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 100001101 01110101
01000000 01000001
00100011 11001010
10010101 01011000
00001000 10101011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010101 01110111 010101011 11110110 1
00000111 11011100 1
10011100 11110100 1
10001010 10101111 1
00101111 01000110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111000 11010010 011000100 01011100 1
11011100 00000010 1
01011100 10111101 0
11000101 10100000 0
11011001 10000001 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:
00001101 01110101 0
01000000 01000001 1
00100011 11001010 1
10010101 01011000 1
00001000 10101011 0
11110011 00001101 1
1. The parity bits for the 16 columns is: 11110011 00001101
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (9,2):
10010101 01110111 0
10101011 11110110 1
00000111 11011100 1
10011100 11110100 1
10001010 10101111 1
00101111 01000110 0
For figure 3, the bits that were flipped are (2,2) and (11,5):
01111000 11010010 0
11000100 01011100 1
11011100 00000010 1
01011100 10111101 0
11000101 10100000 0
11011001 10000001 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: 1111001100001101
The answer was: 01110
The answer was: 1
The answer was: 9,2
The answer was: No