Key Concepts in Signal Encoding Techniques for Data Communications

1. COMP445 Data Communications and Computer Networks Concepts in Signal Encoding Techniques Monday, February 4, 2013

2. 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

3. 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

4. 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)

5. 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

6. 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

7. 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

8. EncodingSchemes • 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)

9. 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

10. 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

11. NRZ

12. 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

13. 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

14. 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

15. Pseudoternary • One represented by absence of line signal • Zero represented by alternating positive and negative • No advantage or disadvantage over bipolar-AMI

16. Bipolar-AMI and Pseudoternary

17. 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)

18. 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

19. Manchester Encoding

20. Differential Manchester Encoding

21. 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

22. Modulation Rate(a note)

23. 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

24. 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

25. HDB3 • High Density Bipolar 3 Zeros • Based on bipolar-AMI • String of four zeros replaced with one or two pulses

26. B8ZSandHDB3

27. 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)

28. Modulation Techniques

29. 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

30. 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

31. FSK on Voice Grade Line (for info)

32. 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

33. Differential PSK • Is the next bit different than the current bit?

34. 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

35. QPSK and OQPSK Modulators

36. Examples of QPSF and OQPSK Waveforms

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

38. 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

39. 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

40. PCM Example

41. 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

42. Delta Modulation - example

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