220 likes | 612 Views
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.
E N D
Differential Coding and Scrambling Six Meeting
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 Last Output: 1 1 0 1 1 0 1 0 0 1 0 0 1
Self-synchronizing Scrambler An n-stage scrambler An n-stage descrambler
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
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
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
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
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
Modulo-2 Cyclic Redundancy Checks Orig. Message: 11100110 Sent Message: 111001100110
Org = 0110 • Div = 01 1110 10 | 01100000 10 111 10 010 10 000 00