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 101101111 00100110
00100110 10011011
11010000 11110101
10100000 00001001
01000001 01100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011010 00000111 100101000 10110001 0
01011011 01110011 0
10110111 11101000 1
11011110 01110010 0
10000000 01011110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100110 01011001 001111111 11010010 1
10111111 11100101 0
11010110 00100111 1
01011000 10010100 1
11111000 11011101 1
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:
01101111 00100110 1
00100110 10011011 0
11010000 11110101 1
10100000 00001001 0
01000001 01100110 0
01111000 00100111 0
1. The parity bits for the 16 columns is: 01111000 00100111
2. The parity bits for the 5 rows is: 10100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (15,3):
10011010 00000111 1
00101000 10110001 0
01011011 01110011 0
10110111 11101000 1
11011110 01110010 0
10000000 01011110 0
For figure 3, the bit that was flipped is (3,4):
10100110 01011001 0
01111111 11010010 1
10111111 11100101 0
11010110 00100111 1
01011000 10010100 1
11111000 11011101 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0111100000100111
The answer was: 10100
The answer was: 0
The answer was: 15,3
The answer was: Yes