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 101001111 01100000
11001000 00001010
00101001 10110101
10101110 10010100
11101011 10111101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100011 00101110 000101100 10100011 0
01001011 00100100 0
11111011 01000100 1
00000011 01011000 1
11111100 11110101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110001 00001100 110000011 11011011 1
11111101 01001100 0
10101000 10011010 1
01001100 11110111 0
11101011 11110100 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:
01001111 01100000 1
11001000 00001010 1
00101001 10110101 0
10101110 10010100 0
11101011 10111101 0
11101011 11110110 0
1. The parity bits for the 16 columns is: 11101011 11110110
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (9,1):
01100011 00101110 0
00101100 10100011 0
01001011 00100100 0
11111011 01000100 1
00000011 01011000 1
11111100 11110101 0
For figure 3, the bit that was flipped is (14,0):
01110001 00001100 1
10000011 11011011 1
11111101 01001100 0
10101000 10011010 1
01001100 11110111 0
11101011 11110100 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: 1110101111110110
The answer was: 11000
The answer was: 0
The answer was: 9,1
The answer was: Yes