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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

- 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

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

- 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)

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

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

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

- 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)

- 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

- 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

- 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

- 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

- Good voice reproduction
- PCM - 128 levels (7 bit) (again 27=128)
- Voice bandwidth 4khz
- Should be 8000 x 7 = 56kbps for PCM