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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

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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 = 2norn = 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

• 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 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

• 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

• 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

• 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

• 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

• 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

• 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

B8ZSandHDB3

• Public telephone system

• 300Hz to 3400Hz

• Use modem (modulator-demodulator)

• Amplitude shift keying (ASK)

• Frequency shift keying (FSK)

• Phase shift keying (PSK)

• 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

• 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 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

• 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

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

• 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

• 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

• 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

DeltaModulation - Performance

• Good voice reproduction

• PCM - 128 levels (7 bit) (again 27=128)

• Voice bandwidth 4khz

• Should be 8000 x 7 = 56kbps for PCM