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Hamming Codes
Hamming Code (8:4)
The Hamming code used in teletext is used to reduce the possibility of
errors for the sending address and control information.
It is possible to correct a single error in the received byte and detect multiple errors,
when there are 2, 4 or 6 error bits. When there are 3, 5, 7 or 8 errors in a byte, this
results in a false message being decoded.
The hamming code used in teletext is a (8,4) (n,k)
Code Rate Efficiency = k/n = 4/8 = 50%
Where D4 D3 D2 D1 are the data bits and C3
C2 C1 and C4 is the parity bit.
| 8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
| D4 |
C4 |
D3 |
C3 |
D2 |
C2 |
D1 |
C1 |
C1 = D1  D2 D4
C2 = D1 D3 D4
C3 = D2 D3 D4
Where represents an Exclusive-OR
operation (addition without carry)
| b8 |
b7 |
b6 |
b5 |
b4 |
b3 |
b2 |
b1 |
| 0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
| 0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
| 0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
| 0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
| 0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
| 0 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
| 0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
| 0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
| 1 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
| 1 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
| 1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
| 1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
| 1 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
| 1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
| 1 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
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Message Bits |
|
Hamming Code Protection Bits |
|
b8 |
b7 |
b6 |
b5 |
b4 |
b3 |
b2 |
b1 |
| A |
o |
|
o |
|
|
|
o |
o |
| B |
o |
|
|
|
o |
o |
o |
|
| C |
|
|
o |
o |
o |
|
o |
|
| D |
o |
o |
o |
o |
o |
o |
o |
o |
| Results
of |
Parity
Tests |
Inference |
Action |
| A,B,C |
D |
|
|
| All Correct |
Correct |
no errors |
accept message bits |
| All Correct |
Not Correct |
error in b7 |
accept message bits |
| Not all Correct |
Correct |
multiple errors |
reject message bits |
| Not all Correct |
Not Correct |
single errors |
refer to table above to identify error.
Correct error if in message bit |
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Hamming Code (24:18)
Byte 1
Byte 2
Byte 3
| D8 |
D9 |
D10 |
D11 |
D12 |
D13 |
D14 |
C10 |
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