COMP445 Data Communications and Computer Networks

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# COMP445 Data Communications and Computer Networks - PowerPoint PPT Presentation

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

Concepts in

Signal Encoding Techniques

Monday, February 4, 2013

UsefulTerms;mustknow
• 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
• 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...)
• 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 (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 (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 (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

EncodingSchemes
• Bipolar –AMI (Alternate Mark Inversion)
• Pseudoternary
• Manchester
• Differential Manchester
• B8ZS (Bipolar With 8 Zero Substitution)
• HDB3 (High Density Bipolar 3 Zeros)
• Two different voltages for 0 and 1 bits
• Voltage constant during bit interval
• 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
• 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 level
• 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 problem)
• No net DC component
• Lower bandwidth
• Easy error detection
Pseudoternary
• One represented by absence of line signal
• Zero represented by alternating positive and negative
• 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)
Biphase
• 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
• 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
• 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
B8ZS
• 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
HDB3
• High Density Bipolar 3 Zeros
• Based on bipolar-AMI
• String of four zeros replaced with one or two pulses
Digital Data, Analog Signal
• Public telephone system
• 300Hz to 3400Hz
• Use modem (modulator-demodulator)
• Frequency shift keying (FSK)
• Phase shift keying (PSK)
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
• 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
• Even higher frequency on LANs using co-ax
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
• Is the next bit different than the current bit?
• 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)
• 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 64kbps
Delta Modulation