Differential Coding and Scrambling

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Differential Coding and Scrambling

• Six Meeting

2
Channel coding for error correction
3
Channel coding by scrambling
4
Differential coding
5
Differential Coding Example
1
Last Output
0
1
1
1
0
1 1 0 0 1 0
0
1
1
1
0
0
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Differential Coding Example 2
1
Last Output
0
0
1
0
0
1 0 1 1 0 1
0
0
1
0
0
1
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Scrambling Shift Register
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Self-synchronizing Scrambler
An n-stage scrambler
An n-stage descrambler
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Scrambler Example
Stage 1 2 3 4 5
0 1 1 1 0
Initial code
0
0
0
0
0 0 0 0
0
0
0
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Scrambler Example
Stage 1 2 3 4 5
0 1 1 1 0
Initial code
0
1
1
1
0 0 0 0
0
0
0
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Self-synchronizing Descrambler


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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

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Setreset 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

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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

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Modulo-2 Cyclic Redundancy Checks
Orig. Message 11100110 Sent Message 11100110011
0
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• Org 0110
• Div 01
• 1110
• 10 01100000
• 10
• 111
• 10
• 010
• 10
• 000
• 00

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CRC With Shift Register (Nice View)