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 100000100 00100101
00011010 10001111
11110000 01000000
00100101 00000100
10101011 10010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101011 10010111 000100101 10110001 1
11110010 01100011 0
00111101 10101000 0
10000010 11001111 0
11000011 00110010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111000 00011100 010010011 11011010 1
01100110 10110000 1
10001111 11101100 0
10110100 01100000 0
11111110 11111010 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:
00000100 00100101 0
00011010 10001111 0
11110000 01000000 1
00100101 00000100 0
10101011 10010000 1
01100000 01111110 0
1. The parity bits for the 16 columns is: 01100000 01111110
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,2):
10101011 10010111 0
00100101 10110001 1
11110010 01100011 0
00111101 10101000 0
10000010 11001111 0
11000011 00110010 1
For figure 3, the bit that was flipped is (4,5):
00111000 00011100 0
10010011 11011010 1
01100110 10110000 1
10001111 11101100 0
10110100 01100000 0
11111110 11111010 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: 0110000001111110
The answer was: 00101
The answer was: 0
The answer was: 11,2
The answer was: Yes