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 101110001 11101111
01111011 01101011
11101000 00000101
01110111 10101111
00000101 11110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11000000 00100010 011100100 10101111 0
11101001 10111111 1
00100011 00110111 0
01011101 00001111 1
11110011 00001010 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011110 00010001 010100110 01110111 0
11010000 00110001 0
01110000 00000110 0
00000011 01011000 1
00011011 00100001 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:
01110001 11101111 1
01111011 01101011 1
11101000 00000101 0
01110111 10101111 0
00000101 11110011 0
10010000 11011101 0
1. The parity bits for the 16 columns is: 10010000 11011101
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 (1,2):
11000000 00100010 0
11100100 10101111 0
11101001 10111111 1
00100011 00110111 0
01011101 00001111 1
11110011 00001010 0
For figure 3, the bits that were flipped are (10,3) and (12,5):
00011110 00010001 0
10100110 01110111 0
11010000 00110001 0
01110000 00000110 0
00000011 01011000 1
00011011 00100001 1
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: 1001000011011101
The answer was: 11000
The answer was: 0
The answer was: 1,2
The answer was: No