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 101110011 00110111
10111000 01001110
11001000 01111110
00101111 11010010
10110111 11011101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011000 00110111 000010100 10000010 0
01001010 10101011 0
00011111 11111100 1
00010111 10111001 1
11001110 01011001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100111 00110011 100011001 10100010 0
01000110 01100110 1
00111011 00011011 0
01110001 01110001 0
00110010 10011101 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:
01110011 00110111 0
10111000 01001110 0
11001000 01111110 1
00101111 11010010 1
10110111 11011101 0
10011011 00001000 0
1. The parity bits for the 16 columns is: 10011011 00001000
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,5):
10011000 00110111 0
00010100 10000010 0
01001010 10101011 0
00011111 11111100 1
00010111 10111001 1
11001110 01011001 0
For figure 3, the bit that was flipped is (0,3):
10100111 00110011 1
00011001 10100010 0
01000110 01100110 1
00111011 00011011 0
01110001 01110001 0
00110010 10011101 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: 1001101100001000
The answer was: 00110
The answer was: 0
The answer was: 14,5
The answer was: Yes