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 110000000 11101010
11011011 01000111
01110011 11110000
01111000 10100110
11001110 11100110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100100 01011001 111000110 10000001 0
11111000 11011010 0
01101011 01100100 0
00001111 10001101 0
10111110 11100011 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000001 11011011 011110001 01111001 0
00001011 00011001 0
11001011 00111110 0
10011101 01111111 0
10101101 11111010 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:
10000000 11101010 0
11011011 01000111 0
01110011 11110000 1
01111000 10100110 0
11001110 11100110 0
10011110 00011101 1
1. The parity bits for the 16 columns is: 10011110 00011101
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (12,0):
11100100 01011001 1
11000110 10000001 0
11111000 11011010 0
01101011 01100100 0
00001111 10001101 0
10111110 11100011 1
For figure 3, the bit that was flipped is (16,0):
00000001 11011011 0
11110001 01111001 0
00001011 00011001 0
11001011 00111110 0
10011101 01111111 0
10101101 11111010 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: 1001111000011101
The answer was: 00100
The answer was: 1
The answer was: 12,0
The answer was: Yes