Golay Code Implementation – Detecting Errors » History » Version 9
ABDALLAH, Hussein, 03/13/2016 12:34 PM
| 1 | 1 | ABDALLAH, Hussein | h1. Golay Code Implementation – Detecting Errors |
|---|---|---|---|
| 2 | 9 | ABDALLAH, Hussein | It is easy to detect errors in a codeword. |
| 3 | 9 | ABDALLAH, Hussein | • Using the parity bit to check for odd numbers of errors |
| 4 | 9 | ABDALLAH, Hussein | If parity is correct |
| 5 | 9 | ABDALLAH, Hussein | • Computing the 23-bit syndrome of the codeword and check for zero |
| 6 | 9 | ABDALLAH, Hussein | The syndrome is the reminder left after the codeword is divided by the polynomial, modulo-2. It is equal to zero if the Golay code is valid, else non-zero. |
| 7 | 9 | ABDALLAH, Hussein | A hand computation example is shown below using the previous 686555h, bit reversed for the division process. |
| 8 | 1 | ABDALLAH, Hussein | |
| 9 | 8 | ABDALLAH, Hussein | |
| 10 | 8 | ABDALLAH, Hussein | 101011100011 10101010101001100001011 ( AE3h then 555h then checkbits) |
| 11 | 1 | ABDALLAH, Hussein | 101011100011 (checkbits) |
| 12 | 1 | ABDALLAH, Hussein | ------------ <---------- Exclusive-OR |
| 13 | 1 | ABDALLAH, Hussein | 100100101100 |
| 14 | 1 | ABDALLAH, Hussein | 101011100011 |
| 15 | 1 | ABDALLAH, Hussein | ------------ |
| 16 | 1 | ABDALLAH, Hussein | 111100111100 |
| 17 | 1 | ABDALLAH, Hussein | 101011100011 |
| 18 | 1 | ABDALLAH, Hussein | ------------ |
| 19 | 1 | ABDALLAH, Hussein | 101110111111 |
| 20 | 1 | ABDALLAH, Hussein | 101011100011 |
| 21 | 1 | ABDALLAH, Hussein | ------------ |
| 22 | 1 | ABDALLAH, Hussein | 101011100011 |
| 23 | 1 | ABDALLAH, Hussein | 101011100011 |
| 24 | 1 | ABDALLAH, Hussein | ------------ |
| 25 | 3 | ABDALLAH, Hussein | 000000000000 <-- syndrome = 0 |