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 111011100 00110111
00001000 11000010
11110100 01000101
11100111 11010010
01101111 00001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100111 11101010 100111100 11000101 0
00001101 00001010 1
01010111 00001001 0
01011110 10010110 1
11011111 10101010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000000 11001001 000010100 00010001 0
10010110 11110110 0
01111001 01111111 1
01100101 00000111 1
00011111 11010110 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:
11011100 00110111 0
00001000 11000010 0
11110100 01000101 0
11100111 11010010 0
01101111 00001011 1
10101000 01101001 1
1. The parity bits for the 16 columns is: 10101000 01101001
2. The parity bits for the 5 rows is: 00001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (11,3):
11100111 11101010 1
00111100 11000101 0
00001101 00001010 1
01010111 00001001 0
01011110 10010110 1
11011111 10101010 1
For figure 3, the bits that were flipped are (7,3) and (8,0):
10000000 11001001 0
00010100 00010001 0
10010110 11110110 0
01111001 01111111 1
01100101 00000111 1
00011111 11010110 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: 1010100001101001
The answer was: 00001
The answer was: 1
The answer was: 11,3
The answer was: No