1. Differential Coding and Scrambling Six Meeting

2. Channel coding for error correction

3. Channel coding by scrambling

4. Differential coding

5. Differential Coding Example 0 1 1 1 0 Last Output: 1 1 1 0 0 1 0 0 1 1 1 0 0

6. Differential Coding Example 2 0 0 1 0 0 Last Output: 1 1 0 1 1 0 1 0 0 1 0 0 1

7. Scrambling: Shift Register

8. Self-synchronizing Scrambler An n-stage scrambler An n-stage descrambler

9. Scrambler: Example Stage 1 2 3 4 5 Initial code 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

10. Scrambler: Example Stage 1 2 3 4 5 Initial code 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0

11. Self-synchronizing Descrambler + +

12. Tap Polynomial • Self-synchronizing. • scramblers do not need the frame synchronization, • The x in the polynomial can be interpreted as a shift operator • Pseudo-random binary sequences (PRBS) • Put the shift register stages into a known start-up condition

13. Set–reset scrambling • Sending • Combining the input data with a PRBS in an exclusive-OR gate. • Receiving • Combining, in an exclusive-OR gate, the coded data with the identical pseudo-random sequence used at the transmitter, • synchronization. • Frame alignment must take place

14. Error Detection: Cyclic Redundancy Checks • Original message = X • X = 7654321. • Divide this message number by G, • G = 99 • X = 7654321 = 77316 × 99 + 37 • Reminder = 37 • Sent message = Y • Y = 765432137

15. Modulo-2 Cyclic Redundancy Checks Orig. Message: 11100110 Sent Message: 111001100110

16. Org = 0110 • Div = 01 1110 10 | 01100000 10 111 10 010 10 000 00

17. CRC With Shift Register (Nice View)