vegihat
Newbie level 2
suppose that i have a gray-scale image which pixels are
| 0 1 |
| 2 3 |
and each pixel is 2-bit, so the image is
| 00 01 |
| 10 11 |
and i have 4 symbols, -3,-1,+1,+3, for which the mapping is
00 | -3
01 | -1
10 | +1
11 | +3
Also suppose that i want to add a channel coding, for example a binary linear block code (5,2),
with generator matrix
G= | 1 0 1 0 1 |
| 0 1 0 1 1 |
and parity check matrix
H= | 1 0 1 |
| 0 1 1 |
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
The above code bundles the bits into pairs, and the four corresponding code words are
x1 = 00 ↔ c1 = x1*G = 00000
x2 = 01 ↔ c2 = x2*G = 01011
x3 = 10 ↔ c3 = x3*G = 10101
x4 = 11 ↔ c4 = x4*G = 11110
so now my image is
| 00000 01011 |
| 10101 11110 |
ok now i need to map them to numbers which will corespond to the amplitude of pulse.
but which is the mapping?
is the below mapping
00000 -> -3
01011 -> -1
10101 -> +1
11110 -> +3
or the first mapping
00 | -3
01 | -1
10 | +1
11 | +3
(?)
| 0 1 |
| 2 3 |
and each pixel is 2-bit, so the image is
| 00 01 |
| 10 11 |
and i have 4 symbols, -3,-1,+1,+3, for which the mapping is
00 | -3
01 | -1
10 | +1
11 | +3
Also suppose that i want to add a channel coding, for example a binary linear block code (5,2),
with generator matrix
G= | 1 0 1 0 1 |
| 0 1 0 1 1 |
and parity check matrix
H= | 1 0 1 |
| 0 1 1 |
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
The above code bundles the bits into pairs, and the four corresponding code words are
x1 = 00 ↔ c1 = x1*G = 00000
x2 = 01 ↔ c2 = x2*G = 01011
x3 = 10 ↔ c3 = x3*G = 10101
x4 = 11 ↔ c4 = x4*G = 11110
so now my image is
| 00000 01011 |
| 10101 11110 |
ok now i need to map them to numbers which will corespond to the amplitude of pulse.
but which is the mapping?
is the below mapping
00000 -> -3
01011 -> -1
10101 -> +1
11110 -> +3
or the first mapping
00 | -3
01 | -1
10 | +1
11 | +3
(?)