Error Detection and Correction: Two Dimensional Parity
Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):
Figure 110011010 00010100
01011001 01110101
01110001 00011011
01110110 10101011
00100011 01011001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00001000 01101011 011100111 00010100 0
01110101 01110101 0
01110100 00010100 1
11100000 10100010 0
00001100 10111100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001001 00111100 100000110 01000111 0
11001101 10010101 1
10101000 00010111 0
00000001 11101010 0
00111011 00010011 0
Question List
1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string
2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string
3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.
4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0
5. For figure 3, is it possible to detect and correct the bit flips? Yes or No
Solution
The full solution for figure 1 is shown below:
10011010 00010100 0
01011001 01110101 1
01110001 00011011 0
01110110 10101011 0
00100011 01011001 1
11100111 10001000 0
1. The parity bits for the 16 columns is: 11100111 10001000
2. The parity bits for the 5 rows is: 01001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,3):
00001000 01101011 0
11100111 00010100 0
01110101 01110101 0
01110100 00010100 1
11100000 10100010 0
00001100 10111100 1
For figure 3, the bit that was flipped is (3,3):
01001001 00111100 1
00000110 01000111 0
11001101 10010101 1
10101000 00010111 0
00000001 11101010 0
00111011 00010011 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1110011110001000
The answer was: 01001
The answer was: 0
The answer was: 6,3
The answer was: Yes