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Differential Coding and Scrambling

Differential Coding and Scrambling. Six Meeting. Channel coding for error correction. Channel coding by scrambling. Differential coding. Differential Coding Example. 0. 1. 1. 1. 0. Last Output:. 1. 1 1 0 0 1 0. 0. 1. 1. 1. 0. 0. Differential Coding Example 2. 0. 0. 1. 0. 0.

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Differential Coding and Scrambling

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  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)

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