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 111001011 10010111
01101000 00100110
00001001 01000100
11100010 11000101
00110111 01011101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101101 01010001 001110001 11101011 0
11001000 00010011 0
10100111 01010100 0
00011100 11110000 1
00101111 00000101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011110 00010111 000010111 10011111 0
11100000 01011101 1
11100101 11001011 0
10111100 10100011 1
10100000 10110101 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:
11001011 10010111 0
01101000 00100110 0
00001001 01000100 0
11100010 11000101 0
00110111 01011101 0
01111111 01101101 0
1. The parity bits for the 16 columns is: 01111111 01101101
2. The parity bits for the 5 rows is: 00000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (12,0):
00101101 01010001 0
01110001 11101011 0
11001000 00010011 0
10100111 01010100 0
00011100 11110000 1
00101111 00000101 1
For figure 3, the bits that were flipped are (12,2) and (3,5):
00011110 00010111 0
00010111 10011111 0
11100000 01011101 1
11100101 11001011 0
10111100 10100011 1
10100000 10110101 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0111111101101101
The answer was: 00000
The answer was: 0
The answer was: 12,0
The answer was: No