binary linear block code

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vegihat

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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

(?)
 

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