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