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 101010101 11000010
10111110 01000110
11111100 10100010
00110011 00110001
10000110 00000000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10001001 10101001 101001011 11011100 1
10100010 00010000 0
10000111 01011000 1
01010111 10010000 1
10110000 00101101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010100 10111101 010001001 11001001 1
11001110 11100010 1
10000011 00101101 1
10001111 00100111 1
01011111 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:
01010101 11000010 1
10111110 01000110 1
11111100 10100010 1
00110011 00110001 1
10000110 00000000 1
10100010 00010111 1
1. The parity bits for the 16 columns is: 10100010 00010111
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (8,5):
10001001 10101001 1
01001011 11011100 1
10100010 00010000 0
10000111 01011000 1
01010111 10010000 1
10110000 00101101 0
For figure 3, the bit that was flipped is (15,5):
00010100 10111101 0
10001001 11001001 1
11001110 11100010 1
10000011 00101101 1
10001111 00100111 1
01011111 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: 1010001000010111
The answer was: 11111
The answer was: 1
The answer was: 8,5
The answer was: Yes